Month: March 2006

  • ART WARS:
    The Crimson Passion continues...

    How to Grow
    a Crimson Clover

    Published in the Harvard Crimson

    on Thursday, March 16, 2006, 6:24 PM

    by Patrick R. Chesnut,

    Crimson staff writer


    Stephen Dedalus, James
    Joyce's literary alter ego, once described the
    trappings of Irish culture as nets that hold a soul back from flight.
    By his standards, Harvard has soared.

    Irish
    culture has been an indelible part of Boston, but the names on our
    red-brick buildings tell a different story: Adams, Lowell, Winthrop. It
    would be easy to assume that for Harvard students, Irish culture
    consists of little more than guzzling alcohol in Tommy Doyle's Irish
    Pub or at St. Patrick's Day Stein Club.

    Recently, however, a
    small but lively Irish subculture, centered on Celtic music and
    language, has been developing at Harvard. But despite its vivacity, it
    remains largely unnoticed by the broader student body.

    Efforts
    by groups like the Harvard College Celtic Club and by the producers of
    the upcoming Loeb mainstage of J.M. Synge's "The Playboy of the Western
    World" may be just the sort of first step needed to finally make
    Harvard a place where Irish artistic culture lives....

    REACHING OUT

    "The Playboy"-- which will run
    from April 28 through May 6-- revolves around the disruption of life in a
    provincial Irish village when an outsider arrives with an extravagant
    story. All points converge at this play's production: members of the
    Celtic Club coordinated and will perform the play's music, the
    producers hope to draw Boston's Irish community, and the production
    will present Harvard's students with a script deeply entrenched in
    Irish history, but that boasts a universal appeal.

    As Kelly
    points out, the Irish roots of "The Playboy" are clearer than in the
    plays of the nominally Irish, but Francophone, absurdist writer Samuel
    Beckett. And unlike the plays of Sean O'Casey, which are extremely
    rooted in Irish culture, "The Playboy" boasts a visceral appeal that
    will be accessible to Harvard students.

    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."

    From the obituary
    in today's online New York Times of fashion designer Oleg Cassini, who
    died at 92 on St. Patrick's Day, Friday, March 17, 2006:

    "... he was always seen in the company of heiresses, debutantes,
    showgirls, ingenues. Between, before or after [his first] two marriages, he
    dated young starlets like Betty Grable and Lana Turner and actresses
    like Ursula Andress and Grace Kelly, to whom he was briefly engaged.

    'He
    was a true playboy, in the Hollywood sense,' said Diane von
    Furstenberg, the fashion designer and a friend of Mr. Cassini's. 'Well
    into his 90's, he was a flirt.'"

    "How strange the change from major to minor...
          Ev'ry time we say goodbye."
       -- Cole Porter

  • 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 " - 0.618," the approximate value of the negative
    solution to the equation

    x2 - x - 1 = 0

    The image “http://www.log24.com/log/pix05/050208-Crowe.jpg” cannot be displayed, because it contains errors.

    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:

    The image “http://www.log24.com/log/pix05/050208-pentagon2.gif” cannot be displayed, because it contains errors.

    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:

    The image �http://www.log24.com/log/pix06/060125-ZenerKeys.jpg� cannot be displayed, because it contains errors.


    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


  • George W. Mackey,
    Harvard mathematician,
    is dead at 90.

    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

    • Introduction
    • Harmonic analysis as the exploitation of symmetry: A historical survey
    • Herman Weyl and the application of group theory to quantum mechanics
    • The significance of invariant measures for harmonic analysis
    • Weyl's program and modern physics
    • Induced representations and the applications of harmonic analysis
    • Von Neumann and the early days of ergodic theory
    • Final
      remarks

    Related material:
    Log24, Oct. 22, 2002.
    Women's history month continues.

  • Women's History Month
    continues...

    The image “http://www.log24.com/log/pix06/060315-LifeX3sm.jpg” cannot be displayed, because it contains errors.

    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

  • Club

     From today's Harvard Crimson:


    Harvard Math Department Pi Day event

    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."

  • Frame

    The image “http://www.log24.com/log/pix06/060314-Frame.jpg” cannot be displayed, because it contains errors.

