Wednesday, January 14, 2026

Today Is World Logic Day 2026

Filed under: General — Tags: Art Space, Cullinane AI — m759 @ 12:34 pm

"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.

Diamond Theory
by NotebookLM

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.

How does the diamond theorem bridge visual tile patterns and abstract group theory?

In what ways does PG(3,2) serve as a foundation for Diamond Theory?

How do symmetry and automorphism groups link 4×4 arrays to the Mathieu group?

__________________________________________________________________

Thursday, November 20, 2025

How are algebraic, combinatorial, and geometric structures unified within the Brick Space model?

The unification of algebraic, combinatorial, and geometric structures within the Brick Space model is achieved through its role as a graphic, isomorphic representation of key finite geometries, particularly the projective spaces PG(5,2) and PG(3,2), and their fundamental relationship via the Klein correspondence.

————————————————————————————.

The term "Brick Space" originates from the

2 \times 4

arrays, or "bricks," coined by R. T. Curtis as component parts of his Miracle Octad Generator (MOG)

. These physical or graphic arrangements serve as a concrete visualization (or model) of highly abstract mathematical structures.

1. Geometric Unification

The Brick Space model provides a geometric foundation for combinatorial objects through direct visualization of finite geometries defined over the two-element field, GF(2)

• Modeling Projective Space: The Brick Space model is the natural geometric setting for the MOG's components, which may be regarded as forming both the 5-dimensional projective space

PG (5, 2)

and the 3-dimensional projective space

PG (3, 2)

• Visualizing PG(5,2) and the Klein Quadric: The model visually represents the

PG (5, 2)

space, which has 63 points, by partitioning these points into 28 points lying off the Klein quadric and 35 points lying on the Klein quadric

. The geometry of $PG (5, 2)$ is linked to the concept of the 8-set

• The Klein Correspondence: The geometric relationship between

PG (3, 2)

and

PG (5, 2)

is formalized by the Klein correspondence

. The $PG (5, 2)$ model, developed as a brick space, is analogous to the "line diagrams" construction of $PG (3, 2)$ found in the Cullinane diamond theorem

• Lines and Points: The Brick Space implicitly models how the 35 lines of

PG (3, 2)

correspond to the 35 points on the Klein quadric in

PG (5, 2)

2. Combinatorial Unification

Combinatorial structures, primarily partitions of sets and block designs, are mapped directly onto geometric entities within the Brick Space framework

• Partitions and Lines: The central combinatorial equivalence involves mapping partitions of sets to geometric objects

. The 35 combinatorial structures arising from permutations of $4 \times 4$ diamond tiles (related to the $2 \times 4$ bricks) are isomorphic to the 35 lines of $PG (3, 2)$ . These 35 structures also mirror the 35 square patterns within the original MOG

• Partitions of the 8-Set: The

PG (3, 2)

lines correspond to the 35 partitions of an 8-set into two 4-sets

. 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

• Latin Squares: The combinatorial property of orthogonality of Latin squares (specifically, order-4 Latin squares) is unified geometrically by corresponding exactly to the property of skewness of lines (non-intersecting lines) in

PG (3, 2)

. This provides a geometric dictionary for abstract algebraic combinatorics

3. Algebraic Unification

Algebraic structures, rooted in finite field theory and group theory, govern the behavior and symmetries observed in the combinatorial and geometric models

• Binary Field

GF (2)

: The foundation of the geometry is the Galois field of two elements,

GF (2)

(binary arithmetic:

1 + 1 = 0

)

. The algebraic rules of $GF (2)$ dictate the structure of the affine and projective spaces represented by the bricks

• Binary Addition (XOR): The line diagrams used to formalize the

4 \times 4

patterns (related to the bricks) can be "added" via component-wise binary addition (XOR)

. The closure property of lines in $PG (3, 2)$ is represented algebraically by the fact that the three line diagrams corresponding to a pattern always sum to zero ( $D 1 \oplus D 2 \oplus D 3 = 0$ )

• Group Theory and Symmetry: The massive permutation group

G

(of order 322,560) that transforms the visual patterns is isomorphic to the affine group

AGL (4, 2)

