This post was suggested by the two previous posts, Sermon and Structure.
Vide below the final paragraph— in Chapter 7— of Cameron’s Parallelisms ,
as well as Baudelaire in the post Correspondences :
Comme de longs échos qui de loin se confondent
Dans une ténébreuse et profonde unité….
— Baudelaire, “Correspondances “
A related image search (click to enlarge):
From this journal on Saturday, August 6, 2011—
Comme de longs échos qui de loin se confondent
Dans une ténébreuse et profonde unité….
— Baudelaire, "Correspondances " (in The Flowers of Evil )
From the New York Times philosophy column "The Stone" earlier that day—
"… a magnificent and colorful parade of disorganized and rhapsodic thoughts"
— Baudelaire
From Uncle Walt— (See yesterday's "Coordinated Steps")—
For a better organized, less rhapsodic parade, see Saturday's Correspondences.
Comme de longs échos qui de loin se confondent
Dans une ténébreuse et profonde unité….
— Baudelaire, “Correspondances ”
From “A Four-Color Theorem”—
Figure 1
Note that this illustrates a natural correspondence
between
(A) the seven highly symmetrical four-colorings
of the 4×2 array at the left of Fig. 1, and
(B) the seven points of the smallest
projective plane at the right of Fig. 1.
To see the correspondence, add, in binary
fashion, the pairs of projective points from the
“points” section that correspond to like-colored
squares in a four-coloring from the left of Fig. 1.
(The correspondence can, of course, be described
in terms of cosets rather than of colorings.)
A different correspondence between these 7 four-coloring
structures and these 7 projective-line structures appears in
a structural analysis of the Miracle Octad Generator
(MOG) of R.T. Curtis—
Figure 2
| Here the correspondence between the 7 four-coloring structures (left section) and the 7 projective-line structures (center section) is less obvious, but more fruitful. It yields, as shown, all of the 35 partitions of an 8-element set (an 8-set ) into two 4-sets. The 7 four-colorings in Fig. 2 also appear in the 35 4×4 parts of the MOG that correspond, in a way indicated by Fig. 2, to the 35 8-set paritions. This larger correspondence— of 35 4×2 arrays with 35 4×4 arrays— is the MOG, at least as it was originally defined. See The MOG, Generating the Octad Generator, and Eightfold Geometry.
For some applications of the Curtis MOG, see |
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