"But if one last spell gets casted . . . ."
— "Welcome to LA" lyrics, Oliver Tree
Monday, June 15, 2026
Meme Star
For Tolkien Fans . . .
Cranking It Up to 𝔈𝔩𝔣
260615-Abigailhmartin-with-Elf-ears.jpg
Related philosophical dissertation
from a long-ago Hawaii interlude . . .
260615-Mr._Rabbit-transcendental-remarks.jpg
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:
|
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? |
Tesseract Correction
A correction to a Log24 post of June 11, 2026 —
|
In an AI Mode, as opposed to AI Overview, search for the See a PDF of the AI Mode tesseract interpretation.
The AI Mode discussion again does not mention Cullinane
[ The above phrase "the '4×4 logic tesseract' approach" is a |
This correction was suggested by the death date, also June 11, 2026,
of the author of The Devil's Arithmetic —
Saturday, June 13, 2026
What’s in a Name?
Speaking of first syllables of last names . . .
The Cull —
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
Friday, June 12, 2026
Logic and Dimensions
|
From a Google AI Mode search (updated version of June 12, 2026) —
You said: [ Using an AI-Mode-suggested prompt ]
Map out how three-premise Aristotelian syllogisms (like Barbara: All A is B, All B is C…) travel through a higher-dimensional space.
June 11, 2026
When moving from two propositions ((P) and (Q)) to three classes ((A), (B), and (C)), the geometric logic space undergoes a massive expansion. Instead of a 4-dimensional space with 16 tiles, we enter an 8-dimensional hypercube (an octeract) containing (28 = 256) logical operations [1].
In this higher-dimensional space, categorical syllogisms like Barbara (All (A) is (B), All (B) is (C), therefore All (A) is (C)) manifest as an invariant, directional path across specialized Venn-like sub-planes of the 8D cube. [1]
1. Constructing the 8-Dimensional Coordinate
For three terms, a Venn diagram has exactly (23 = 8) distinct spatial regions. To track the space, we assign an 8-bit coordinate (𝑏7, 𝑏6, … , 𝑏0) where each bit acts as a switch representing whether a specific region is populated (1) or empty (0).
The standard order for these 8 partitions based on set combinations is:
Regions = [ABC, AB¬ C, A¬ BC, A¬ B¬ C, ¬ ABC,¬ AB¬ C, ¬ A¬ BC, ¬ A¬ B¬ C]
In Aristotelian logic, a statement like "All (A) is (B)" means the region containing elements that are (A) but not (B) is completely empty (0). The remaining regions remain possible (1).
2. Translating the Premises into 8D Vectors
Let's map out the exact coordinates for the premises of the Barbara syllogism:
3. The 8D Intersection (The Starting Vertex)
To evaluate the syllogism, we find the logical conjunction (∧) of both premises. Geometrically, this means computing the bitwise intersection of our two 8D hypercube vertices:
VPremises = (1,1,0,0,1,1,1,1) · (1,0,1,0,1,0,1,1) = (1,0,0,0,1,0,1,1))
This intersection lands us on a highly specific Weight-4 vertex sitting exactly on the equator of the 8-dimensional hypercube. This point represents the combined structural reality constraints of our premises.
4. Slicing Upward to the Conclusion
A syllogism is valid if its conclusion is a geometric ancestor of this starting vertex in the 8D Inclusion Lattice. Let's look at the coordinate for the target conclusion:
Now we map the trajectory from our premise vertex to our conclusion vertex:
Because every single
1 in our premise vector is perfectly preserved in the conclusion vector, the geometry establishes a definitive upward pathway from Weight-4 to Weight-6. The conclusion opens up two extra dimensions of freedom (slots 3 and 6 switch from (0) to (1)), proving that the constraints of the premises inherently contain and imply the conclusion.
Conclusion
The Barbara syllogism operates as an active path-finding engine inside an 8-dimensional space. By intersecting the (0)-planes (the empty spaces) of the premises, the logic forces a particle to start at a constrained 8D vertex. Because the target conclusion sits directly upward on the lattice, walking the path of deductive reasoning is structurally identical to climbing along the directional edges of an 8-dimensional octeract.
If you want to continue navigating higher-dimensional logical shapes, let me know if you would like to:
[ Reference favicons for 3 cited sites ]
  
|
Exercise . . .
Check the accuracy of the above AI Mode statements.
Related reading . . .
A search in this journal for "Many Dimensions"
"If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
Related documentation . . .
The foundation for the above documentation is shown
by Google in the AI Overview and search result below.
