260721-Ellie-Balkcom-Slane-Castle-RHCP-Don't-Forget-Me.jpg
Tuesday, July 21, 2026
Monday, July 20, 2026
Harrison Ford’s “Air Force One” soundtrack —
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"L'Internationale", original French version
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International anthem of anarchists, communists, |
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| Also known as | « L'Internationale » |
|---|---|
| Lyrics | Eugène Pottier, 1871 |
| Music |
Pierre De Geyter, 1888 |
| Audio sample | |
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Instrumental rendition in A major
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Update at 2:08 PM ET on July 20, 2026 . . .
with footnotes screenshot of 9:16 PM ET the same day:
For some news today of interest to mathematicians internationally ,
see Wikipedia on a reported finding by the AI Claude Fable 5
of a counterexample to the Jacobian conjecture.
Update of 9:38 AM ET July 21 —
(Claude Fable 5 appeared recently in this journal . . .
See July 8 — "Affine Generation: Claude Fable 5 Weighs In,"
http://m759.net/wordpress/?p=136411.)
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Saturday, July 18, 2026
Hillbilly Chess: Castling
Note the "Art Space" tag. I prefer the art space
of my old Harvard room, Lowell M33.
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Thursday, July 16, 2026
Planes of Reality: The Field
"You meet people on their plane of reality." — White Lotus
260716-The_Uni-Context-Derek_Thompson-substack-
July_14_2026-with-added-4×4-grid.jpg
"Time for you to see the field." — Bagger Vance
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Monday, July 13, 2026
Saturday, July 11, 2026
For Harlan Kane . . . The Copenhagen Gesture
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Saturday, June 27, 2026
Byte* Bite: A Tender Buttons Riddle from Cara
* Avant-garde fans may prefer the above
Delevingne-Lillis amalgam to yesterday's
more abstract 8-part "Big Byte" image . . .
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Thursday, June 25, 2026
Highway Sign
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Wednesday, June 24, 2026
Space Endings — Utopia, Dystopia, Atopia
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Tuesday, June 23, 2026
Monday, June 22, 2026
Tomorrowland Art: A Pattern for Gibson
The art is by Tolkien, the pattern is three cubes, the Gibson is William.
"Human perception is a saga of created reality." — Point Omega
"Omega is a real as we need it to be." — "The Osterman Weekend"
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Saturday, June 20, 2026
Cayley Superlines as Alpha- and Beta- Planes
Previous posts in this journal mentioning Cayley's "superlines"
were in error and have been removed. Cayley's own remarks —
In the finite space PG(5,2), there are 30 such "superlines" . . .
-Google_AI_Mode.jpg)
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Friday, June 19, 2026
Low Concept for Bunker Hill Community College*
"Shouldn't I have this,
shouldn't I have all of this?"
— Mary Chapin Carpenter
"How about a passage to . . . a redacted backwater?"
260619-Lockscreen-June-19-2026-Coconut-Palms-
and-Kerala-Houseboats-1.09amEDT-redacted.jpg
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Thursday, June 18, 2026
For Harlan Kane . . .
The Carpenter Question
"Shouldn't I have this,
shouldn't I have all of this?"
— Mary Chapin Carpenter
260618-Gimme_Shelter-Official_Lyric_Video.jpg
260618-Myrkia-Gimme_Shelter.jpg
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The Carpenter Question
The Carpenter Question
Wednesday, June 17, 2026
“The Geometry of Symmetry and
Cullinane’s Diamond Theorem”
The above title was written today by Google's NotebookLM
for its summary of the Diamond Theory notebook based on
sources provided by Steven H. Cullinane —
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The provided sources detail the mathematical research of Steven H. Cullinane, specifically his work on the symmetry and geometry of finite spaces. His central contribution, the Cullinane diamond theorem, explores how symmetry is preserved across transformations within binary affine spaces and 4×4 coordinate grids. This research establishes deep links between projective geometry, the Mathieu group M24, and combinatorial tools like R. T. Curtis’s Miracle Octad Generator. Cullinane’s work also reinterprets the orthogonality of Latin squares through the lens of line skewness in finite projective 3-space. Beyond pure mathematics, the texts highlight the visual and philosophical dimensions of his work, connecting abstract group theory to artistic patterns and Plato's classical dialogues. These documents collectively record a lifelong investigation into the structural foundations of finite geometry and its aesthetic representations. |
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Cullinane’s Diamond Theorem”
Cullinane’s Diamond Theorem”
Monday, June 15, 2026
High Concepts
Happy Bottom Riding Club
260615-Elliebalkcom-patches-with-song-of-same-title.jpg
… https://www.youtube.com/watch?v=Bxvvj5-e0vc
A Love Shack for Barbara
260529-Diamond_Theory-1976-Art_Space-figures.jpg
… http://m759.net/wordpress/?p=135709
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Sunday, June 14, 2026
Book Now
Contact, by Carl Sagan . . .
