Log24

Tuesday, March 19, 2024

Art Grid News: Abra Meets Cadabra

Filed under: General — Tags: — m759 @ 6:00 am

The New York Times  reports a February 8 death —

Related fashion images —

Grid Geometry and Language Models: Grande et Petite

Filed under: General — Tags: — m759 @ 1:49 am

For more about grid geometry, see the previous post as well as
this journal 20 years ago.

Monday, March 18, 2024

Ekphrasis for Lily

Filed under: General — m759 @ 8:31 pm

Speech

Filed under: General — Tags: — m759 @ 7:33 pm

Before and After . . .

" David Seidler in 2011 after winning two British Academy Film Awards,
or BAFTAs, for his screenplay for 'The King’s Speech.' " —

A Chandelier for Sia

Filed under: General — Tags: — m759 @ 6:53 pm

"Whose barn, what barn, my barn" — Song lyric

Dialogue for Nolan

Filed under: General — m759 @ 6:23 pm

Dark Horse

Filed under: General — Tags: , — m759 @ 6:00 pm

See as well Macbeth and the Black Arts, and a report today
by The New York Times  of a death on February 7th.

At the Gate

Filed under: General — Tags: — m759 @ 5:00 pm
 

" 'The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness' (C, 15:170 [2: 315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind’s momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable)."

C   Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61)

This is from page 157 of . . .

Flight from Eden: The Origins of
Modern Literary Criticism and Theory
,
by Steven Cassedy, U. of California Press, 1990.

"Time for you to see the field." — Bagger Vance.

Sunday, March 17, 2024

Max Bill Revisited

Filed under: General — m759 @ 1:59 pm

I noticed today that the April 2024 issue of the AMS Notices
is now online.  Its cover features art by Max Bill (uncredited
on the cover, though not inside).  Bill appeared here  last week:

For some background, see a webpage at artsandculture.google.com.

The Livingstone Dies Natalis

Filed under: General — Tags: — m759 @ 4:53 am

The above Livingstone obituary is dated January 29, 2024.
See as well that date in this  journal, and some remarks
by Bernd Witte on Walter Benjamin, science, language, and religion.

Saturday, March 16, 2024

For Harlan Kane: The Benjamin Interrogation

Filed under: General — Tags: — m759 @ 10:20 pm

" if the system were complete, it would turn out to have been
interrogated during the investigation of one problem or another."

Vide . . .

(Illustration updated at 6:32 AM ET Mon., March 18, 2024.)

See also the post "Fundamental Figurate Geometry"
in this  journal on Monday, March 11, 2024.

Saturday Evening Word

Filed under: General — m759 @ 8:51 pm

The word "creamy" in this journal suggests a look at . . .

Tools

Filed under: General — m759 @ 8:07 pm

Immanentizing the Eschaton: The Source

Filed under: General — m759 @ 6:56 pm

See also "Circle in the Square" and Fulcrum.


The above is from a post, "Immanentizing the Eschaton," in this
journal on March 6, 2024.  For the significance of that date to
San Juan Capistrano , see a New York Times  obituary online today.

See as well the source of the above remarks by Walter Benjamin.

For Jena’s Word Farm …

Filed under: General — Tags: , — m759 @ 9:48 am

See other posts now tagged Word Farm and  Whanganui.

And for Whanganui's Cullinane College, an "OED" that
does not  mean "Oxford English Dictionary" . . .

“Great Caesar’s Ghost!” — Cartoon Religious Exclamation

Filed under: General — Tags: , — m759 @ 12:30 am

From Theodore Sturgeon's story "What Dead Men Tell. . .

Update of 1:09 AM ET Saturday, March 16, 2024

(Source: a Substack email received at 12:37 AM ET) —

Friday, March 15, 2024

Corrections to Post from Monday, March 11

Filed under: General — Tags: — m759 @ 2:56 pm

The post, on triangles and figurate geometry, has had some
minor image corrections, and these corrections have now
also been made in a new Zenodo version.

(Some aesthetic background:  In the words of Alan D. Perlis,
that post concerns "a conception that embodies action and
the passing of time in the rigid and timeless structure of an
art form.")

Thursday, March 14, 2024

South Dakota Review:  Perlis on Faulkner

Filed under: General — Tags: — m759 @ 8:36 pm

"Alan Perlis also addresses the artist’s freezing of
time as he looks at As I Lay Dying He sees Darl as
an artist-figure who catches “action in the tension
of stopped-time” (104). Both critics link Faulkner to
John Keats, whose poetry often seeks immortality,
like that of an object such as a Grecian urn or an
Ozymandian monument. Perlis sums this up, saying
that Faulkner 'is an idealist in the manner of a Keats
or a Wallace Stevens, who ponder the paradoxical
nature of a conception that embodies action and the
passing of time in the rigid and timeless structure of
an art form.' "

The work cited:

Perlis, Alan D. “As I Lay Dying  as a Study of Time.”
South Dakota Review  10.1 (1972): 103-10

The source of the citation:

I SEE, HE SAYS, PERHAPS, ON TIME:
VISION, VOICE, HYPOTHETICAL NARRATION,
AND TEMPORALITY IN WILLIAM FAULKNER’S FICTION

*****
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
The Degree Doctor of Philosophy in
the Graduate School of The Ohio State University
By David S. FitzSimmons, B.A., M.A.

*****
The Ohio State University, 2003.


A search in this  journal for Dakota yields the author Kathleen Norris.
See, for instance . . .

https://www.americamagazine.org/content/dispatches/
writing-death-and-monastic-wisdom-conversation-kathleen-norris
.

For Aestheticians:  Seeds, Good and Not So Good

Filed under: General — Tags: , , , — m759 @ 7:08 pm

In memory of . . .

Good Seed:  Sydell.

Not So Good:  Pearl.