. This group, which explains the pervasive symmetry found in all $G$ -images, is the automorphism group of the underlying finite geometry, establishing the algebraic control over the system's geometric and combinatorial properties

• Ring Theory: The

4 \times 4

patterns can be endowed with algebraic structure to generate an ideal within a ring of symmetric patterns, leading to an infinite family of "diamond rings" isomorphic to rings of matrices over

GF (4)

. This links the geometry to the machinery of abstract algebra

• M24 Connection: The affine group

AGL (4, 2)

is identified as the octad stabilizer subgroup of the Mathieu group

M_{24}

, 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 Brick Space model, therefore, functions as a visual tapestry where graphic arrangements (geometry/visualization) encode set partitions (combinatorics) that behave according to the rules of binary algebra (

GF (2)

and affine groups)

. The entire structure is unified by powerful isomorphisms relating these three mathematical domains through finite geometries like $PG (3, 2)$ and $PG (5, 2)$

Comments (0)

Friday, December 12, 2025

NotebookLM Today

Filed under: General — Tags: Color Fields, Cullinane AI — m759 @ 11:39 am

Related reading for Smart Buoy —

Comments Off

Sunday, December 7, 2025

Not So ABC* . . .

Filed under: General — Tags: Cullinane AI, Toying — m759 @ 7:14 pm

* See previous post.

Comments Off

Saturday, December 6, 2025

For Blue Two* — “A Dictionary Between”

Filed under: General — Tags: Cullinane AI — m759 @ 12:03 pm

* Compare and contrast . . . the previous post's title.

Comments Off

Friday, December 5, 2025

Today’s “Diamond Theory” NotebookLM Summary

Filed under: General — Tags: Cullinane AI, NotebookLM Summaries — m759 @ 12:17 pm

Diamond Theory by NotebookLM

92 sources

The collected sources discuss the intricate confluence of finite geometry and abstract combinatorics, focusing heavily on the smallest three-dimensional projective space, PG(3,2), which acts as the geometric model for structures derived from the 6-set and 8-set. A primary focus is the Cullinane Diamond Theorem and the visual representation of abstract symmetries using 4×4 arrays, whose enormous automorphism group, the Affine group AGL(4,2), relates combinatorial design to geometric transformations. These connections are formalized using the Miracle Octad Generator (MOG) and the Klein Correspondence, which map partitions of an 8-set onto geometric objects like the lines of PG(3,2) and the points of the Klein quadric in PG(5,2). Furthermore, this framework bridges pure mathematics to applied fields, establishing relationships between geometric concepts like Conwell's Heptads and spreads (line partitions) and applications in algebraic ring theory, error-correcting codes, and the study of the sporadic simple group M24. Ultimately, the sources highlight how the symmetry inherent in these designs offers essential geometric insight into complex algebraic and combinatorial problems.

Comments Off

Thursday, December 4, 2025

Today’s NotebookLM “Diamond Theory” Summary

Filed under: General — Tags: Cullinane AI, NotebookLM Summaries — m759 @ 8:13 am

Diamond Theory by NotebookLM

92 sources

The documents provide a comprehensive overview of advanced abstract algebra and combinatorics, centered on the finite projective space PG(3,2), which models the geometry of the 6-set. A primary focus is the Diamond Theorem, which uses the symmetries of 4×4 array patterns to establish deep connections between the visual arts, group theory, and geometry. The vast transformation set known as the Affine Group AGL(4,2), possessing an order of 322,560, is shown to preserve the structural relations of these arrays, which in turn are linked to the properties of lines and planes in PG(3,2). These geometric and combinatorial linkages are essential for understanding the Miracle Octad Generator (MOG) of R. T. Curtis and its relationship to the sporadic simple group Mathieu group M24. Additionally, the sources examine complex geometric partitions, such as Conwell’s Heptads and isotropic spreads within spaces like PG(5,2), demonstrating how group actions classify these objects and relate to applications in error-correcting codes. Ultimately, this body of work illustrates a powerful mathematical unity, presenting geometry, algebra, and combinatorics as tightly interwoven disciplines.

