"Twenty-four Seven" . . . may be interpreted as
24×7 = 168, the number of hours in a week
and also the number of elements in the group GL(3,2).
Related geometry —
http://www.log24.com/log08/saved/080510-Modernism.html
and . . .
Update at 11:48 AM EDT Thursday, August 20, 2026 —
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"Against Dryness" is the title of a 1961 essay by Iris Murdoch.
As an example of what Murdoch called "dryness," see the Log24 post
of 2:48 PM EDT Tuesday, August 18, 2026. As examples of less dry
remarks, see the posts that followed, up to and including a post
of 2:48 PM EDT Wednesday, August 19, 2026.
From Log24 on July 19, 2026 . . .
ENM
From the online New Yorker today . . .
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bottom-center-and-Palm_Swings.jpg
Michelle Monaghan in a dress by Valentino —
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260819-Riviera_Swingtime-Treasure_Chest.jpg
From a search in this journal for Queen's Gambit —
"That the topless towers be burnt
And men recall that face . . . ."
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Note written by AI at notebook.google.com The Geometry of the Cullinane Diamond Theorem The provided sources detail the Cullinane diamond theorem and its foundation in the intersection of finite geometry, group theory, and combinatorial design. This theorem describes how a 4×4 array of two-color square tiles maintains structured symmetry under a specific group of permutations, which is shown to be isomorphic to the affine group AGL(4,2). These visual patterns serve as models for the 35 lines of the projective space PG(3,2) and are intimately connected to the Klein quadric and the Miracle Octad Generator (MOG). By mapping abstract geometric properties to graphic arrangements, the research links traditional visual motifs to complex structures like the Mathieu group M24, the Leech lattice, and the binary Golay code. Ultimately, Cullinane’s work demonstrates that seemingly simple artistic symmetries are rooted in the deep mathematical logic of Galois geometry and sporadic simple groups. |
"… the war of 70-some years ago
has already become something like the Trojan War
had been for the Homeric bards:
a major event in the mythic past
that gives structure and sense to our present reality."
— Justin E. H. Smith, a professor of philosophy at
the University of Paris 7–Denis Diderot, in
The New York Times, Sunday, June 5, 2016
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See as well D-Day 2026.
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Wikipedia — " Cabilao is a Philippine island . . . ."
Related material for Spider Man . . .
From Log24 posts tagged Philippine —
260817-Mystery_Model_with_Beach_Umbrella.jpg
The "Naughty Lotus" position?
♫ "Swingin' with the old stars . . . ." "Outside of technical constraints, one of the hardest problems in storytelling in video games is making player choices meaningful, which has some interesting overlap with some of the the fundamental intractable problems of human existence." (Link added.)
— https://paperairplane.substack.com/p/on-narrative-design-2
(Inside of technical constraints, problems are even harder.)
Related cinematic illustration . . .
A scene from the upcoming "Plumbers' Helper — The Musical!"
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The Source — https://www.patreon.com/MysteryIslandMusical/
posts/page-1-166431019
“There exists a considerable literature
devoted to the Lo shu , much of it infected
with the kind of crypto-mystic twaddle
met with in Feng Shui.”
— Lee C. F. Sallows, Geometric Magic Squares ,
Dover Publications, 2013, page 121
260816-Revised-Google-Notebook-AI-summary-
after-new-source-added.jpg —
For the new source itself, see the previous post.
The second sentence should be rewritten . . .
"… the mapping of 4×4 square patterns, where the permutations
of rows, columns, and columns correspond to specific affine
group actions, onto the geometric structure of PG(3,2)."
An illustration of this mapping from a July 12, 2012, post—
The 35 lines in the 3-dimensional Galois projective space PG(3,2)—
_lines_as_arrays.jpg)
Exercise: Show that Dürer's 1514 "magic" square is an affine automorphism.
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AI Summary from notebook.google.com, Aug. 16, 2026 These sources explore the Cullinane diamond theorem and its profound links between visual symmetry and finite projective geometry. The research demonstrates that patterns in a 4×4 array of square tiles are governed by the affine group AGL(4,2) and the geometric properties of PG(3,2). This mathematical framework connects simple graphic designs to high-level structures like the Klein quadric, the Miracle Octad Generator, and the Mathieu group M24. By mapping combinatorial partitions of an 8-set to geometric lines, Cullinane bridges sporadic simple groups with tangible models used in coding theory and quilt art. The collection further extends into Boolean logic, Walsh functions, and the Leech lattice, illustrating a unified theory of discrete symmetry. Visual representations, such as line diagrams and triangular tile orientations, serve as an "alphabet" to decode these complex algebraic relationships. |
Mikey would waltz with a strawberry blonde . . .
And the band played on.
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