This post was suggested by Sam Levinson's work in Whanganui NZ
and Alan D. Perlis's work in Birmingham AL

From South Dakota, related material for Bible fans —

TIME Date: 1984/09/16

Filed under: General — m759 @ 8:28 am

SPACE Date: 1984/09/15.

Indiana Jones and The Fulcrum of Destiny

Filed under: General — Tags: , , — m759 @ 1:38 am

An image suggested by the posts Fulcrum (Feb. 19, 2024)
and "Fundamental Figurate Geometry" (March 11, 2024) —

Wednesday, March 13, 2024

“Time flies like an arrow….” — Attributed to Anthony Oettinger

Filed under: General — m759 @ 11:49 pm

Related reading — http://m759.net/wordpress/?s="Arrow+in+the+Blue" .

For Harlan Kane, a post from this journal on July 26, 2022 —
the date of Oettinger's reported death:

Related reading: a death on Oscars weekend . . .

Agent Training

Filed under: General — Tags: — m759 @ 3:21 pm

Max Bill in the Basque Country:
¿Qué vemos cuando miramos?

Filed under: General — Tags: , — m759 @ 12:15 pm

A Sam Levinson Special — Wednesday in Whanganui:
Nevermore Academy Meets Cullinane College

Filed under: General — Tags: , — m759 @ 3:27 am

Tuesday, March 12, 2024

The X Version

Filed under: General — Tags: , , , — m759 @ 4:28 pm

Tools Dream

Filed under: General — Tags: , — m759 @ 2:50 pm

The above meditation was adapted from . . .

“Wilde Abyss”

Filed under: General — Tags: , — m759 @ 1:50 pm

“And Moss Grows…” — American Pie

Filed under: General — Tags: — m759 @ 4:40 am

"So we beat on…"

Monday, March 11, 2024

“For Ten Years* We’ve Been on Our Own…” — American Pie

Filed under: General — Tags: , , — m759 @ 4:53 pm

* See as well today's previous post.

Fundamental Figurate Geometry: Triangle Subdivision

Filed under: General — Tags: , , — m759 @ 5:41 am

Click to enlarge.

See as well "Triangles are Square," at
http://finitegeometry.org/sc/16/trisquare.html.

(I happened to find the Basu-Owen paper tonight
via a Google image search for "congruent subsets" . . .
as opposed to the "congruent subarrays" of
the previous post.)

Update of 3:54 PM ET Monday, March 11, 2024 —

This Stanford version of my square-to-triangle mapping
is the first publication in a new Zenodo community —

Citation for the research note:
Cullinane, Steven H. (2024). Fundamental Figurate Geometry:
Triangle Subdivision (Version 2). Zenodo.
https://doi.org/10.5281/zenodo.10822848
(latest version as of March 15, 2024)
 

Sunday, March 10, 2024

Permutations of Congruent Subarrays

The groups generated as above are affine groups in finite geometries.

What other results are known from this area of research,
which might be called "groups generated by permutations of
congruent subarrays"? (Search phrase: "congruent subarrays")

Saturday, March 9, 2024

For Auld Hensyne

Filed under: General — Tags: — m759 @ 9:15 pm

Finnegans Wake  —

"The quad gospellers may own the targum
but any of the Zingari shoolerim may pick a peck
of kindlings yet from the sack of auld hensyne."

Eliot’s Octopus

Filed under: General — Tags: , — m759 @ 8:04 pm

Contrast the following page from Daniel Albright in 1997
with the previous post's remarks by Sarah Kennedy in 2018.

Related reading:  The Log24 post "Real Beyond Artifice," with a
"Seventh Seal" image from the date of Albright's death.

Annals of Deceptive Fiction —
Dark Materials: Milton, Eliot, Pullman

Filed under: General — Tags: , , — m759 @ 12:45 pm

For Pullman, see previous instances of "wilde abyss" in this journal.

For a less fictional approach to the abyss, see the following.

From T. S. Eliot and the Dynamic Imagination
by Sarah Kennedy,
Cambridge University Press, 2018 —

Chapter 7
His Dark Materials

Would you have me
False to my nature? Rather say, I play
The Man I am.

Shakespeare, Coriolanus, III.ii. [Link added.]

. . . .

Eliot describes the creative germ as the
‘unknown, dark psychic material . . .
with which the poet struggles’.

The phrase echoes Milton’s Paradise Lost :

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 their pregnant causes mixt
Confus’dly, and which thus must ever fight,
Unless th’ Almighty Maker them ordain
His dark materials to create more Worlds . . .

Eliot’s creative logic retains an aspect of the divine
poet-as-maker, but the effect is not hubristic.
Where Milton’s Almighty may ordain, Eliot’s poet
can only struggle against something unknown.
Yet even in the image of struggle, reminiscent of
Jacob’s struggle with the obscured figure who
appears in the darkness and departs at dawn,
there is a sense of the poet as more than human,
both blessed and maimed by the confrontation.
Like Milton, Eliot locates the struggle in a ‘wilde abyss’:
he once described human consciousness
(following The Tempest ) as extending into a
‘dark . . . backward and abysm of time’. Importantly,
this space is not an aspect of the world as constructed
by a presiding intention (as in Paradise Lost ), but exists
within the poet.
. . . .

"The phrase echoes Milton's Paradise Lost" —

In describing his  abyss, Milton invokes not "psychic material" but
rather the classical view of Nature as composed of the four elements
Water, Earth, Air and Fire.

Note that one source* of the "psychic material" phrase in Eliot's work
gives a rather different picture . . .

"And now I should like to return for a moment to Gottfried Benn
and his unknown, dark psychic material —
we might say, the octopus or angel with which the poet struggles."

* "The Three Voices of Poetry," by T. S. Eliot, The Atlantic, April 1954.

Related entertainment . . .