Comments Off

Wednesday, December 3, 2025

Today’s Diamond Theory Summary from NotebookLM

Filed under: General — Tags: Cullinane AI, NotebookLM Summaries — m759 @ 9:42 am

Diamond Theory by NotebookLM

92 sources

The sources detail the profound mathematical correspondences linking visual, combinatorial, and abstract algebraic structures, primarily focusing on the finite projective space PG(3,2) and the affine group AGL(4,2). A central component is the Cullinane diamond theorem, which uses highly symmetric 4×4 grid patterns to model the AGL(4,2) transformation group, whose large order of 322,560 governs the symmetry of the arrangements. These geometric models are tied directly to deep combinatorial structures, specifically the Miracle Octad Generator (MOG) and the sporadic simple group Mathieu group M24, offering a unified framework for understanding octads and partitions like Conwell's Heptads. Further discussion establishes how geometric entities such as spreads, packings, and the Klein correspondence provide solutions for classic problems like the "schoolgirl problem" and inform contemporary areas like error-correcting codes and the classification of group orbits. This interplay extends even to physics, connecting the geometries to quantum space-time and two-qubit observables, demonstrating how abstract finite geometry underlies sophisticated concepts across various scientific and artistic disciplines.

Comments Off

Tuesday, December 2, 2025

Today’s NotebookLM “Diamond Theory” Summary

Filed under: General — Tags: Cullinane AI, NotebookLM Summaries — m759 @ 10:07 am

Diamond Theory by NotebookLM

92 sources

This collection of texts examines the profound mathematical unity connecting finite geometry, group theory, and visual combinatorics, centered largely on the projective space PG(3,2) and the associated Affine Group AGL(4,2). The geometry is often modeled using structures like the 4×4 array or "Brick Space," where the action of the group AGL(4,2) (order 322,560) explains the symmetries of abstract diamond patterns. Central to this framework are classical structures like Conwell's Heptads and the Klein Quadric, which are shown to be crucial in partitioning spaces like PG(5,2) and constructing spreads used in coding theory. The material extensively links these geometric models, including the Miracle Octad Generator (MOG), to the exceptional symmetries of the Mathieu group M24 through stabilizer subgroups. Furthermore, these abstract concepts find applications in diverse fields, providing geometric insights into Mutually Orthogonal Latin Squares (MOLS), algebraic ring structures, and analogies within quantum physics related to qubit observables. The overarching theme demonstrates how symmetry, whether in abstract geometric configurations or visual quilt designs, is rooted in the deep logic of finite algebraic structure.

Comments Off

Monday, December 1, 2025

“Diamond Theory” at NotebookLM Today

Filed under: General — Tags: Cullinane AI, NotebookLM Summaries — m759 @ 8:29 am

NotebookLM — Dec. 1, 2025 — "A Unifying Framework"

Diamond Theory by NotebookLM

92 sources

These documents comprehensively examine the tight relationships among abstract algebra, combinatorics, and finite geometry, primarily through the lens of the projective spaces PG(3,2) and PG(5,2). A central focus is the Cullinane Diamond Theory, which utilizes highly symmetric 4×4 arrays over the Galois field GF(2) to model affine space, whose transformation group is the extensive Affine Group AGL(4,2). This visual and geometric structure connects directly to classic combinatorial objects, such as Conwell's Heptads and Dye's Partitions, which define specific sets and orbits within the geometry. Critically, these underlying symmetries are fundamental to the operation of the Miracle Octad Generator (MOG), establishing a direct link between the patterns of the 4×4 arrays and the intricate structure of the sporadic simple Mathieu group M24. The established correspondence provides crucial geometric interpretations for abstract algebraic problems, including the classification of reguli and the construction of Mutually Orthogonal Latin Squares. Collectively, the material demonstrates a unifying mathematical framework that spans theoretical geometry, error-correcting codes, quantum information science, and visual art.

Comments Off

Friday, November 28, 2025

“Crucially”

Filed under: General — Tags: Cullinane AI — m759 @ 10:20 am

From the NotebookLM notebook "Diamond Theory" today —

"Crucially, the underlying geometric symmetry
ties directly into the functionality of the
Miracle Octad Generator (MOG),
which models the highly exceptional properties of
the sporadic simple group M24."