  • Fearful Symmetry
    and Minkowski Space-Time

    (For the tigers of Princeton,
    a selection suggested by
    the work of Richard Parker
     on Lorentzian lattices)

    The image “http://www.log24.com/log/pix06/060314-Lorentzian.jpg” cannot be displayed, because it contains errors.

  • Burning Bright
     
    The image “http://www.log24.com/log/pix06/060314-LifeOfPi2.jpg” cannot be displayed, because it contains errors.
     
    The image “http://www.log24.com/log/pix06/060314-CC2.jpg” cannot be displayed, because it contains errors.
     

    Click on pictures
    for details.

  • Christ at the

    Lapin Agile

    The image “http://www.log24.com/log/pix06/060313-WasleyChrist1.jpg” cannot be displayed, because it contains errors.

    "The Christ by Wasley,
    on wall under his right arm
    the Picasso painting."

    Le Républicain Lorrain du 14 janvier 2001

    Le Lapin Agile veille sur la Butte (par Michel Genson)


    24 décembre 1900. Dans son atelier glacial du Bateau Lavoir, à  flanc
    de la colline de Montmartre, Picasso se frotte les yeux. C’est bien
    Wasley, son ami Wasley, qu’il aperçoit traversant la place Ravignan,
    courbé sous le poids d’un grand Christ en croix. Le sculpteur titube et
    s’en va gravissant un à un les escaliers qui mènent au sommet de la
    Butte, direction la rue des Saules. Car l’œuvre est destinée aux murs
    du petit estaminet où la bande a trouvé asile, pour y échanger chaque
    soir des refrains, bocks et vaticinations les plus folles. La bande,
    c’est à dire Utrillo, Max Jacob, Modigliani et les autres… Un siècle et
    un souffle de légende plus tard, le même Christ blanc occupe toujours
    la même place, sous les lumières tamisées du Lapin Agile. À l’abri sous
    son aisselle droite, l’autoportrait de Picasso en Arlequin a été
    authentique en son temps. Jusqu’au jour où le grand Frédé, tenancier
    mythique du lieu, s’est gratté la barbe avant de le céder à un amateur
    suédois de passage. Depuis l’original a fait le voyage du MAM (Modern
    Art Museum) de New-York, et la Butte se contente d’une copie.

    Pour le reste, rien a changé ou presque pour le doyen des cabarets
    parisiens. Ni le décor, ni l’esprit. L’incroyable patine noire des
    murs, posée là par des lustres de tabagies rigolardes ou inspirées,
    rappelle au générique les voix des habituées de jadis, Apollinaire,
    Carco, Dullin, Couté, puis Pierre Brasseur, et plus proches de nous
    encore d’autres débutants, Caussimon, Brassens, François Billetdoux… La
    liste exhaustive serait impossible à dresser de tous ceux qui ont
    émargé au livre d’or du Lapin Agile.
     

    « En
    haut de la rue Saint-Vincent… » La goualante roule sa rime chaotique
    sur le pavé de la Butte. Au carrefour de la rue des Saules, la façade
    est avenante, sans apprêts, avec son acacia dans la cour, et cette
    étrange dénomination, née des amours burlesques entre l’imagination
    d’un dessinateur et les facéties des usagers. En 1875, André Gill,
    caricaturiste ami de Rimbaud, croque en effet, pour l’enseigne de
    l’ancien Cabaret des Assassins, un lapin facétieux sautant d’une
    marmite. Le temps d’un jeu de mots et le Lapin à Gill gagne son brevet
    d’agilité. L’épopée commence, que perpétue Yves Mathieu, aujourd’hui
    propriétaire, mémoire et continuateur d’une histoire somme toute
    unique. Histoire, qui, pour l’anecdote, faillit se terminer
    prématurément, sous la pioche des démolisseurs. Vers 1900, les bicoques
    du maquis montmartrois doivent laisser place à un grand projet
    immobilier. C’est Aristide Bruant qui sauvera in extremis le cabaret.
    Il achète l’établissement, laisse Frédé dans les murs qu’il revendra
    pour « un prix amical » à Paulo, le fils du même Frédé. Lequel Paulo
    n’est autre que le beau-père de l’actuel patron : « C’est un truc de
    famille. J’ai commencé à chanter ici en 48, égrène Yves Mathieu.
    Ensuite j’ai fait de l’opérette à la Gaîté Lyrique, de la revue aux
    Folies Bergères, je suis parti en Amérique… En revenant j’ai repris le
    cabaret, ma femme y chante, mes fils sont là, ils apprennent le métier…
    C’est comme le cirque, c’est le même esprit. »

