Claude in "Notorious" (1946) —
"I'm in with the in grid, I go where the in grid goes."
Midrash for storytellers . . .
Saturday, October 11, 2025
Wednesday, October 8, 2025
Cube-Brick Columns
This post was suggested by yesterday's update to
the "Analogy Between Analogies" post of October 6.
The reason for the above columns . . .
The action of S8 on the rows of an 8-row 3-column matrix
000
001
010
011
100
101
110
111
is intimately connected, via the 30 labelings of a Fano plane
and via the Klein quadric in PG(5, 2), with the action of a
group of order 322,560 on the 16 squares of a 4×4 array.
See Conwell, 1910 [1] and the Log24 tag 105 partitions.
1. Conwell, George M. “The 3-Space PG(3, 2) and Its Group.”
Annals of Mathematics, vol. 11, no. 2, 1910, pp. 60–76.
JSTOR, https://doi.org/10.2307/1967582.
For those who prefer narratives to mathematics: The Cubes.
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Tuesday, October 7, 2025
Fano-Plane Incidence-Matrix Structures
How best to depict the 30 essentially different such structures is
not clear. See an update to yesterday's post on the structures.
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Monday, October 6, 2025
Analogy Between Analogies
Consider . . .
A. The nontrivial analogy between the two parts of the well-known natural
15+15 partition of the 30 labelings of the Fano plane PG(2, 2)
B. The nontrivial analogy between the two parts of the well-known natural
15+15 partition of the 30 planes of the Klein quadric in PG(5, 2)
Are A and B nontrivially analogous? If so, how?
Update of 6:58 PM EDT Oct. 7 . . .
Hint:
Use as labels for PG(2, 2) points the seven nonzero vectors in the
3-space over GF(2), expressed as 001, 010, 011, 100, 101, 110, 111.
Then form three seven-digit vectors by taking the first, second, and third
digit in each 3-digit vector. View these seven-digit vectors as points of
the Klein quadric in PG(5, 2).
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Vibe-coded Illustration of
30 Fano-Plane Labelings
(Distinctness as labelings requires verification.)
Update of 1:35 PM EDT Oct. 7
The above incidence matrices are clearly distinct as matrices, but
whether they show the well-known 30 labelings that are structurally
distinct as labelings is not clear. There seems to be little discussion
of Fano-plane incidence matrices on the Web. One example of such
a matrix with a well-formed structure of cyclically shifted rows —
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30 Fano-Plane Labelings
30 Fano-Plane Labelings
The October Country:
“Bradbury, Aiken … Aiken, Bradbury”
Related reading for fans of Bradbury's phrase
"patterning windows" and/or Aiken's phrase
"shadow guests" —
The Strong Law of Small Shapes (May 29, 2024).
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“Bradbury, Aiken … Aiken, Bradbury”
“Bradbury, Aiken … Aiken, Bradbury”
Saturday, October 4, 2025
For the Feast of St. Francis:
Geometric Theology
A Log24 search —
http://m759.net/wordpress/?s=Bonaventure —
yields . . .
St. Bonaventure on the
Trinity at math16.com
and
A trinity:
Click on picture for further details.
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Geometric Theology
Geometric Theology
Friday, October 3, 2025
A Unifying Framework
|
Finite Geometry: A Unifying Framework "In essence, finite geometry, exemplified by the Cullinane diamond theorem, acts as a 'portal' that unveils profound mathematical structures underlying seemingly simple patterns, demonstrating the interconnectedness of geometry, algebra, combinatorics, and visual art, with significant implications for fields ranging from error-correcting codes to experimental design and signal processing." — NotebookLM AI on 18 September 2025 |
See as well a dies natalis on 18 September 2025 —
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Thursday, October 2, 2025
Wednesday, October 1, 2025
For Wallace Stevens’s Birthday — October 2.
Posts now tagged Incipient Colorings.
Some related mathematics:
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