Log24

Tuesday, April 12, 2011

The Monolith Epiphany

Filed under: Uncategorized — m759 @ 2:45 AM

Continued from March 7, 2011

" One for my baby, and one more… "

http://www.log24.com/log/pix11/110412-IconicArt.jpg

See also this morning's previous posts "Unique Figure" and "One of a Kind."

Monday, March 7, 2011

Point Taken

Filed under: Uncategorized — m759 @ 4:00 PM

Recommended— An essay (part 1 of 5 parts) in today's New York TImes—

THE ULTIMATUM

I don’t want to die in
a language I can’t understand.
— Jorge Luis Borges

Comment 71

"I agree with one of the earlier commenters that this is a piece of fine literary work. And in response to some of those who have wondered 'WHAT IS THE POINT?!' of this essay, I would like to say: Must literature always answer that question for us (and as quickly and efficiently as possible)?"

For an excellent survey of the essay's historical context, see The Stanford Encyclopedia of Philosophy article

"The Incommensurability of Scientific Theories,"
First published Wed., Feb. 25, 2009,
by Eric Oberheim and Paul Hoyningen-Huene.

Related material from this journal—

Paradigms, Paradigms Lost, and a search for "mere geometry." This last includes remarks contrasting Euclid's definition of a point ("that which has no parts") with a later notion useful in finite geometry.

See also (in the spirit of The Abacus Conundrum )…

The Monolith Epiphany

http://www.log24.com/log/pix11/110307-Monolith.jpg

(Note the Borges epigraph above.)

Sunday, February 15, 2009

Sunday February 15, 2009

Filed under: Uncategorized — m759 @ 11:00 AM
From April 28, 2008:

Religious Art

The black monolith of
Kubrick's 2001 is, in
its way, an example
of religious art.

Black monolith, proportions 4x9

One artistic shortcoming
(or strength– it is, after
all, monolithic) of
that artifact is its
resistance to being
analyzed as a whole
consisting of parts, as
in a Joycean epiphany.

The following
figure does
allow such
  an epiphany.

A 2x4 array of squares

One approach to
 the epiphany:

"Transformations play
  a major role in
  modern mathematics."
– A biography of
Felix Christian Klein

See 4/28/08 for examples
of such transformations.

 
Related material:

From Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, pp. 117-118:

"… his point of origin is external nature, the fount to which we come seeking inspiration for our fictions. We come, many of Stevens's poems suggest, as initiates, ritualistically celebrating the place through which we will travel to achieve fictive shape. Stevens's 'real' is a bountiful place, continually giving forth life, continually changing. It is fertile enough to meet any imagination, as florid and as multifaceted as the tropical flora about which the poet often writes. It therefore naturally lends itself to rituals of spring rebirth, summer fruition, and fall harvest. But in Stevens's fictive world, these rituals are symbols: they acknowledge the real and thereby enable the initiate to pass beyond it into the realms of his fictions.

Two counter rituals help to explain the function of celebration as Stevens envisions it. The first occurs in 'The Pediment of Appearance,' a slight narrative poem in Transport to Summer. A group of young men enter some woods 'Hunting for the great ornament, The pediment of appearance.' Though moving through the natural world, the young men seek the artificial, or pure form, believing that in discovering this pediment, this distillation of the real, they will also discover the 'savage transparence,' the rude source of human life. In Stevens's world, such a search is futile, since it is only through observing nature that one reaches beyond it to pure form. As if to demonstrate the degree to which the young men's search is misaligned, Stevens says of them that 'they go crying/The world is myself, life is myself,' believing that what surrounds them is immaterial. Such a proclamation is a cardinal violation of Stevens's principles of the imagination. For in 'Notes Toward a Supreme Fiction' he tells us that

... the first idea was not to shape the clouds
In imitation. The clouds preceded us.      

There was a muddy centre before we breathed.
There was a myth before the myth began,
Venerable and articulate and complete.      

From this the poem springs: that we live in a place
That is not our own and, much more, not ourselves
And hard it is in spite of blazoned days.      

We are the mimics.

                                (Collected Poems, 383-84)

Believing that they are the life and not the mimics thereof, the world and not its fiction-forming imitators, these young men cannot find the savage transparence for which they are looking. In its place they find the pediment, a scowling rock that, far from being life's source, is symbol of the human delusion that there exists a 'form alone,' apart from 'chains of circumstance.'

A far more productive ritual occurs in 'Sunday Morning.'…."

For transformations of a more
specifically religious nature,
see the remarks on
Richard Strauss,
"Death and Transfiguration,"
(Tod und Verklärung, Opus 24)

in Mathematics and Metaphor
on July 31, 2008, and the entries
of August 3, 2008, related to the
 death of Alexander Solzhenitsyn.
 

Monday, April 28, 2008

Monday April 28, 2008

Filed under: Uncategorized — Tags: — m759 @ 7:00 AM
Religious Art

The black monolith of
Kubrick's 2001 is, in
its way, an example
of religious art.

Black monolith, proportions 4x9

One artistic shortcoming
(or strength– it is, after
all, monolithic) of
that artifact is its
resistance to being
analyzed as a whole
consisting of parts, as
in a Joycean epiphany.

The following
figure does
allow such
  an epiphany.

A 2x4 array of squares

One approach to
 the epiphany:

"Transformations play
  a major role in
  modern mathematics."
– A biography of
Felix Christian Klein

The above 2×4 array
(2 columns, 4 rows)
 furnishes an example of
a transformation acting
on the parts of
an organized whole:

The 35 partitions of an 8-set into two 4-sets

For other transformations
acting on the eight parts,
hence on the 35 partitions, see
"Geometry of the 4×4 Square,"
as well as Peter J. Cameron's
"The Klein Quadric
and Triality" (pdf),
and (for added context)
"The Klein Correspondence,
Penrose Space-Time, and
a Finite Model
."

For a related structure–
  not rectangle but cube– 
see Epiphany 2008.

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