How are algebraic, combinatorial, and geometric structures unified within the Brick Space model?
From a search in this journal for Moon Knight —
From a search in this journal for Moon Knight —
From the current New Yorker,
a link for Katherine Neville —
Sagan as Fagin —
[A verse suggested by a Facebook post today . . .
"The cast of Sentimental Value all received
their first-ever Oscar nominations" . . .
and by the Jan. 22, 2026, New Yorker Cartoon of the Day.]

"A witch hiding a dangerous secret is thrust
into an elite magical academy, where survival
means risking her life and her heart.
Dark secrets. Deadly choices. A destiny that
can’t be outrun. Welcome to Shadowcraft Academy."
— https://www.breannerandall.com/
The Source . . . A Titusville bookstore —
Other May Tricks —
"We keep coming back to the real . . . ." — Wallace Stevens
"Facets and labyrinths . . . ." — Nicole Kidman
Illustration — Biarritz Balcony Scene.
Related reading for cultural historians — Quantum Lumps.
From http://m759.net/wordpress/?s=Faustus —
Design from 1514
"One of those bells that now
and then rings" — Song lyric
From http://m759.net/wordpress/?tag=zauberberg —
From the Web today —

Likewise.com is now pix-media.com.
Adapted song lyric for Pennywise fans . . .
♫ "Floating . . . takes me away to where I'm going . . . ."
For a different, but not unrelated, Bellevue, see
Wechsler Adult Intelligence Scale and WAIS Blocks.
From the home of Claude,
https://www.anthropic.com/ —
Claude in "Notorious" (1946) —
"I'm in with the in grid, I go where the in grid goes."

In memory of a biblical archaeologist who reportedly
died at 81 on Sunday, January 11, 2026 —
See as well this journal on Sunday, January 11 —
An Instagram flashback yesterday to 2016 suggests . . .
The date on a cartoon in the previous post — Sept. 19, 2019 —
suggests a review of the same date six years later . . .
See as well other posts now tagged Cullinane AI .
Related concept: "ghostly heptagons" —
Related art —
See this journal on the day of Becket (not Beckett), 2025.
It is extremely high in spice level (5/5). The intimate scenes
are frequent, explicit, and often intertwined with themes of
dominance, submission, and power exchange."
Cha-ching!

"The date chosen to celebrate World Logic Day, 14 January, corresponds to
the date of death of Kurt Gödel and the date of birth of Alfred Tarski,.
two of the most prominent logicians of the twentieth century." — Wikipedia
Some "presentatonal symbols" — The Gray Lotus.
94 sources
The Cullinane diamond theorem establishes a profound link between visual 4×4 patterns and advanced mathematical structures such as finite geometry and group theory. By analyzing symmetry-preserving transformations within a group of 322,560 permutations, the research connects simple grid designs to the complex projective space PG(3,2). These geometric frameworks further extend into coding theory, illustrating how "diamond" rings are isomorphic to matrix algebras over the finite field GF(4). The sources also highlight the Miracle Octad Generator (MOG) and its relationship to the Mathieu group M24, which is essential for understanding error-correcting codes and sphere packings. Beyond pure mathematics, the text explores "brick space" and the Klein correspondence, suggesting that these abstract symmetries represent a "universal" order found in both art and nature. Ultimately, this body of work bridges the gap between ancient motifs and modern computational science through the elegant study of structural invariants.
————————————————————————————.
. These physical or graphic arrangements serve as a concrete visualization (or model) of highly abstract mathematical structures.
. The geometry of is linked to the concept of the 8-set
. The model, developed as a brick space, is analogous to the "line diagrams" construction of found in the Cullinane diamond theorem
. The 35 combinatorial structures arising from permutations of diamond tiles (related to the bricks) are isomorphic to the 35 lines of . These 35 structures also mirror the 35 square patterns within the original MOG
. This same framework connects to the 105 partitions of an 8-set into four 2-sets, which are essentially the same as the 105 lines contained in the Klein quadric
. This provides a geometric dictionary for abstract algebraic combinatorics
. The algebraic rules of dictate the structure of the affine and projective spaces represented by the bricks
. The closure property of lines in is represented algebraically by the fact that the three line diagrams corresponding to a pattern always sum to zero ()
. This group, which explains the pervasive symmetry found in all -images, is the automorphism group of the underlying finite geometry, establishing the algebraic control over the system's geometric and combinatorial properties
. This links the geometry to the machinery of abstract algebra
, linking the visual patterns and the underlying geometries to the abstract world of sporadic simple groups, coding theory (Golay code), and lattice theory (Leech lattice)
. The entire structure is unified by powerful isomorphisms relating these three mathematical domains through finite geometries like and
Grok showed admirable persistence and depth in its research, but failed
to completely understand what is meant by "coordinatization of a 3×3 array."
It did, however, indicate a related concept in a suggested further prompt.
For the example that suggested the original prompt, see The Coxeter Aleph.
See as well other posts tagged Out Today.
The previous post's title, "Unfolding," and a search in this
journal for "porpentine," yield . . .
Cynthia Zarin in The New Yorker, issue dated April 12, 2004 –
"Time, for L'Engle, is accordion-pleated. She elaborated,
'When you bring a sheet off the line, you can't handle it until
it's folded, and in a sense, I think, the universe can't exist until
it's folded– or it's a story without a book.'"
For James Joyce, courtesy of Guillermo del Toro.
I prefer the flower window illustrated here
on December 29, 2025 —

https://www.nytimes.com/2026/01/10/magazine/george-saunders-interview.html
suggests a flashback to a 2022 Burning-Man-related post,
https://m759.net/wordpress/?p=102678 . . . "Come into my parlor."
This suggests a review . . .
Meanwhile, at Davos . . .


Adapted song lyric —
"What's that sweater you have on?
Is that a faded heart from days gone by?"
See as well other posts tagged Mossman.
Possible coded reply: "He played knick-knack on my gate ."
Dramatic prequel . . .
|
https://subslikescript.com/movie/Hurlyburly-119336 — So what do you want to do?
You want to go to your place, You want to go to a sex motel? They got waterbeds.
They got porn I'm hungry. You want a Jack-in-the-Box? I love Jack-in-the-Box. Is that code for something? What? What? Is what code for what? I don't know. I don't know the goddamn code! |
From a search tonight in this journal for "Drexel" —
See also a different usage of the highlighted "spearhead"
concept, starring Kristen Stewart and Elvis —
Related Twin Peaks metadata —
* A favorite word of author Dan Brown, a Langdon enthusiast.
From this journal on August 26, 2025 —
Some may prefer Bo Derek's choice.
I prefer Jaime's talent and beauty . . .
Synchronology check of
the above YouTube date —

Earlier . . .
"Why don't you come with me, little girl,
on a magic carpet ride?" — Steppenwolf lyrics
"I love the theater as I love Anne Hathaway . . ."
See illustration.
Sometimes a man's grasp exceeds his reach. — Adapted aphorism
Scholium —

3D Chess on a 4D Board
“The sigil was an eight-limbed asterisk
made of fine dark lines . . . . An X
superimposed on a plus sign.
It looked permanent.”
— Fritz Leiber, “Damnation Morning,”
1959 short story in Changewar

— ♫ "Remember what the dormouse said . . ."
— "Chmod 755?"

Related song lyric suggested by the above
placement of the "o" in "Dog" —
"This old man, he played three . . ."
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