Annals of Deceptive Fiction

Filed under: General — Tags: , — m759 @ 3:10 am

The remarks of Charles Taylor in the previous post, and
the date — Nov. 4, 2020 — of an article by legal scholar
Chloë Kennedy on deceptive sex  that referenced Taylor's
work suggest a look back at a Nov. 4, 2020, post on deceptive
fiction fiction about the politics of gender, not of sex —

Taylor: “The Politics of Recognition”

Filed under: General — m759 @ 2:19 am

I found the above essay via the references cited in . . .

https://www.cambridge.org/core/journals/legal-studies/article/abs/
criminalising-deceptive-sex-sex-identity-and-recognition/
7A5589286B535E30B88A9765A5844CFC
.

Friday, March 8, 2024

Character Design

Filed under: General — m759 @ 1:37 pm

Hill-Walking

Filed under: General — Tags: , — m759 @ 1:11 pm

The Seven-Year Glitch

Filed under: General — Tags: , — m759 @ 12:40 pm

From a post of March 8, 2017 —

This is from posts tagged Glitch.

"There's plenty of dives
to be someone you're not. . . ."

— Rosanne Cash, Seven-Year Ache

"Dr Kennedy’s project, entitled ‘Identity Deception: A Critical History’,
asks when, if ever, it is appropriate to punish a person who engages
in identity deception (pretending to be someone they are not)."

Edinburgh Law School, "Wed 14 August 2019"

Decepticon Law School:  C. is for Chloë

Filed under: General — Tags: , , — m759 @ 1:24 am

Also on the above "Double Veil" date, 14 August 2019

Summary for International Women's Day

"Why can't a woman be more like a man?"

— Professor Henry Higgins

Thursday, March 7, 2024

Taking Center Stage

Filed under: General — m759 @ 3:53 pm

State of the Intersection

Filed under: General — Tags: , , — m759 @ 1:12 pm

T. S. Eliot on the intersection of the timeless with time

See as well a post from this  journal on 26 Oct. 2017
and other posts now tagged Nowhere Legitimated.

Wednesday, March 6, 2024

One of a Kind Function: The Utrecht Strahlenkreis*

Filed under: General — Tags: — m759 @ 11:48 pm

The phrase "one of a kind malfunction" from the previous post
suggested the title of this  post.

For what that title might mean, see remarks on the concept
"beauty bare" in posts tagged The Utrecht Models.

An illustration from those posts —

*

* Ray-circle. See an image search.

In Memory of an AutoCAD Cofounder

Filed under: General — Tags: — m759 @ 3:54 pm

One of a Kind Malfunction

Old News Revisited

Filed under: General — Tags: — m759 @ 3:00 pm

See as well this  journal on the above Yitoons date —

Boxing Day 2016.

“Show Me All  Your Sources”
— Adapted from Leo DiCaprio

Filed under: General — Tags: — m759 @ 6:59 am

Immanentizing the Eschaton:*  Circle and Square

Filed under: General — Tags: — m759 @ 12:58 am

Related literary remarks —

See also "Circle in the Square" and Fulcrum.

*For the title phrase, vide  Wikipedia.

Tuesday, March 5, 2024

Deep Snow at Donner Pass

Filed under: General — Tags: — m759 @ 11:38 pm

Some irrelevant Super Tuesday literary background
for spring songbirds

https://en.wikipedia.org/wiki/Coriolanus .

Related social media from New Year's Eve 2021 —
A 3×3 Instagram array, and a Reno parking lot.

“If It’s Tuesday…”

Filed under: General — m759 @ 4:14 pm

https://www.sadanduseless.com/adam-douglas-thompson/

NY Times Meditation:  Dimensions and Synergy

Filed under: General — Tags: — m759 @ 3:39 pm

"Her work gave a new dimension to the words 'holy land'
and to the synergy between heaven and earth."

"… the time of the songbird has come …."
     — Song of Songs

— Obituary by Sam Roberts in The New York Times,
     2:27 PM ET today

Related material for students of dimensions, synergy,
and "Where Madness Lies" —

Other Log24 posts tagged "The Button."

Metadata for Sam Levinson:  Turning 16

Filed under: General — Tags: , — m759 @ 2:27 pm

In the recent film "Stars at Noon," the protagonist said . . .

Perhaps she should also have investigated Hell's coordinates . . .

The above XYZ record label metadata refers to
August 23, 1958 … The day I turned sixteen.

The Button Source

Filed under: General — Tags: — m759 @ 2:00 pm

Continuing the Ojo de Dios  theme from recent Delving posts . . .

. . . and from posts now tagged Tepoztlan Dance . . .

New York Times  Fashion Note…

Filed under: General — Tags: , , , , — m759 @ 1:24 am

Requiem for a Poodle Skirt . . .

"… a New York native who died at her home in
Tepoztlán, Mexico, on Sunday [March 3, 2024*] at 101…."

Related material from this  journal:  Leary and . . .

*

#modellife

Filed under: General — Tags: , , — m759 @ 12:00 am

For another coincidence, see this  journal on the above #modellife date:

Related reading:

Monday, March 4, 2024

Crimson Top News:  Art Heart

Filed under: General — Tags: — m759 @ 4:27 pm

"It's pretty, but is it Art?" — Harvard Philosophy Department
graduate student quoting Kipling in Aeon,  February 2024

"Through my art, I aim to offer more than just visual delight;
I seek to share a piece of my heart…."

Marcela Nowak, August 2023

"I want you to come on, come on, come on, come on and take it,
Take another little piece of my heart now, baby"

Janis Joplin, August 1968

Report on the Diamond Theorem
by Google Gemini (Advanced)

Filed under: General — Tags: — m759 @ 3:26 pm
 

Diamond Theorem Report

by Google Gemini AI

Monday, March 4, 2024


Can you write an academic paper, with source citations, about the Cullinane  diamond theorem?

