Aiello's Mural Style —
Cullinane's Abstract Style —
A Cayley superline of the Klein quadric in PG(5,2)
is actually a plane of the quadric. Any such plane can be
pictured as a set of seven partitions of an 8-set into four 2-sets,
with the partitions satisfying certain geometric conditions.
A prototypical example of such a set: the four-colored bricks
numbered 1 through 7 at left in the picture below.
https://notebook.google.com/notebook/
62ad8daa-277e-4fea-a680-9b209883f232
| These sources examine the Cullinane diamond theorem, a mathematical framework that links visual symmetry in 4×4 tiled arrays to the abstract principles of finite projective geometry. By applying a specific group of permutations to these two-color patterns, the research demonstrates that every resulting image maintains a consistent geometric or color-interchange symmetry. This work establishes a deep correspondence between combinatorial partitions of an 8-set and the 105 lines of the Klein quadric within the projective space PG(5,2). Furthermore, the sources connect these patterns to advanced topics such as the Mathieu group M24, the Miracle Octad Generator, and the Leech lattice. Beyond pure mathematics, the text explores how these structures manifest in quilt designs, Walsh functions, and the geometry of logic. This synthesis reveals how elementary graphic arrangements act as tangible models for complex sporadic simple groups and error-correcting codes. |
For some related remarks on art illustrating the geometry of latin squares,
vide The Order-4 Latin Squares.
* See the term "Waymark" in this journal.
260127-Elliott_Smith-memorial-mural-in-LA.jpg
In 2004 —
See as well this journal on the above upload date, 7 August 2010 —
"the reflection in the water showed an iron man"
is the line of verse by Elliott Smith that lay hidden
in a fold of cloth on the breast of Soundwavesoffwax
in an Instagram post yesterday.
Related meditation —
Tony Stark in The Avengers , May the Fourth, 2012
collider.com/kate-mara-sci-fi-movie-the-astronaut-
streaming-hulu-february-2026
* See as well Waymark in this journal.
Earlier:
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.
The previous post suggests a review of
a Log24 post from August 22, 2020 —
From a web page —
From YouTube, for the Church of Synchronology —
For some context, see Holocron in this journal.
The previous post (Pathmark Meets Hallmark) suggests
a review of the Waymark Prize in mathematics.
Notes on Mathematics and Narrative, continued
Patrick Blackburn, meet Gideon Summerfield…
From a summary of a politically correct 1995 feminist detective novel about quilts, A Piece of Justice—
The story deals with “one Gideon Summerfield, deceased.” Summerfield, a former tutor at (the fictional) St. Agatha’s College, Cambridge University, “is about to become the recipient of the Waymark prize. This prize is awarded in Mathematics and has the same prestige as the Nobel. Summerfield had a rather lackluster career at St. Agatha’s, with the exception of one remarkable result that he obtained. It is for this result that he is being awarded the prize, albeit posthumously.” Someone is apparently trying to prevent a biography of Summerfield from being published.
Compare and contrast with an episode from the resume of a real Gideon Summerfield—
Head of Strategy, Designer City (May 1999 — January 2002)
Secured Web agency business from new and existing clients with compelling digital media strategies and oversaw delivery of creative, production and technical teams…. Clients included… Greenfingers and Lord of the Dance .
For material related to Greenfingers and Lord of the Dance , see Castle Kennedy Gardens at Wicker Man Locations.
“… in 1896 Alfred Nobel,
the inventor of dynamite and
founder of the Nobel prizes,
died in San Remo, Italy,
at age 63.”
— “Today in History,”
by The Associated Press
author and co-producer of
The Librarian: Quest for the Spear.
A Piece of Justice.
From a summary of the novel:
From the current
American Mathematical Society
“Mathematical Imagery” page:
That entry contained an excerpt from
Tom Wolfe’s The Painted Word—
Diamond Theory
and a politically correct
1995 feminist detective novel
about quilts,
From a summary of the novel:
Meanwhile, back in real life…
It is said that the late Ms. Tompkins
liked to work while listening to the
soundtrack of “Saturday Night Fever.”
“It’s just your jive talkin’
you’re telling me lies, yeah
Jive talkin’
you wear a disguise
Jive talkin’
so misunderstood, yeah
Jive talkin’
You really no good”
These lyrics may also serve
to summarize reviews
of Diamond Theory written
in the summer of 2005.
For further details, see
Mathematics and Narrative.
For Bloomsday 2006:
Hero of His Own Story
"The philosophic college should spare a detective for me."
— Stephen Hero. Epigraph to Chapter 2, "Dedalus and the
Beauty Maze," in Joyce and Aquinas, by William T. Noon, S. J.,
Yale University Press, 1957 (in the Yale paperback edition of
1963, page 18)
"Dorothy Sayers makes a great deal of sense when she points out
in her highly instructive and readable book The Mind of the Maker
that 'to complain that man measures God by his own measure is
a waste of time; man measures everything by his own experience;
he has no other yardstick.'"
— William T. Noon, S. J., Joyce and Aquinas (in the Yale paperback
edition of 1963, page 106)
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