Mathematics and Narrative

Rebecca Goldstein, Mathematics and the Character of Tragedy:

"It was Plato who best expressed-- who veritably embodied-- the tension between the narrative arts and mathematics."

Veritably.

Inscape

My entry for New Year's Day links to a paper by Robert T. Curtis* from The Arabian Journal for Science and Engineering (King Fahd University, Dhahran, Saudi Arabia), Volume 27, Number 1A, January 2002.

From that paper:

"Combinatorially, an outer automorphism [of S₆] can exist because the number of unordered pairs of 6 letters is
equal to the number of ways in which 6 letters can be partitioned into three pairs. Which is to say that the
two conjugacy classes of odd permutations of order 2 in S₆
contain the same number of elements, namely 15. Sylvester... refers to
the unordered pairs as duads and the partitions as synthemes. Certain
collections of five synthemes... he refers to as synthematic totals or simply totals; each total is stabilized within S₆ by a subgroup acting triply transitively on the 6 letters as PGL₂(5)
acts on the projective line. If we draw a bipartite graph on (15+15)
vertices by joining each syntheme to the three duads it contains, we
obtain the famous 8-cage (a graph of valence 3 with minimal cycles of
length 8)...."

Here is a way of picturing the 8-cage and a related configuration of points and lines:

Diamond Theory shows that this structure
can also be modeled by an "inscape"
made up of subsets of a
4x4 square array:

The illustration below shows how the
points and lines of the inscape may
be identified with those of the
Cremona-Richmond configuration.

Beyond the Fire


"Who Needs a White Cube These Days?"

-- Headline in today's New York Times

-- Poem title, Gerard Manley Hopkins

-- Wallace Stevens,

    from The Auroras of Autumn, 1950


Related material:
The five entries ending on Christmas, 2005.

Time in the Rock

"a world of selves trying to remember the self

speak to me Babel, that I may strive to assemble
of all these syllables a single word
before the purpose of speech is gone."

-- Conrad Aiken, "Prelude" (1932),

    paperback, 2003, page 156

"The rock is the habitation of the whole,
Its strength and measure, that which is near, point A
In a perspective that begins again

-- Wallace Stevens in The Rock (1954)

"Poetry is an illumination of a surface,
  the movement of a self in the rock."
-- Wallace Stevens, introduction to
    The Necessary Angel, 1951

An anonymous commenter's answer: "The title character announces the coming of the end, suffers mockery
and condemnation, and ends up saving the world through his actions."

(The "real" answer: "The music for each was composed by John Debney.")