Absolutely! Here's an academic paper about the Cullinane diamond theorem. Please note that while I provide citations, in a fully formatted paper you'd need to adhere to your chosen academic style guide for proper formatting:

The Cullinane Diamond Theorem:
Exploring Symmetries in Graphic Design

Abstract

This paper examines the Cullinane diamond theorem, a principle in finite projective geometry that offers unexpected insights into the symmetries found in graphic designs. The theorem, initially formulated by Steven H. Cullinane, reveals that patterns built from simple geometric components, like diamonds or chevrons, possess inherent symmetry properties under specific transformation groups. We will discuss the mathematical foundations of the theorem, its relation to the Miracle Octad Generator, and its applications in design and the study of finite fields.

Introduction

Symmetry plays a vital role in art and design, contributing to a sense of balance, harmony, and aesthetic appeal. While often associated with classical forms, symmetry also manifests in surprising ways within seemingly simple graphic patterns. The Cullinane diamond theorem provides a mathematical framework to understand and predict these hidden symmetries.

Mathematical Background

    Finite Projective Geometries: The Cullinane diamond theorem has its roots in finite projective geometry. A finite projective geometry PG(n, q) consists of a finite set of points and lines, where each line contains q + 1 points, and any two distinct points lie on a unique line ([1]).

    Diamond Figure: Cullinane focuses on a specific pattern called the four-diamond figure (D). This figure is composed of 16 tiles arranged in a 4×4 array, where each tile is divided diagonally into two colors ([2]).

    Transformation Group: The group G of transformations is formed by all possible permutations of rows, columns, and 2×2 quadrants of the diamond figure, along with color interchanges. The size of this group is 322,560 ([2]).

The Cullinane Diamond Theorem

Theorem:
Any image produced by applying transformations from the group G to the original diamond figure (D) will possess some form of ordinary or color-interchange symmetry ([2]).

Proof:
Cullinane's proof employs a decomposition technique for functions into a finite field.  It demonstrates that the G-images of the diamond figure create an ideal within a ring of symmetric patterns. This ideal has 1024 patterns where any horizontal or vertical "cut" through the pattern remains uninterrupted ([2]).

Connections to the Miracle Octad Generator

The Cullinane diamond theorem shares a relationship with R.T. Curtis's Miracle Octad Generator (MOG). The MOG is a combinatorial structure within the study of sporadic simple groups with symmetry properties similar to those described by the theorem ([3]).

Applications

    Graphic Design: The theorem informs artistic compositions employing diamond and chevron-like shapes. Designers can leverage the inherent symmetries to generate visually pleasing and intricate patterns.

    Quilt Patterns: Many traditional quilt designs incorporate the geometries described by the theorem, leading to the emergence of symmetrical patterns, even when randomness might be involved in the selection of colors or tiles.

    Finite Fields: The Cullinane diamond theorem establishes an isomorphism between specific "diamond" rings and rings of matrices over GF(4), offering insights into the structure of finite fields ([2]).

Conclusion

The Cullinane diamond theorem elegantly connects abstract mathematics with the world of graphic design. It unveils latent symmetries embedded within basic geometric shapes, providing a tool for understanding and creating visually balanced patterns. The theorem's connections to finite fields and combinatorial structures highlight its significance in broader mathematical research.

Citations

[1] Weisstein, E. W. “Finite Projective Geometry.” From MathWorld–A Wolfram Web Resource. [invalid URL removed]

[2] Cullinane, S. H. "Cullinane Diamond Theorem." Encyclopedia of Mathematics. https://encyclopediaofmath.org/wiki/Cullinane_diamond_theorem

[3] Curtis, R. T. (1976). A New Combinatorial Approach to M₂₄. Mathematical Proceedings of the Cambridge Philosophical Society, 79(1), 25–42. doi:10.1017/S0305004100052075

Let me know if you'd like me to expand on any particular aspect or provide additional citations!


Sources [I.e., the source of the Curtis citation]

   1. www.hellenicaworld.com/Science/Mathematics/en/MathieuGroup.html


Gemini may display inaccurate info, including about people, so double-check it.

Sunday, March 3, 2024

Deep Blue Research: A Report by You.com AI

Filed under: General — Tags: — m759 @ 12:34 pm
 

Cullinane Diamond Theorem Research Report

by https://you.com/?chatMode=research on March 3, 2024

Overview of the Cullinane Diamond Theorem

The Cullinane Diamond Theorem is a mathematical concept developed by Steven H. Cullinane that explores the symmetrical properties of certain geometric patterns. It is particularly concerned with the structure of finite projective geometry as it relates to the 35 square patterns found in R. T. Curtis's Miracle Octad Generator (MOG).

The theorem asserts that every G-image of a diamond figure D possesses some form of ordinary or color-interchange symmetry.

Symmetry and Group Theory

The theorem is deeply rooted in group theory, with G being isomorphic to the affine group A on the linear 4-space over the finite field GF(2).

This group has a significant order of 322,560 and underlies the symmetry of both the diamond-theorem figures and the square patterns of the MOG . The 35 structures of the 840 G-images of D are isomorphic to the 35 lines in the 3-dimensional projective space over GF(2), which explains the symmetry of the line diagrams and the two-color patterns.

The Diamond Theorem in Various Dimensions

The diamond theorem can be applied to different cases, such as the 4×4, 2×2, and even 3-dimensional cubes like the 2x2x2 and 4x4x4 cubes.

The generalized statement of the theorem involves inscribing a white diamond in a black square and dividing it into four quadrants, each with a diagonal split into black and white halves.

Algebraic Implications

The theorem has algebraic implications, such as the ability to express every 4-coloring as a sum of three 2-colorings.

This algebraic formulation is useful for demonstrating that certain four-colored graphic images can form a ring under multiplication. There is also an infinite family of such 'diamond' rings, isomorphic to rings of matrices over GF(4).

Philosophical and Cultural Context

Steven H. Cullinane has also explored the philosophical implications of the diamond theorem, referring to it in the context of Plato's Meno dialogue and opposing it to the 'Story Theory of truth' as discussed by Richard J. Trudeau.

The theorem is seen as a correct statement of the relation between geometry and the physical universe.