The above geometric symmetry is based on properties of
the unique even prime number 2. For an introduction to
symmetry propeties of odd primes, see the previous post.

"If it's a seamless whole you want, pray to Apollo."

— M argaret Atwood on tricksters.

Comments Off

Thursday, November 20, 2025

On Brick Space

Filed under: General — Tags: Brick Space, Cullinane AI — m759 @ 6:24 pm

A question suggested by NotebookLM in the "Diamond Theory" notebook,
and its answer today by NotebookLM —

How are algebraic, combinatorial, and geometric structures unified within the Brick Space model?

The term "Brick Space" originates from the

2 \times 4

arrays, or "bricks," coined by R. T. Curtis as component parts of his Miracle Octad Generator (MOG)

. These physical or graphic arrangements serve as a concrete visualization (or model) of highly abstract mathematical structures

1. Geometric Unification

The Brick Space model provides a geometric foundation for combinatorial objects through direct visualization of finite geometries defined over the two-element field, GF(2)

• Modeling Projective Space: The Brick Space model is the natural geometric setting for the MOG's components, which may be regarded as forming both the 5-dimensional projective space

PG (5, 2)

and the 3-dimensional projective space

PG (3, 2)

• Visualizing PG(5,2) and the Klein Quadric: The model visually represents the

PG (5, 2)

space, which has 63 points, by partitioning these points into 28 points lying off the Klein quadric and 35 points lying on the Klein quadric

. The geometry of $PG (5, 2)$ is linked to the concept of the 8-set

• The Klein Correspondence: The geometric relationship between

PG (3, 2)

and

PG (5, 2)

is formalized by the Klein correspondence

. The $PG (5, 2)$ model, developed as a brick space, is analogous to the "line diagrams" construction of $PG (3, 2)$ found in the Cullinane diamond theorem

• Lines and Points: The Brick Space implicitly models how the 35 lines of

PG (3, 2)

correspond to the 35 points on the Klein quadric in

PG (5, 2)

2. Combinatorial Unification

Combinatorial structures, primarily partitions of sets and block designs, are mapped directly onto geometric entities within the Brick Space framework

• Partitions and Lines: The central combinatorial equivalence involves mapping partitions of sets to geometric objects

• Partitions of the 8-Set: The

PG (3, 2)

lines correspond to the 35 partitions of an 8-set into two 4-sets

. 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

PG (3, 2)

. This provides a geometric dictionary for abstract algebraic combinatorics

3. Algebraic Unification

Algebraic structures, rooted in finite field theory and group theory, govern the behavior and symmetries observed in the combinatorial and geometric models

• Binary Field

GF (2)

: The foundation of the geometry is the Galois field of two elements,

GF (2)

(binary arithmetic:

1 + 1 = 0

)

. The algebraic rules of $GF (2)$ dictate the structure of the affine and projective spaces represented by the bricks

• Binary Addition (XOR): The line diagrams used to formalize the

4 \times 4

patterns (related to the bricks) can be "added" via component-wise binary addition (XOR)

. The closure property of lines in $PG (3, 2)$ is represented algebraically by the fact that the three line diagrams corresponding to a pattern always sum to zero ( $D 1 \oplus D 2 \oplus D 3 = 0$ )

• Group Theory and Symmetry: The massive permutation group

G

(of order 322,560) that transforms the visual patterns is isomorphic to the affine group

AGL (4, 2)

• Ring Theory: The

4 \times 4

patterns can be endowed with algebraic structure to generate an ideal within a ring of symmetric patterns, leading to an infinite family of "diamond rings" isomorphic to rings of matrices over

GF (4)

. This links the geometry to the machinery of abstract algebra

• M24 Connection: The affine group

AGL (4, 2)

is identified as the octad stabilizer subgroup of the Mathieu group

M_{24}

, 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)

GF (2)

and affine groups)

. The entire structure is unified by powerful isomorphisms relating these three mathematical domains through finite geometries like $PG (3, 2)$ and $PG (5, 2)$ .