    Malgré les tempêtes
    et les modes, le Lapin Agile dure et perdure donc. Et sa silhouette
    pour carte postale inspire toujours les peintres venus de partout.
    Comme si la halte faisait partie d’un parcours initiatique immuable.
    Deux pièces pour un minuscule rez-de-chaussée, dans la première,
    mi-loge, mi-vestiaire, une guitare attend son tour de projecteur. En
    l’occurrence un faisceau unique clouant le chanteur (l’humoriste ou le
    diseur) au rideau rouge de la seconde salle. Là où le spectacle se
    déroule depuis toujours, là où l’on s’accoude sans vergogne à la table
    d’Apollinaire, sous les lampes toujours drapées de rouge, pour écouter
    Ferré, Aragon, Mac Orlan ou les rengaines du Folklore populaire
    montmartrois. Yves Mathieu reste ferme, « ici, pas de sonorisation, pas
    de haut-parleur. Les gens découvrent la voix humaine. » Un refrain de
    Piaf glisse jusqu’au « laboratoire », le réduit où les autres artistes
    du programme dissertent sur l’état du monde. Les meubles de Bruant sont
    encore là, au hasard d’un coffre breton, un autre de marine, la façade
    d’un lit clos… « Des trucs d’origine » pour Yves Mathieu, qui malgré
    les vicissitudes du temps - il s’ingénie toute l’année durant à
    entretenir un établissement qui ne bénéficie d’aucun classement
    officiel, ni d’aucun subside - prêche haut et fort sa confiance,
    « parce qu’on aura plus que jamais besoin de racines, de repères, et
    qu’ici, c’est tout un pan de patrimoine qu’on défend à travers la
    chanson française, celle qu’on chante tous ensemble… » Le même secoue
    sa longue carcasse et se fend d’un sourire entendu : « Quand je
    descends à Paris, c’est pas pareil. Ici, le jour, c’est comme dans une
    église. Il y a le silence, et l’impression de ressentir les ondes
    laissées pare les cerveaux de ces types, là… » Aux murs, dessins ou
    tableaux laissés par Mac Orlan, Maclet ou Suzanne Valadon jouent avec
    l’ombre amicale.

    Le Lapin Agile, 22 rue des Saules, 75018 Paris. Tel : 01 46 06 85 87

    Source:

    http://www.au-lapin-agile.com/info4.htm

    Note the above description
    of Christmas Eve 1900,
    and the remark that
    "Ici, le jour, c’est comme
    dans une
    église."

    A search for more material on
    the Wasley Christ leads to
    Princeton's Nassau Church:

    The fullness of time. I don’t have to call on the physicists
    among us to conclude that this fullness was not meant to be the end
    of the time line. That Paul must not have been talking about time in
    a linear way. Fullness. Complete. Almost perfect. Overflowing with
    grace. Just right. Fullness. As in “the earth is the Lord’s
    and the fullness thereof.” Fullness. As in “I pray that
    you may have the power to comprehend with all of the saints, what is
    the breadth, and length, and height and depth, and to know the love
    of Christ that surpasses all knowledge, so that you may be filled with
    all the fullness of God.” Fullness. As in “For in Christ,
    all the fullness of God was pleased to dwell.” “When the
    fullness of time had come, God sent his Son, born of a woman.”

    I can remember Christmas Eve as a child....

    -- Christmas Eve, 2004,
        Sermon at Nassau Church by
        The Rev. Dr. David A. Davis


    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.

  • 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."

    The image “http://www.log24.com/log/pix06/060312-PaulBamberg21.jpg” cannot be displayed, because it contains errors.