Clarification on Cullinan Diamonds

It is important to note that the Cullinane Diamond Theorem is unrelated to the Cullinan diamond, which is a famous large gemstone discovered in South Africa and now part of the British Crown Jewels.

The Cullinan diamond has its own historical and cultural significance, with its various cut shapes and ownership history.

In summary, the Cullinane Diamond Theorem is a mathematical concept that reveals the symmetrical properties of certain geometric patterns, with applications in group theory and algebra. It also has philosophical implications, drawing connections to classical ideas about truth and geometry.

Instagram ad for You.com AI in research mode

"Show me ALL  your sources, babe."

— Line adapted from Leonardo DiCaprio

“Let Noon Be Fair” — Motley
“A Fair Thought” — Hamlet

Filed under: General — Tags: — m759 @ 12:00 pm

“You Say Aeon, I Say Aion…”

Filed under: General — Tags: — m759 @ 10:26 am

Aeon . . . Aion.

Saturday, March 2, 2024

Eden for Emma

Filed under: General — Tags: , — m759 @ 11:50 pm

… And for Aaron Webman:

Search this journal for "Eden Express."

Storyboard for Harvard Philosophy Department

Filed under: General — Tags: — m759 @ 4:03 pm

From a Feb. 26 Aeon  essay, "Folklore is Philosophy," by
Abigail Tulenko, "a PhD student in philosophy at Harvard University,
and a research assistant for the Anansi Story Project at Harvard’s
Culture, Cognition, and Coevolution Lab" —

"In his wry poem ‘The Conundrum of the Workshops’ (1890),
Rudyard Kipling describes Adam’s first sketch scratched
in the dirt of Eden with a stick:

… [It] was joy to his mighty heart,
Till the Devil whispered behind the leaves:
‘It’s pretty, but is it Art?’

And so we may ask: folklore may be inclusive, but is it philosophy?"

A related storyboard —

Song by Copilot: Prompt and Response*

Filed under: General — Tags: — m759 @ 2:09 pm

Prompt:  Compose a song about the Cullinane diamond theorem.

Response by Microsoft Copilot on Saturday afternoon,
March 2, 2024:

Sure, here’s a song inspired by the Cullinane diamond theorem:

(Verse 1)
In the realm where logic reigns and numbers intertwine,
Lies a theorem, diamond-bright, its facets all align.
Cullinane's the name it bears, a gem in math's grand crown,
In the grid of sixteen squares, its truths are written down.

(Chorus)
Oh, Cullinane, your diamond shines with symmetry so fine,
In the field of finite forms, your theorem does define.
A structure pure, a pattern clear, for all of us to see,
In the heart of mathematics, lies your geometry.

(Verse 2)
Rows and columns interplay in a dance so grand,
Quadrants align in perfect time, like notes in a band.
Through the chaos and the whirl, an order does descend,
In the world of abstract thought, your theorem is a friend.

(Chorus)
Oh, Cullinane, your diamond theorem, a beacon in the night,
Guiding us through complex realms, with its brilliant light.
In the vast expanse of knowledge, where truth and beauty blend,
Your theorem stands, a testament, a guide until the end.

(Outro)
So here's to you, Cullinane, and your diamond theorem's might,
In the endless quest for truth, you've brought us greater light.
In the language of the universe, where numbers never lie,
Your diamond theorem's shining bright, beneath the math's clear sky.

Added note from Copilot:

Please note that this is a creative interpretation and may not accurately reflect
the mathematical concepts of the Cullinane diamond theorem. 😊

Added note from Cullinane:

* The previous post may or may not display a prompt response  to a Zen koan.

One Hand Clapping… Voilà.

Filed under: General — Tags: — m759 @ 1:46 pm

Abstract Art*

Filed under: General — Tags: — m759 @ 1:39 am

* And art that is somewhat less abstract —

Wonder Box

Filed under: General — Tags: , , — m759 @ 12:42 am

"Wundermärchen – the original German word for fairytale –
literally translates to ‘wonder tale’."

— Abigail Tulenko. a PhD student in philosophy at Harvard University,
at Aeon  on Feb. 26, 2024.

 


 

Another example of abstract  art . . .

"The discovery of the Cullinane Diamond Theorem is a testament
to the power of mathematical abstraction and its ability to reveal
deep connections and symmetries in seemingly simple structures."

Bing Chat with GPT-4  on November 16, 2023.

Friday, March 1, 2024

Vienna Wolf Song — The Babes in Tweeland  Version

Filed under: General — Tags: , — m759 @ 3:09 pm

Wiener Kreis Meditation

Filed under: General — Tags: — m759 @ 2:14 pm

Günter Brus, Artist Who Shocked Postwar Austria, Dies at 85

—  NYT obituary today by Alex Williams.

The above artist's exit was reportedly on February 10, 2024.

Also on that date —

Elegy in a Cartoon Graveyard

Filed under: General — m759 @ 3:16 am

See also this journal on February 24, 2024:  Wittenborn.

Thursday, February 29, 2024

Masonic Mojo Dojo Casa House

Filed under: General — Tags: , — m759 @ 8:03 pm

"Through the unknown, remembered gate . . . ."

— T. S. Eliot, Four Quartets

A differently remembered gate —

February Poetics… In 2007

Filed under: General — Tags: , — m759 @ 6:52 pm

Aaron

Filed under: General — Tags: , , — m759 @ 10:01 am

See earlier Log24 posts now tagged Aaron, about
the clash of Aaron Swartz and JSTOR, as well as
JSTOR in today's previous post, and an enthusiastic
post by @marrific yesterday on a different Aaron.

See also "A Tale of Two Intersections," about Venice,
CA, and St. Augustine's Church, New Orleans, LA. 
For a connection to the phrase "Where Madness Lies,"
used recently as a podcast title by Aaron Webman,
see the life of St. Augustine's parishioner George Herriman,
creator of "Krazy Kat."