Comments Off

Monday, November 3, 2025

The Monolith Mystery

Filed under: General — Tags: 5x5.foundation, Brick Space, Cullinane AI, Monolith Mystery — m759 @ 1:25 pm

Transcript of NotebookLM video
"The Mystery of Brick Space" —

Okay, so our first clue
0:35
comes from the movies. You've got
0:37
Stanley Kubrick's masterpiece, 2001: A
0:39
Space Odyssey. And this … this bizarre
0:42
black monolith just shows up. It's this
0:45
object of perfect almost unsettling
0:47
geometry that always signals some huge
0:50
leap in evolution. And what's really
0:52
wild is that while Kubrick was filming
0:53
this, minimalist artists like John
0:55
McCracken were creating nearly identical
0:57
sculptures totally independently of the
1:00
film.

Scholium

Related material —

From a post for the opening of Cullinane College
on January 29, 2003:

"Young man sings 'Dry Bones'"

Illustrations:

See as well "Monolith" in this journal.

Bullshit fans may also enjoy "the monolith to El"
in James Michener's archaeology epic The Source :

Levels of Tell Makor, from Michener's 'The Source'

Comments Off

Sunday, November 2, 2025

The Mystery of Brick Space . . .

Filed under: General — Tags: Brick Space, Cullinane AI — m759 @ 11:42 pm

. . . is the title of a NotebookLM video now on YouTube —

See https://youtu.be/6zUKg4dNEbM .

The current NotebookLM summary for the Diamond Theory notebook, the source of the above video —

"These sources comprehensively explore the deep connections between finite geometry, particularly the projective spaces PG(3,2) and PG(5,2) over GF(2), and various topics in combinatorics, group theory, and coding theory. Central to this discussion are the Miracle Octad Generator (MOG) and the Cullinane Diamond Theorem, which model highly symmetric structures like the affine group AGL(4,2) and the sporadic Mathieu group M24 using geometric figures such as 4×4 arrays or 'brick space.' The geometry of PG(3,2), described as the 'smallest perfect universe,' is shown to be crucial, relating to concepts like Conwell's Heptads, Klein correspondence, spreads, and mutually orthogonal Latin squares (MOLS), which also have applications in error-correcting codes and quantum information theory involving n-qubits. Ultimately, these texts demonstrate how abstract mathematical symmetry is intrinsically linked across algebra, geometry, and visual art, often leveraging automorphism groups to reveal structural invariants."

Comments Off

Saturday, November 1, 2025

Brick Space Update

Filed under: General — Tags: Brick Space, Cullinane AI, Junction Stone — m759 @ 1:22 pm

Last night at the museum . . .

Today . . . The Mystery of Brick Space

Comments Off

Sunday, October 26, 2025

Minority Opinion:
The Geometry of Logic Is Galois Geometry

Filed under: General — Tags: Boole vs. Galois, Cullinane AI, The Righteous Gemstone — m759 @ 11:02 pm

See The Righteous Gemstone and Boole vs. Galois.

Update of 9:48 AM EDT Oct. 28 . . .

Related material —

Markdown version uploaded Oct. 28, 2025, to NotebookLM.

Comments Off

Friday, October 3, 2025

A Unifying Framework

Filed under: General — Tags: Cullinane AI, Fano Labelings, Matroids, The Fano Hallows, The Omega Portal — m759 @ 1:15 am

Finite Geometry: A Unifying Framework
for Art and Mathematics

"In essence, finite geometry, exemplified by the Cullinane diamond theorem, acts as a 'portal' that unveils profound mathematical structures underlying seemingly simple patterns, demonstrating the interconnectedness of geometry, algebra, combinatorics, and visual art, with significant implications for fields ranging from error-correcting codes to experimental design and signal processing."

— NotebookLM AI on 18 September 2025

See as well a dies natalis on 18 September 2025 —

Comments Off

Saturday, September 20, 2025

Origin

Filed under: General — Tags: Art News, Cullinane AI — m759 @ 3:17 am

From the artificial intelligence at NotebookLM on Sept. 18, 2025 —

"Bridging Visual Art and Combinatorics
with Finite Projective Geometry

The Cullinane diamond theorem is a prime example,
originating from observations of symmetries in
traditional quilt designs and graphic art."

This is false.