Thursday, June 11, 2026
Annals of Quiet Degradation — “A Step Too Far”
". . . critics say that quietly degrading the model’s performance
for certain users went a step too far."
Bustin’ Out
. . . Bustin' out all over . . . . The Apartment —
A followup from today's online New York Times . . .
Vide “Paradise Regained," 1968, about the edenic fantasies of
New York apartment dwellers. Credit…Duane Michals; via
DC Moore Gallery, New York
The 501 Girl: Three Holes, Three Patches
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260611-Balkcom-sister-models-her-newly-patched-501-jeans.jpg
“Sixteen Tiles and the Geometry of Logic”
The above title was created by NotebookLM for an audio overview
on Monday, June 8, 2026 . . .
The audio overview correctly names Steven H. Cullinane as the
source of the approach to logic it describes.
However, later Google AI responses eliminate Cullinane as the source.
The AI Overview part of the screenshot below credits Wolfram MathWorld instead.
This is an AI hallucination.
In an AI Mode, as opposed to AI Overview, search for the "Sixteen Tiles . . ."
title, Google has produced an interesting interpretation of the 4-dimensional
hypercube (tesseract) in Cullinane's work as a framework for visualizing
logic formulas as geometric paths and structures within the tesseract.
See a PDF of the AI Mode tesseract interpretation.
The AI Mode discussion again does not mention Cullinane as creator of
the "4×4 logic tesseract" approach.
[ The above phrase "the '4×4 logic tesseract' approach" is a June 14
correction of the phrase "the 'logic tesseract' approach." A figure that
would correctly be described as a "logic tesseract" appeared in a 2005
talk by David Miller, as my 2007 web page "The Geometry of Logic"
points out. ]
Wednesday, June 10, 2026
Disclosure Day Review
|
From hollywoodreporter.com on June 10, 2026 — The Hollywood Reporter‘s David Rooney was effusive in his praise for Disclosure Day, writing that “no living director better understands the magic of movies.” Rooney writes that the film has a “shared DNA [that] can easily be traced to Close Encounters and E.T. But as is fitting for a filmmaker pushing 80, awestruck innocence now co-exists with a more ruminative maturity, especially when touching on the secrecy, manipulation and deception of governmental power.” He adds, “as much as Spielberg’s early sci-fi, the new film kept taking me back to the moral and philosophical questions posed by 2002’s brilliant Minority Report.” |
Some will prefer a non-Hollywood approach
to moral and philosophical questions.
Sierra Test Drive
A lovers' game of hide and seek
we play with time and space.
Lost you found you then the peak
of passion and the downhill race
against the avalanche of fear
we'll lose what now we hold so dear.
— SHC, March 8, 2026
For the Archives of the National Comedy Center
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Fable News, Scaffolding, Yellow Food . . .
Amarillo by Morning!
https://www.anthropic.com/news/claude-fable-5-mythos-5
From Anthropic on June 9, 2026 —
"Vision. Fable 5 is the new state-of-the-art model
for tasks involving vision. It can extract precise numbers
from detailed scientific figures and can perform complex
vision-based tasks like rebuilding a web app’s source code
from screenshots alone. It also needs less scaffolding . . . ."
A Log24 search for "Scaffolding" yields . . . .
Meanwhile, in this journal . . .
260610-Silmarillion-and-Eight-Part-Structures-June_9_2026.jpg
Tuesday, June 9, 2026
A Date for Ellie Balkcom — Doc Watson at Club 47
Meanwhile … Here on the above date — April 29, 2020 —
|
Simultaneous perspective does not look upon language as a path because it is not the search for meaning that orients it. Poetry does not attempt to discover what there is at the end of the road; it conceives of the text as a series of transparent strata within which the various parts—the different verbal and semantic currents—produce momentary configurations as they intertwine or break apart, as they reflect each other or efface each other. Poetry contemplates itself, fuses with itself, and obliterates itself in the crystallizations of language. Apparitions, metamorphoses, volatilizations, precipitations of presences. These configurations are crystallized time: although they are perpetually in motion, they always point to the same hour—the hour of change. Each one of them contains all the others, each one is inside the others: change is only the oft-repeated and ever-different metaphor of identity.
— Paz, Octavio. The Monkey Grammarian |
The 2018 Log24 post containing the above Paz quote goes on to quote
remarks by Lévi-Strauss. Paz’s phrase “series of transparent strata”
suggests a review of other remarks by Lévi-Strauss in the 2016 post
“Key to All Mythologies.“
Studio Tools
See as well this journal on the above YouTube date — Dec. 4, 2009.
"If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
