Log24

"Look out kid, they keep it all hid." — Bob Dylan

Wednesday's Marginal Remarks pictured Robert De Niro
and Sean Penn in "We're No Angels." De Niro appeared
again in a Saturday Night Live sketch linked to
in last night's 9:29 post.

Here are some remarks featuring Penn related to
Peter J. Cameron's description yesterday of Sudoku
as an example of mathematics.

(Recall that the symbol #, known as 'hash,"
can stand for checkmate.)

For a sample chess problem, see a post from Oct. 10, 2005,
the day that the Sudoku remark Cameron describes was
in the news.

“Wallace Stevens’s remarkable oeuvre is a quasi-spiritual quest for the supreme fiction, for a poetry that ‘must take the place / Of empty heaven and its hymns’ and thus help modern man find meaning in a godless world. The poet’s role, for Stevens, is that of high priest of the imagination: it is the poet who ‘gives to life the supreme fictions without which we are unable to conceive of it.’ ….
… Stevens’s hallmark ‘imagination-reality’ complex… is pursued almost obsessively in his poetry and prose of the 1940s. Parts of a World, published in 1942, and the poem-sequence of the same year, ‘Notes toward a Supreme Fiction’ (‘Notes’ was subsequently collected in Transport to Summer in 1947), comprise a prolonged meditation in a time of war on poetry and the poet’s role, in the face of what Stevens, in his essay ‘The Noble Rider and the Sound of Words,’ terms ‘the pressure of reality.’ Parts of a World is riven by its competing vocabularies. A discourse of desire, of process, of the poet’s contemplation of the mind in the act of finding what will suffice, is elaborated in ‘the never-resting mind’ of ‘The Poems of Our Climate’ and in ‘The Well Dressed Man with a Beard,’ in which ‘It can never be satisfied, the mind, never’ [occurs]. A very different idiom, that of the ‘hero’ or ‘major man,’ the figure of capable imagination, dominates and directs such poems as ‘Mrs Alfred Uruguay,’ ‘Asides on the Oboe’ and ‘Examination of the Hero in a Time of War,’ where

    Summer, jangling
         the savagest diamonds and
    Dressed in its
         azure-doubled crimsons,
    May truly bear
         its heroic fortunes
    For the large,
         the solitary figure.”

— Lee M. Jenkins,
    University College Cork,
   “Wallace Stevens,”
    The Literary Encyclopedia,
    9 Dec., 2004.

For some related serious, but less solemn, remarks, click on the above date.

Introduction to Aesthetics

“Chess problems are the
hymn-tunes of mathematics.”
— G. H. Hardy,
A Mathematician’s Apology

“We do not want many ‘variations’ in the proof of a mathematical theorem: ‘enumeration of cases,’ indeed, is one of the duller forms of mathematical argument.  A mathematical proof should resemble a simple and clear-cut constellation, not a scattered cluster in the Milky Way.

A chess problem also has unexpectedness, and a certain economy; it is essential that the moves should be surprising, and that every piece on the board should play its part.  But the aesthetic effect is cumulative.  It is essential also (unless the problem is too simple to be really amusing) that the key-move should be followed by a good many variations, each requiring its own individual answer.  ‘If P-B5 then Kt-R6; if …. then …. ; if …. then ….’ — the effect would be spoilt if there were not a good many different replies.  All this is quite genuine mathematics, and has its merits; but it just that ‘proof by enumeration of cases’ (and of cases which do not, at bottom, differ at all profoundly*) which a real mathematician tends to despise.

* I believe that is now regarded as a merit in a problem that there should be many variations of the same type.”

(Cambridge at the University Press.  First edition, 1940.)

Brian Harley in
Mate in Two Moves:

“It is quite true that variation play is, in ninety-nine cases out of a hundred, the soul of a problem, or (to put it more materially) the main course of the solver’s banquet, but the Key is the cocktail that begins the proceedings, and if it fails in piquancy the following dinner is not so satisfactory as it should be.”

(London, Bell & Sons.  First edition, 1931.)