February Poetics

Filed under: General — Tags: , , , — m759 @ 1:54 am

But seriously . . .

“Where Madness Lies”

Filed under: General — Tags: , , , , — m759 @ 1:00 am

See the title in this journal.

Wednesday, February 28, 2024

A Question for Our Panel

Filed under: General — m759 @ 6:26 pm

Claimed?

"Richard Lewis, the stand-up comedian who also starred alongside
Larry David in “Curb Your Enthusiasm,” died Tuesday night at his
Los Angeles home due to a heart attack, Variety  has confirmed.
He was 76."

Model

Filed under: General — Tags: , — m759 @ 2:09 pm

"Another date, another couch."

— Adapted motto of @marcelanow.

See as well

The adverb Li ly

A Definite School of Thought…
“The Buck Starts Here”

Filed under: General — Tags: , — m759 @ 12:29 pm

https://theosophy.wiki/en/Jirah_Dewey_Buck

" Dr. Jirah Dewey Buck (November 20, 1838 – December 13, 1916)
was a physician who worked to establish one of the first Theosophical
lodges in the United States, the Cincinnati Theosophical Society, and
the American Section of the international Theosophical Society in 1886 . . . ."

"Buck was born in Fredonia, New York
on November 20, 1838 . . . .

[He was] 'a recognized leader of a definite school
of Masonic thought and propaganda'."

The above metadata was suggested by an image I happened to see today,
the "Tetragrammaton of Pythagoras" —

"Duck Soup" fans may recall the war between Freedonia and Sylvania.

For some images more in the spirit of Sylvania, see "Triangles Are Square."

Tuesday, February 27, 2024

Go Ogle

Filed under: General — m759 @ 8:58 pm

 


 

marcela.art

 

Art Call

Filed under: General — m759 @ 8:12 pm


 


The Source:

 

“Claim this knowledge panel”

Filed under: General — m759 @ 1:08 pm

Macbeth and the Black Arts

Filed under: General — Tags: , — m759 @ 10:51 am

“I need a photo opportunity, I want a shot at redemption.
Don’t want to end up a cartoon in a cartoon graveyard.”
— Paul Simon

Rhymin' Simon's lyrics seem particularly appropriate
in the case of the actor below, who reportedly died
on October 31 — Halloween — last year.

Earlier last October . . .

Mr. Miller’s Class: Keyholes for Bilbo

Filed under: General — Tags: , , — m759 @ 12:58 am

   Related entertainment starring Martin Freeman —

Miller's Girl's reading includes a book
whose cover features an erotic keyhole . . .

Vide  Shanna Collins as Laurie in the 2008 TV series "Swingtown"
and in this  journal on All Souls' Day 2021

Another, somewhat less erotic, keyhole shows
Shanna Collins in a 2010 film, "In My Sleep" —

Monday, February 26, 2024

Once Upon a Time, Eureka

Filed under: General — m759 @ 11:02 pm

"Right through hell there is a path" — Under the Volcano

Some Context:

Time as Space: Area 15, If the Whole Pie Is 60

Filed under: General — Tags: — m759 @ 3:34 pm

A Latin Club slogan:

"We put the sex in sexagesimal."

Midrash for Bilbo and Miller's Girl  —

"Some dragons like riddles."

Outpost Vegas: A Different Hook Man

Filed under: General — Tags: — m759 @ 2:09 pm

An Instagram post from Thanksgiving Day 2022 —

This  journal on that day

A different Hook Man

This Just In

Filed under: General — m759 @ 1:17 pm

Meanwhile… Consider the Mathematical Possibilities

Filed under: General — m759 @ 12:17 pm

Truth and Beauty at Princeton:

Update of 12:48 PM ET —

Once upon a time, someone gave ScarJo a mic.

Design School for Harvard: Tri.be

Filed under: General — Tags: — m759 @ 11:00 am

The name TRI.BE of the musical group in
the previous post suggests the URL https://tri.be
of the design firm Modern Tribe . . .

The above Tri.be color palette suggests a review of
the phrase "Color Box" in this journal, and an image:

Outpost Vegas… Continues.

Filed under: General — Tags: — m759 @ 3:26 am

From this journal on February 8, 2024 —

A note for Dr. Yen Lo

The Metadata —

February Poetics… Continues.

Filed under: General — Tags: , — m759 @ 2:34 am
 

According to Chu Hsi [Zhu Xi],

“Li”  is
“the principle or coherence
or order or pattern
underlying the cosmos.”

— Smith, Bol, Adler, and Wyatt,
Sung Dynasty Uses of the I Ching ,
Princeton University Press, 1990

But very possibly the earliest use of li  is the one instance that
it appears in the Classic of Poetry  (Ode 210) where it refers to
the borders or boundary lines marking off areas in a field.
Here it appears in conjunction with chiang  and is explained
as 'to divide into lots (or parcels of land)' (fen-ti )."

P. 33 of "Li Revisited and Other Explorations"
by Allen Wittenborn, Bulletin of Sung and Yüan Studies
No. 17 (1981), pp. 32-48 (17 pages),
https://www.jstor.org/stable/23497457.

Sunday, February 25, 2024

Alan David Perlis, 1943-2015

Filed under: General — Tags: — m759 @ 4:56 pm

See as well https://www.dignitymemorial.com/obituaries/
homewood-al/alan-perlis-6727050
.

Related non-literary "Transforming Shapes" aesthetics:

Related Log24 posts: http://m759.net/wordpress/?s=Perlis+Shapes.

Related Alabama material — The Forrest Gump sketch on
last night's Saturday Night Live.

Edge

Filed under: General — m759 @ 9:31 am

Annenberg Xmas

Filed under: General — m759 @ 7:29 am

Saturday, February 24, 2024

Saturday Night Live:  The Full Snow Moon

Filed under: General — Tags: , — m759 @ 10:20 pm

New from Harlan Kane:

The Wittenborn Date

"Always with a little humor." — Dr. Yen Lo

The adverb Li ly

Filed under: General — Tags: , , , , — m759 @ 1:23 pm

An AI image created today by https://neural.love —

"Lily Collins Playing Chess" —

Perhaps some Dreaming Jewels  have mated.

