Month: March 2006

  • 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.


    Related material:

    Log24, Jan. 1-15, 2006.

    The image “http://www.log24.com/log/pix06/060101-SixOfOne.jpg” cannot be displayed, because it contains errors.

    The image “http://www.log24.com/theory/images/060311-Arabic.jpg” cannot be displayed, because it contains errors.

    For details, click on the Six of One.

  • Holy the Firm
    by Annie Dillard

        Esoteric Christianity, I read, posits a
    substance.  It is a created substance, lower than metals and
    minerals on a "spiritual scale" and lower than salts and earths,
    occurring beneath salts and earths in the waxy deepness of planets, but
    never on the surface of planets where men could discern it; and it is
    in touch with the Absolute, at base.  In touch with the
    Absolute!  At base.  The name of this substance is Holy the
    Firm.
        Holy the Firm: and is Holy the Firm in touch with
    metals and minerals?  With salts and earths?  Of course, and
    straight on up, till "up" ends by curving back.  Does something
    that touched something that touched Holy the Firm in touch with the
    Absolute at base seep into ground water, into grain; are islands rooted
    in it, and trees?  Of course.
        Scholarship has long distinguished between two
    strains of thought which proceed in the West from human knowledge of
    God.  In one, the ascetic's metaphysic, the world is far from
    God.  Emanating from God, and linked to him by Christ, the world
    is yet infinitely other than God, furled away from him like the end of
    a long banner falling.  This notion makes, to my mind, a vertical
    line of the world, a great chain of burning.  The more accessible
    and universal view, held by Eckhart and by many peoples in various
    forms, is scarcely different from pantheism: that the world is
    immanation, that God is in the thing, and eternally present here, if
    nowhere else.  By these lights the world is flattened on a
    horizontal plane, singular, all here, crammed with heaven, and
    alone.  But I know that it is not alone, nor singular, nor
    all.  The notion of immanence needs a handle, and the two ideas
    themselves need a link, so that life can mean aught to the one, and
    Christ to the other.
        For to immanence, to the heart, Christ is redundant
    and all things are one.  To emanance, to the mind, Christ touches
    only the top, skims off only the top, as it were, the souls of men, the
    wheat grains whole, and lets the chaff fall where?  To the world
    flat and patently unredeemed; to the entire rest of the universe, which
    is irrelevant and nonparticipant; to time and matter unreal, and so
    unknowable, an illusory, absurd, accidental, and overelaborate stage.
        But if Holy the Firm is "underneath salts," if Holy the Firm is matter at its dullest, Aristotle's materia prima,
    absolute zero, and since Holy the Firm is in touch with the Absolute at
    base, then the circle is unbroken.  And it is.  Thought
    advances, and the world creates itself, by the gradual positing of, and
    belief in, a series of bright ideas.  Time and space are in touch
    with the Absolute at base.  Eternity sockets twice into time and
    space curves, bound and bound by idea.  Matter and spirit are of a
    piece but distinguishable; God has a stake guaranteed in all the
    world.  And the universe is real and not a dream, not a
    manufacture of the senses; subject may know object, knowedge may
    proceed, and Holy the Firm is in short the philosopher's stone.

        These are only ideas, by the single handful. 
    Lines, lines, and their infinite points!  Hold hands and crack the
    whip, and yank the Absolute out of there and into the light, God pale
    and astounded, spraying a spiral of salts and earths, God footloose and
    flung.  And cry down the line to his passing white ear, "Old
    Sir!  Do you hold space from buckling by a finger in its
    hole?  O Old!  Where is your other hand?"  His right
    hand is clenching, calm, round the exploding left hand of Holy the Firm.

    -- Annie Dillard, Holy the Firm, Harper & Row 1977, reissued by Harper Perennial Library in 1988 as a paperback, pp. 68-71.

  • Women's History Month continues...

    Raiders of the Lost


    Stone



    The image “http://www.log24.com/log/pix06/060310-Stone.jpg” cannot be displayed, because it contains errors.




    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.



  • 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/.

  • Women's History Month continues.


    Contender

    Miss O'Hara
    on the Oscars:
    The image “http://www.log24.com/log/pix06/060304-CinderellaMan.jpg” cannot be displayed, because it contains errors.

    "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."

  • Found in Translation

    From "Space, Time, and Scarlett"
     (Log24, Feb. 9):

    The image “http://www.log24.com/log/pix06/060209-Blondes.jpg” cannot be displayed, because it contains errors.
    "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."

  • 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....

    The image “http://www.log24.com/log/pix06/060117-Globe.jpg” cannot be displayed, because it contains errors.

    "Some friends of mine
     are in this band....
    "

    -- David Auburn, "Proof"

    "Women and Mathematics
    is a joint program of
    the Institute for Advanced Study
    and Princeton University."

     -- School of Mathematics,  
    1 Einstein Drive,
    Princeton, New Jersey

  • In and Out

    John Updike in
    The New Yorker:

    "Birthday, death-day --
      what day is not both?"

    Annie Dillard in

    For the Time Being

    "in and out of
    time"

    Born on this date:

    Tom Wolfe


    Died on this date:


    Philip K. Dick

  • 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

    The image “http://www.log24.com/log/pix06/060302-Eureka.jpg” cannot be displayed, because it contains errors.

    "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 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, 217.158.203.103Wikipedia 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.

  • Deaconess

    "Teach us to care and not to care."
    -- T. S. Eliot, "Ash Wednesday"

    The image “http://www.log24.com/log/pix06/060301-Hospital2.jpg” cannot be displayed, because it contains errors.

    Related material:

    Beth Israel Deaconess,

    The image “http://www.log24.com/log/pix06/060301-GetDir.jpg” cannot be displayed, because it contains errors.


    The House of God
    ,

    and, from Is Nothing Sacred?,
    the following quotations--

    "I know what 'nothing' means."

    -- Joan Didion in
    Play It As It Lays

    "Nothing is random."

    -- Mark Helprin in
    Winter's Tale

    "692" -- Pennsylvania lottery,
    Ash Wednesday, 2000;

    "hole" -- Page 692,

    Webster's New World Dictionary
    ,
    College Edition, 1960

    "This hospital, like every other,
    is a hole in the universe
    through
    which holiness
    issues in blasts.
    It blows both ways,
    in and out of
    time."

    -- Annie Dillard in
    For the Time Being
    (1999)