Chapter 24 – The Artist’s Signature —
| The anomaly showed up most starkly in Base 2 arithmetic, where it could be written out entirely as zeros and ones. Her program reassembled the digits into a square raster, an equal number across and down. Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts. The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle — another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn’t matter what you look like, or what you’re made of, or where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you’ll find it. It’s already here. It’s inside everything. You don’t have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist’s signature. Standing over humans, gods, and demons… there is an intelligence that antedates the universe. The circle had closed. She found what she had been searching for. |
Song lyric not in Sagan’s book:
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Will the circle be unbroken by and by, Lord, by and by? Is a better home a-waitin’ in the sky, Lord, in the sky? |
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Saturday, June 13, 2026
The Omega Scaffold
The "octeract" so named by Google AI Mode in yesterday's
post "Logic and Dimensions" is viewed by AI Mode as a
sort of eight-dimensional scaffold for logic. Some related
linguistic Verhexung . . . to use a handy term of Wittgenstein's —
Related reading . . .
260613-Clooney-Omega-tag-and-post.jpg
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Friday, June 12, 2026
Thursday, June 11, 2026
“From the West unto the East” — Dylan song
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Friday, June 5, 2026
The Facebook Question
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From this journal on November 7, 2003 . . . “Dr. Blind (pronounced ‘Blend’) was about ninety years old and had taught, for the past fifty years, a course called ‘Invariant Subspaces’ which was noted for its monotony and virtually absolute unintelligibility, as well as for the fact that the final exam, as long as anyone could remember, had consisted of the same single yes-or-no question. The question was three pages long but the answer was always ‘Yes’. That was all you needed to pass Invariant Subspaces.” — The Secret History, by Donna Tartt |
"What's on your mind, Steven?"
— Facebook, 10:16:16 AM today
"Invariant Subspaces."
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Harpstrings Continued . . .
O Captain! Her Captain!
Earlier . . .
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O Captain! Her Captain!
O Captain! Her Captain!
Thursday, June 4, 2026
“Geometric Logic” — Captain Queeg
|
By NotebookLM on June 4, 2026 . . . Geometry of the Diamond Theorem and Mathieu Groups These sources explore the Cullinane diamond theorem and its deep connections to finite projective geometry, group theory, and combinatorial design. Central to this research is the isomorphism between the 35 lines of the projective space PG(3,2) and specific symmetry-preserving patterns found in 4×4 arrays of two-color tiles. This framework bridges visual art and high-level mathematics by linking quilt-like motifs to the Miracle Octad Generator (MOG) and the sporadic Mathieu group M24. Algebraic tools like the Klein correspondence and Conwell’s heptads are utilized to map these combinatorial partitions onto the geometric structure of the Klein quadric. Beyond theoretical geometry, the findings extend into ring theory, coding theory, and the study of the Leech lattice. Ultimately, the text demonstrates that simple decorative symmetries are manifestations of profound, highly symmetric structures underlying multidimensional space. |
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A Mike for Sunrise
260604-Ellie-Balkcom-fan-page-annotated.jpg
Update: The first image above is from . . .
260604-Ellie-Balkcom's-own-
Holy-Saturday-post–
April_4_2026.jpg —
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Emoticons [ :) <3 ]
Versus the Emojis of Meta
Comments Off on Emoticons [ :) <3 ]
Versus the Emojis of Meta
Versus the Emojis of Meta
Tuesday, June 2, 2026
Sunday, May 31, 2026
For the Archives of Mel Brooks (and Donald Newlove) . . .
The Long-Awaited Sequel to Through the Looking Glass . . .
Behind the Bookshelf!
Comments Off on For the Archives of Mel Brooks (and Donald Newlove) . . .
The Long-Awaited Sequel to Through the Looking Glass . . .
Behind the Bookshelf!
The Long-Awaited Sequel to Through the Looking Glass . . .
Behind the Bookshelf!