    Paul Bamberg

    Transcript of the movie "Proof"--

    Some friends of mine are in this band.
    They're playing in a bar on Diversey,
    way down the bill, around...

    I said I'd be there.

    Great.
    They're all in the math department.
    They're good.
    They have this song called "i."
    You'd like it. Lowercase i.
    They just stand there.
    They don't play anything for three minutes.

    Imaginary number?

    It's a math joke.
    You see why they're way down the bill.

    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.
    [13] ALAN SOKAL and JEAN BRICMONT, Fashionable Nonsense, Picador, 1999.

    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 The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. 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
    that p is transcendental can be stated as follows: the homomorphism
    Q[X] --> R taking X to The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. is injective.  In other words, The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. can
    be identified algebraically with X, the variable par excellence.33

    The image “http://www.log24.com/log/pix06/060312-X.jpg” cannot be displayed, because it contains errors.

    More interestingly, one can ask what kind of object The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors. was before the formal definition
    of real numbers. To assume the real numbers were there all along,
    waiting to be defined, is to adhere to a form of Platonism.34  Dedekind wouldn't have agreed.35  In a debate marked by the accusation that
    postmodern writers deny the reality of the external world, it is a
    peculiar move, to say the least, to make mathematical Platonism a
    litmus test for rationality.36 Not that it makes any more sense simply
    to declare Platonism out of bounds, like Lévy-Leblond, who calls
    Stephen Weinberg's gloss on Sokal's comment 'une absurdité, tant il est
    clair que la signification d'un concept quelconque est évidemment
    affectée par sa mise en oeuvre dans un contexte nouveau!'37 Now I find
    it hard to defend Platonism with a straight face, and I prefer to
    regard the formula

    The image “http://www.log24.com/log/pix06/060312-pi.jpg” cannot be displayed, because it contains errors.

    as a creation rather than a discovery. But Platonism does correspond to
    the familiar experience that there is something about mathematics, and
    not just about other mathematicians, that precisely doesn't let us get
    away with saying 'évidemment'!38

    32 There are many circles in Euclid, but no pi, so I can't think of any
    other reason for Sokal to have written 'Euclid's pi,' unless this
    anachronism was an intentional part of the hoax.  Sokal's full
    quotation was 'the The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors.
    of Euclid and the G of Newton, formerly thought to be constant and
    universal, are now perceived in their ineluctable historicity.' 
    But there is no need to invoke non-Euclidean geometry to perceive the
    historicity of the circle, or of pi: see Catherine Goldstein's 'L'un
    est l'autre: pour une histoire du cercle,' in M. Serres, Elements d'histoire des sciences, Bordas, 1989, pp. 129-149.
    33 This is not mere sophistry: the construction of models over number
    fields actually uses arguments of this kind. A careless construction of
    the equations defining modular curves may make it appear that pi is
    included in their field of scalars.
    34 Unless you claim, like the present French Minister of Education [at
    the time of writing, i.e. 1999], that real numbers exist in nature,
    while imaginary numbers were invented by mathematicians. Thus The image “http://www.log24.com/log/pix06/060312-Char-pi.jpg” cannot be displayed, because it contains errors.
    would be a physical constant, like the mass of the electron, that can
    be determined experimentally with increasing accuracy, say by measuring
    physical circles with ever more sensitive rulers. This sort of position
    has not been welcomed by most French mathematicians.
    35 Cf. M. Kline, Mathematics The Loss of Certainty, p. 324.
    36 Compare Morris Hirsch's remarks in BAMS April 94.
    37 IS*, p. 38, footnote 26. Weinberg's remarks are
    contained in his article “Sokal's Hoax,” in the New York Review of
    Books
    , August 8, 1996.
    38 Metaphors from virtual reality may help here."

    * Earlier defined by Harris as "Impostures Scientifiques
    (IS), a collection of articles compiled or commissioned by Baudouin
    Jurdant and published simultaneously as an issue of the journal Alliage and as a book by La Découverte press."
    ** Earlier defined by Harris as "Fashionable Nonsense (FN), the North American translation of Impostures Intellectuelles."

    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).