Log24

Tuesday, August 31, 2021

Summer Knowledge

Filed under: General — Tags: — m759 @ 11:00 PM

The title is that of a book of poems by Delmore Schwartz.

From "Searching for God in the Next Apartment,"
by Stanley Moss, New York Times Book Review ,
Sunday, October 19, 1986 —

Throughout Schwartz's poetry a question of belief is central. He thought we could not live without an interpretation of the whole of life, and that modern social orders were inevitably deficient in satisfying this need. He wrote studies and poetry explicitly concerned with the decline of Christian belief and the impossibility of any belief whatsoever. He read Rimbaud's ''Season in Hell,'' Valery's ''Cimetiere Marin,'' Arnold's ''Dover Beach,'' Hardy's ''Oxen,'' Stevens' ''Sunday Morning'' as poems forged in just such a dilemma. His own preferred poem, ''Starlight Like Intuition Pierced the Twelve,'' continued this argument.

See also Log24 posts tagged Central Myth, and the following image:

Matrix Reloaded

Filed under: General — Tags: — m759 @ 6:01 PM

In today's online New York Times , Kathryn Harrison reviews a new novel:

MATRIX
By Lauren Groff

From the online New York Times Book Review  on May 24, 2018 —

From this  journal on May 24, 2018 —

Further remarks by Lauren Groff on May 24, 2018 —

"Something invisible and pernicious seems to be preventing
even good literary men from either reaching for books with
women’s names on the spines, or from summoning women’s
books to mind when asked to list their influences. I wonder
what such a thing could possibly be."

Quentin Tarantino?

   — 

"It seems no coincidence that all of these titles
are written by women, for a primary angle of 
Gunpowder Milkshake  is one that tries its best
to promote 'feminism' in a Quentin Tarantino
sort of way." 

Or Lévi-Strauss?

See Log24 posts on The Matrix of Lévi-Strauss

Friday, September 2, 2016

Raiders of the Lost Birthday

Filed under: General — Tags: , , — m759 @ 10:00 AM

Some images from the posts of last July 13
(Harrison Ford's birthday) may serve as funeral
ornaments for the late Prof. David Lavery.

IMAGE- Massimo Vignelli, his wife Lella, and cube

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

See as well posts on "Silent Snow" and "Starlight Like Intuition."

Sunday, April 12, 2009

Sunday April 12, 2009

Filed under: General — Tags: — m759 @ 3:09 AM
Where Entertainment
Is God
, continued

Dialogue from the classic film Forbidden Planet

"… Which makes it a gilt-edged priority that one of us gets into that Krell lab and takes that brain boost."

— Taken from a video (5:18-5:24 of 6:09) at David Lavery's weblog in the entry of Tuesday, April 7.

(Cf. this journal on that date.)

Thanks to Professor Lavery for his detailed notes on his viewing experiences.

My own viewing recently included, on the night of Good Friday, April 10, the spiritually significant film Indiana Jones and the Kingdom of the Crystal Skull.

The mystic circle of 13 aliens at the end of that film, together with Leslie Nielsen's Forbidden Planet remark quoted above, suggests the following:

"The aim of Conway’s game M13 is to get the hole at the top point and all counters in order 1,2,…,12 when moving clockwise along the circle." —Lieven Le Bruyn

 

http://www.log24.com/log/pix09/090411-M13.gif

The illustration is from the weblog entry by Lieven Le Bruyn quoted below. The colored circles represent 12 of the 13 projective points described below, the 13 radial strokes represent the 13 projective lines, and the straight lines in the picture, including those that form the circle, describe which projective points are incident with which projective lines. The dot at top represents the "hole."

From "The Mathieu Group M12 and Conway’s M13-Game" (pdf), senior honors thesis in mathematics by Jeremy L. Martin under the supervision of Professor Noam D. Elkies, Harvard University, April 1, 1996–

"Let P3 denote the projective plane of order 3. The standard construction of P3 is to remove the zero point from a three-dimensional vector space over the field F3 and then identify each point x with -x, obtaining a space with (33 – 1)/2 = 13 points. However, we will be concerned only with the geometric properties of the projective plane. The 13 points of P3 are organized into 13 lines, each line containing four points. Every point lies on four lines, any two points lie together on a unique line, and any two lines intersect at a unique point….

Conway [3] proposed the following game…. Place twelve numbered counters on the points… of P3 and leave the thirteenth point… blank. (The empty point will be referred to throughout as the "hole.") Let the location of the hole be p; then a primitive move of the game consists of selecting one of the lines containing the hole, say {p, q, r, s}. Move the counter on q to p (thus moving the hole to q), then interchange the counters on r and s….

There is an obvious characterization of a move as a permutation in S13, operating on the points of P3. By limiting our consideration to only those moves which return the hole to its starting point…. we obtain the Conway game group. This group, which we shall denote by GC, is a subgroup of the symmetric group S12 of permutations of the twelve points…, and the group operation of GC is concatenation of paths. Conway [3] stated, but did not prove explicitly, that GC is isomorphic to the Mathieu group M12. We shall subsequently verify this isomorphism.

The set of all moves (including those not fixing the hole) is given the name M13 by Conway. It is important that M13 is not a group…."

[3] John H. Conway, "Graphs and Groups and M13," Notes from New York Graph Theory Day XIV (1987), pp. 18–29.


Another exposition (adapted to Martin's notation) by Lieven le Bruyn (see illustration above):

 

"Conway’s puzzle M13 involves the 13 points and 13 lines of P3. On all but one point numbered counters are placed holding the numbers 1,…,12 and a move involves interchanging one counter and the 'hole' (the unique point having no counter) and interchanging the counters on the two other points of the line determined by the first two points. In the picture [above] the lines are represented by dashes around the circle in between two counters and the points lying on this line are those that connect to the dash either via a direct line or directly via the circle. In the first part we saw that the group of all reachable positions in Conway's M13 puzzle having the hole at the top position contains the sporadic simple Mathieu group M12 as a subgroup."

For the religious significance of the circle of 13 (and the "hole"), consider Arthur and the 12 knights of the round table, et cetera.

But seriously…
 
Delmore Schwartz, 'Starlight Like Intuition Pierced the Twelve'

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