From The Dreaming Jewels , by Theodore Sturgeon:

"Oh. And the crystals make things — even complete things — like Tin Pan Alley makes songs."

"Something like it." Zena smiled. It was the first smile in a long while. "Sit down, honey; I'll bring the toast. Now — this is my guess — when two crystals mate, something different happens. They make a whole thing. But they don't make it from just anything the way the single crystals do. First they seem to die together. For weeks they lie like that. After that they begin a together-dream. They find something near them that's alive, and they make it over. They replace it, cell by cell. You can't see the change going on in the thing they're replacing. It might be a dog; the dog will keep on eating and running around; it will howl at the moon and chase cats. But one day — I don't know how long it takes — it will be completely replaced, every bit of it."

"Then what?"

"Then it can change itself — if it ever thinks of changing itself. It can be almost anything if it wants to be."

Bunny stopped chewing, thought, swallowed, and asked, "Change how?"

"Oh, it could get bigger or smaller. Grow more limbs. Go into a funny shape — thin and flat, or round like a ball. If it's hurt it can grow new limbs. And it could do things with thought that we can't even imagine. Bunny, did you ever read about werewolves?"

"Those nasty things that change from wolves to men and back again?"

Zena sipped coffee. "Mmm. Well, those are mostly legends, but they could have started when someone saw a change like that."

Wittenborn and The Life of Forms in Art

Filed under: General — Tags: , , — m759 @ 11:41 am

For Focillon's "immobility" that "sparkles with metamorphoses,"
see Theodore Sturgeon's imagined "Dreaming Jewels ."

Li

Filed under: General — Tags: , , , — m759 @ 2:36 am

The Chinese concept of li  in yesterday's post "Logos" is related,
if only by metaphor, to the underlying form (sets of "line diagrams")
of patterns in the Cullinane diamond theorem:

"But very possibly the earliest use of li  is the one instance that
it appears in the Classic of Poetry  (Ode 210) where it refers to
the borders or boundary lines marking off areas in a field.
Here it appears in conjunction with chiang  and is explained
as 'to divide into lots (or parcels of land)' (fen-ti )."

P. 33 of "Li Revisited and Other Explorations"
by Allen Wittenborn, Bulletin of Sung and Yüan Studies
No. 17 (1981), pp. 32-48 (17 pages),
https://www.jstor.org/stable/23497457.

Friday, February 23, 2024

Annals of Artistic Integrity

Filed under: General — Tags: — m759 @ 5:11 pm

Maintaining artistic integrity —
Harder than you might think.


"I can feel the Devil walking next to me"

Song lyric from the musical "Chess"

 

Logos

Filed under: General — Tags: , — m759 @ 3:50 pm

A logo from the previous post

This suggests a flashback to an image from Log24 on Nov. 6, 2003

Moral of the
Entertainment:

According to Chu Hsi [Zhu Xi],

“Li”  is
“the principle or coherence
or order or pattern
underlying the cosmos.”

— Smith, Bol, Adler, and Wyatt,
Sung Dynasty Uses of the I Ching ,
Princeton University Press, 1990

North by Northwest: The Local Edge

Filed under: General — Tags: — m759 @ 3:18 pm

"Looking for what was, where it used to be" — Wallace Stevens

 

— "Is this your business?"

— "No, but this  is."

Turing-Award Winner Memorial

Filed under: General — m759 @ 3:49 am

In memory of the inventor of the Pascal programming language,
who reportedly died on New Year's Day, 2024, an image from
this journal on that date

"Before time began, there was the Cube." — Optimus Prime

See as well a Pascal that some will prefer, and my own ACM card.

That card gives Warren, PA, as my location… which is no longer
always the case… but Warren is where I learned, and worked, in
computing, after a somewhat belated education in pure mathematics
in New York State.

Some personal background is suggested by…

  • Yesterday's post on the words "sexadecimal" and "hexadecimal"
  • The related word "sexagesimal," referring to base-60 numbering
  • My high school class of 1960 —
    quod vide.

Thursday, February 22, 2024

Truchet in the Basque Country

Filed under: General — Tags: — m759 @ 7:50 pm

Annals of Mathematical Aesthetics:  Sex Hex

Filed under: General — Tags: — m759 @ 5:41 pm

Reading suggested by a phrase in The New York Times  today —

Vocabulary for some combinatorial  arts . . . 

SEXadecimal and HEXadecimal —

Related entertainment — "Mathematical Possibilities"

Annals of Entertainment: The Scotch Play  by Clay Risen

Filed under: General — m759 @ 4:29 pm

Symmetry Summary: The Cullinane Cube

Filed under: General — Tags: — m759 @ 3:48 pm

At https://shc759.wordpress.com today —

https://shc759.wordpress.com/2024/02/22/
truchet-tiles-and-cullinane-cubes-the-mathematics-of-symmetry/

For a much larger view of this topic, see other posts in this journal
tagged Cullinane Cube.  For a large (16 MB) downloadable
document containing these posts, see . . .
log24.com/log24/240222-Log24-posts-tagged-Cullinane-Cube.pdf.

Wednesday, February 21, 2024

February Mojo

Filed under: General — Tags: , — m759 @ 5:18 pm

A 1911 essay by T. E. Hulme,
"Romanticism and Classicism" —

"There is a general tendency to think that verse means
little else than the expression of unsatisfied emotion.
People say: 'But how can you have verse without sentiment?'
You see what it is: the prospect alarms them. A classical revival
to them would mean the prospect of an arid desert and the death
of poetry as they understand it, and could only come to fill the gap
caused by that death. Exactly why this dry classical spirit should
have a positive and legitimate necessity to express itself in poetry
is utterly inconceivable to them."