The patterns in the diamond theorem originated from observing
superimposed 4×4 arrays of half-circles.

Vide http://finitegeometry.org/sc/16/overlay.html.

Comments Off

Friday, September 19, 2025

For the Boys of Summerfield

Filed under: General — Tags: Art News, Cullinane AI, Waymark Prize — m759 @ 12:59 am

http://m759.net/wordpress/?s="Gideon+Summerfield"

"This mathematical framework links seemingly simple designs,
like quilt patterns, to complex concepts such as the Mathieu group M₂₄,
the Miracle Octad Generator (MOG), and error-correcting codes."

— NotebookLM AI yesterday, September 18, 2025

Comments Off

Thursday, September 18, 2025

“In other art news . . .”

Filed under: General — Tags: Art News, Cullinane AI — m759 @ 5:40 pm

Art from 1976 —

Art from 2025 —

A mathematician, like a painter or a poet, is a maker of patterns.
If his patterns are more permanent than theirs, it is because
they are made with ideas.

— G. H. Hardy, A Mathematician's Apology (1940).

In other art news . . .

Comments Off

Contrapuntal Structure in Latin Squares

Filed under: General — Tags: Art News, Cullinane AI — m759 @ 4:24 pm

Images from https://shc7596.wixsite.com/website —

This post has been uploaded as a PDF to the NotebookLM
public notebook "Diamond Theory."

A copy of the PDF is at
http://log24.com/log25/250918-Contrapuntal_Structure_
in_Latin_Squares-from-Log24.pdf.

Comments Off

Wednesday, September 17, 2025

Prime-Power Space

Filed under: General — Tags: Cullinane AI, Fields, Galois.space — m759 @ 8:49 am

The number of subsquares in each large square
below is a prime power. Therefore each large square
is a Galois space.

Related material at NotebookLM —

Diamond Theory

and a copy at Log24.com —

http://log24.com/log25/
250917-'Diamond_Theory-NotebookLM'-notebooklm.google.com.pdf

Comments Off

Monday, August 4, 2025

Tesseract Art

Filed under: General — Tags: Congruent Subarrays, Cullinane AI, Multiplane Structure — m759 @ 11:45 am

Some background for the NotebookLM video "Tiles to Deep Space" —

See posts tagged Quantum Tesseract Theorem, Multiplane Structure,
and March 26-29, 2006.

(The diamond theorem on a 4×4 square array involves arbitrary
permutations of rows, columns, and quadrants. These structures
correspond to sets of four parallel hypercube faces, and other such
sets, though less easily pictured, might be used instead.)

Comments Off

Friday, August 1, 2025

“Tiles to Deep Space” — A NotebookLM video

Filed under: General — Tags: Cullinane AI — m759 @ 5:23 pm

See log24.com/log25/Tiles_to_Deep_Space__Cullinane_Diamond_Theorem.mp4.

Comments Off

Monday, June 9, 2025

Circle as Diamond: Ikonologie des Zwischenraums*

Filed under: General — Tags: Cullinane AI, Language Game — m759 @ 10:52 pm

* A Cornell phrase from Sunday evening's post "The Press Pool."

Comments Off

Audio for the Diamond Theorem

Filed under: General — Tags: Cullinane AI, Language Game — m759 @ 9:44 pm

https://notebooklm.google.com/notebook/
62ad8daa-277e-4fea-a680-9b209883f232?authuser=1

Use the "Audio Overview" button.

Comments Off

Tuesday, June 3, 2025

Notebook LM: Diamond Theory

Filed under: General — Tags: Cullinane AI, HOLLIS — m759 @ 4:13 am

https://notebooklm.google.com/notebook/
62ad8daa-277e-4fea-a680-9b209883f232?authuser=1

The notebook is about mathematics from a 1976 document —

Comments Off

Saturday, February 17, 2024

Now at Substack

Filed under: General — Tags: Cullinane AI, February Poetics — m759 @ 3:20 pm

https://open.substack.com/pub/
stevenhcullinane/p/diamond-theorem-a-sonnet.

Comments Off

Friday, February 16, 2024

The Sixteen

Filed under: General — Tags: Cullinane AI, February Poetics, Hidden Structure — m759 @ 7:56 pm

Gemini Sonnet, Feb. 15, 2024

Prompt:

Write a poem, in strict sonnet form, about the Cullinane diamond theorem.

Response (slightly tweaked for grammar):

Within a grid of sixteen squares reside
A diamond's gleams where symmetries do guide.
Though tiles may shift, a pattern shall remain,
By unseen lines of ordered form sustained.
Rows mix and columns twist in playful dance,
Quadrants align with geometric chance.
No matter how the elements may turn,
A hidden balance always will return.

Where Latin squares in secret do align,
And finite fields their subtle powers combine,
An ideal forms, with brilliance all its own,
A ring of light where hidden truths are shown.
Though chaos swirls, an order does descend,
The Cullinane's bright theorem will transcend.

________________________________________________________________

As for "a hidden balance" … See Oct. 10, 2022.

Comments Off

Thursday, February 15, 2024

Gemini Poem

Filed under: General — Tags: Abyssus Abyssum Invocat, Cullinane AI, February Poetics, Gemini.reviews, The Wilde Abyss, Tools — m759 @ 3:58 pm

Or using his research and their tools.

Compare and contrast —

Before thir eyes in sudden view appear
The secrets of the hoarie deep, a dark
Illimitable Ocean without bound,
Without dimension, where length, breadth, and highth,
And time and place are lost; where eldest Night
And Chaos, Ancestors of Nature, hold
Eternal Anarchie, amidst the noise
Of endless warrs and by confusion stand.
For hot, cold, moist, and dry, four Champions fierce
Strive here for Maistrie, and to Battel bring amidst the noise
Thir embryon Atoms....
                                ... Into this wilde Abyss,
The Womb of nature and perhaps her Grave,
Of neither Sea, nor Shore, nor Air, nor Fire,
But all these in thir pregnant causes mixt
Confus'dly, and which thus must ever fight,
Unless th' Almighty Maker them ordain
His dark materials to create more Worlds,
Into this wilde Abyss the warie fiend
Stood on the brink of Hell and look'd a while,
Pondering his Voyage....

-- John Milton, Paradise Lost , Book II

Comments Off

Monday, May 31, 2004

Monday May 31, 2004

Filed under: General — Tags: Cullinane AI — m759 @ 7:00 pm

Language Games:

Now You're Playing
with Power

My latest preoccupation…

Using search-and-replace programs to reformat earlier Xanga entries. This involves the use of "regular expressions," which lead to the following thoughts….

It seems that pure mathematics (i.e., the theory of finite automata) is not without relevance even in very practical data formatting problems. One of the first math books I ever bought — perhaps the very first —was Automata Studies (Princeton's Annals of Mathematics Studies, No. 34, 1956). This book, which I still have, begins with an essay by Stephen Cole Kleene.

Kleene's legacy includes regular expressions and Kleene's theorem. For further details, see

Notes on

Formal Language Theory

and Parsing

James Power

Department of Computer Science
NATIONAL UNIVERSITY OF IRELAND, MAYNOOTH
Maynooth, Co. Kildare, Ireland.

Click on picture
for details.

Here's more on
language games and robot wisdom
from an authority on James Joyce,

Comments (1)

Wednesday, January 14, 2026

Diamond Theory by NotebookLM

Friday, December 12, 2025

Sunday, December 7, 2025

Saturday, December 6, 2025

Friday, December 5, 2025

Thursday, December 4, 2025

Wednesday, December 3, 2025

Tuesday, December 2, 2025

Monday, December 1, 2025

Friday, November 28, 2025

Thursday, November 20, 2025

Monday, November 3, 2025

Sunday, November 2, 2025

Saturday, November 1, 2025

Sunday, October 26, 2025

Friday, October 3, 2025

Saturday, September 20, 2025

Friday, September 19, 2025

Thursday, September 18, 2025

Wednesday, September 17, 2025

Monday, August 4, 2025

Friday, August 1, 2025

Monday, June 9, 2025

Tuesday, June 3, 2025

Saturday, February 17, 2024

Friday, February 16, 2024

Thursday, February 15, 2024

Monday, May 31, 2004

Diamond Theory
by NotebookLM