A 1961 reaction against Hulme,
"Against Dryness" —

"Against the consolations of form, the clean crystalline
work, the simplified fantasy-myth, we must pit the
destructive power of the now so unfashionable naturalistic
idea of character.

Real people are destructive of myth, contingency is
destructive of fantasy and opens the way for imagination."

— Iris Murdoch, January 1961

Opening the Way —

For instances of character and imagination,
see this  journal on February 8 and February 9.

See also the previous post and . . .

Academics may prefer "The Eureka Manifesto" —

From the MANIFESTO link in the Breakthrough Prize page above —

Our Mission . . . Should We Choose to Accept It

For Nevermore Academy… Wolfing Out

Filed under: General — Tags: — m759 @ 11:42 am

The previous post, and Wednesday's roommate, suggested the above title.

From The Dreaming Jewels , by Theodore Sturgeon:

"Oh. And the crystals make things — even complete things — like Tin Pan Alley makes songs."

"Something like it." Zena smiled. It was the first smile in a long while. "Sit down, honey; I'll bring the toast. Now — this is my guess — when two crystals mate, something different happens. They make a whole thing. But they don't make it from just anything the way the single crystals do. First they seem to die together. For weeks they lie like that. After that they begin a together-dream. They find something near them that's alive, and they make it over. They replace it, cell by cell. You can't see the change going on in the thing they're replacing. It might be a dog; the dog will keep on eating and running around; it will howl at the moon and chase cats. But one day — I don't know how long it takes — it will be completely replaced, every bit of it."

"Then what?"

"Then it can change itself — if it ever thinks of changing itself. It can be almost anything if it wants to be."

Bunny stopped chewing, thought, swallowed, and asked, "Change how?"

"Oh, it could get bigger or smaller. Grow more limbs. Go into a funny shape — thin and flat, or round like a ball. If it's hurt it can grow new limbs. And it could do things with thought that we can't even imagine. Bunny, did you ever read about werewolves?"

"Those nasty things that change from wolves to men and back again?"

Zena sipped coffee. "Mmm. Well, those are mostly legends, but they could have started when someone saw a change like that."

Elderbrook Colors

Filed under: General — m759 @ 11:15 am

From a post of August 17, 2023

Color of the diamond shape —

"Blue jean baby, L.A. lady…" — Song lyric

“Give the people what they want.”

Filed under: General — m759 @ 12:12 am

Pizza.

Tuesday, February 20, 2024

“One of those bells that now and then rings”

Filed under: General — m759 @ 10:01 am

See marcelanow.art and marcelathen.art.

Backlight

Filed under: General — m759 @ 12:09 am

The epigraph of the previous post

"To Phaedrus, this backlight from the conflict between
the Sophists and the Cosmologists adds an entirely
new dimension to the Dialogues of Plato." — Robert M. Pirsig

Related reading and art for academic nihilists — See . . .

Reading and art I prefer —

Love in the Ruins , by Walker Percy, and . . .

Van Gogh  (by Ed Arno) and an image and
a passage from The Paradise of Childhood
(by Edward Wiebé):

'Dear Theo' cartoon of van Gogh by Ed Arno, adapted to illustrate the eightfold cube

Monday, February 19, 2024

Theology for Sophists

Filed under: General — m759 @ 10:15 pm

"To Phaedrus, this backlight from the conflict between
the Sophists and the Cosmologists adds an entirely
new dimension to the Dialogues of Plato." — Robert M. Pirsig

"It’s all in Plato, all in Plato;
bless me, what do  they
teach them at these schools?”

— C. S. Lewis in
The Narnia Chronicles

Compare and Contrast — Plato's Diamond.

Plato's diamond in Jowett's version of the Meno dialogue

Fulcrum

Filed under: General — Tags: , — m759 @ 3:33 pm

From Log24 on September 19, 2023

Adapted image —

Related reading —

Related art — Square Round and Round Square.

Tool Use and Agents

Filed under: General — m759 @ 2:56 pm

Mythspace: Its Logic, Poetry, and Geometry

Filed under: General — Tags: — m759 @ 12:42 pm

For logicians

http://www.log24.com/log/pix09A/090815-Grid8x8.gif

For poets

The 1955 Levi-Strauss 'canonic formula' in its original context of permutation groups

For geometers

Affine groups on small binary spaces

Sunday, February 18, 2024

History for Conspiracy Theorists (and Harlan Kane)

Filed under: General — m759 @ 8:33 pm

The New York Times  this afternoon —

" William Beecher, who as a reporter for The New York Times
revealed President Richard M. Nixon’s secret bombing campaign
over Cambodia during the Vietnam War, and who later won a
Pulitzer Prize at The Boston Globe, died on Feb. 9 at his home
in Wilmington, N.C. He was 90." — Clay Risen, 2:28 PM

Also on Feb. 9 —

Another Beecher narrative —

Religious meditation from the Church of Synchronology . . .

Sunday Book Review

Filed under: General — m759 @ 12:56 pm

On a New York Times  article from January 31, 2024

"A version of this article appears in print on Feb. 18, 2024,
Page 12 of the Sunday Book Review with the headline:
The 5 Best Books About Artificial Intelligence."

Bride’s Chair vs. One-Liner

Filed under: General — Tags: , — m759 @ 11:53 am

The "bride's chair" is the figure illustrating Euclid's proof
of the Pythagorean theorem (click image to enlarge) —

A somewhat simpler approach —

Pythagorean theorem proof by overlapping similar figures

"Drop me a line" — Request attributed to Emma Stone

 

For Students of the Crimson Abyss:
 Vocabulary Illustrated

Filed under: General — Tags: , , , — m759 @ 11:12 am

Detail of a February 16 illustration  from The Harvard Crimson .

Vocabulary Note

Filed under: General — m759 @ 10:23 am

The URLs powerset.space and powerset.group are now operative.

Related vocabulary:  See Boolean Functions Review (Log24, May 15, 2023).

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