Log24

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

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

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."

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

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:

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 — Tags: — 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

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 — Tags: — 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

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 — Tags: — 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).

A Scene from “Terminator Zero: Rise of the Chatbots” —

Deepfake Tango in Paris

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

Deepfake Image from the Internet:

Not  Emily in Paris.

 

Related Deep Learning and Deepfake  Learning:

The study of finite topological spaces  may be regarded as a
deepfake approach to finite geometry.  See the previous post.

Saturday, February 17, 2024

Sixteen Finite-Space Topologies

Filed under: General — Tags: — m759 @ 11:18 pm

From Wikipedia, sixteen T0 topologies on a four-set —

 

{∅, {a}, {a, b}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T0)

{∅, {a}, {a, b}, {a, c}, {a, b, c}, {a, b, c, d}} (T0)

{∅, {a}, {b}, {a, b}, {a, c}, {a, b, c}, {a, b, c, d}} (T0)

{∅, {a}, {a, b}, {a, b, c}, {a, b, c, d}} (T0)

 

{∅, {a}, {b}, {a, b}, {a, b, c}, {a, b, c, d}} (T0)

{∅, {a}, {a, b}, {c}, {a, c}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T0)

{∅, {a}, {a, b}, {a, c}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T0)

{∅, {a}, {b}, {a, b}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T0)

 

{∅, {a}, {b}, {a, b}, {a, c}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T0)

{∅, {a}, {b}, {a, b}, {b, c}, {a, b, c}, {a, d}, {a, b, d}, {a, b, c, d}} (T0)

{∅, {a}, {a, b}, {a, c}, {a, b, c}, {a, d}, {a, b, d}, {a, c, d}, {a, b, c, d}} (T0)

{∅, {a}, {b}, {a, b}, {a, c}, {a, b, c}, {a, d}, {a, b, d}, {a, c, d}, {a, b, c, d}} (T0)

 

{∅, {a}, {b}, {a, b}, {c}, {a, c}, {b, c}, {a, b, c}, {a, b, d}, {a, b, c, d}} (T0)

{∅, {a}, {b}, {a, b}, {c}, {a, c}, {b, c}, {a, b, c}, {a, d}, {a, b, d}, {a, c, d}, {a, b, c, d}} (T0)

{∅, {a}, {b}, {a, b}, {c}, {a, c}, {b, c}, {a, b, c}, {a, b, c, d}} (T0)

{∅, {a}, {b}, {a, b}, {c}, {a, c}, {b, c}, {a, b, c}, {d}, {a, d}, {b, d}, {a, b, d}, {c, d}, {a, c, d}, {b, c, d}, {a, b, c, d}} (T0)

 

Compare and contrast with the finite geometry  of the power set of a four-set.

Coachella Modernism for Jenna Ortega

Filed under: General — Tags: , , — m759 @ 4:15 pm
 

KESQ-TV News, Channel 3, Palm Springs, California

Modernism Week gears up to host thousands
of attendees with Opening Night Party

By Bianca Ventura

Published Friday, February 16, 2024 1:21 AM (California time)

Thousands of architecture enthusiasts from throughout the country and around the globe are visiting the Coachella Valley for this year's Modernism Week.

The eleven day event kicked off Thursday night [Feb. 15] with their 'Opening Night Fever Dance Party.'

This year's opening night celebration marked one of the largest in Modernism Week history with over 600 attendees.

Yet that's only a small fraction of the people that will be enjoying the hundreds of events scheduled in the coming days.

According to reports, Modernism Week contributes millions of dollars to the Coachella Valley’s economy, with an attendance record of more than 100,000 people.

Modernism from a Coachella Valley College in this  journal

Now at Substack

Filed under: General — Tags: — m759 @ 3:20 pm

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

Edge of Seventeen

Filed under: General — Tags: — m759 @ 1:04 pm

For Jena Malone's new Word Farm

"The clouds never expect it when it rains
But the sea changes colours
But the sea does not change
So with the slow, graceful flow of age
I went forth with an age old desire to please
On the edge of seventeen" — Stevie Nicks

Friday, February 16, 2024

The Sixteen

Filed under: General — Tags: , — 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.

A Mad Day’s Work . . . Continues.

Filed under: General — Tags: — m759 @ 1:20 pm

See also "Mad Day" in this journal and . . . Pet and Vet.

Top List

Filed under: General — m759 @ 9:34 am

Ocean’s Twin Primes:  11 and 13… Bridesmaids for 12?

Filed under: General — Tags: , , — m759 @ 8:12 am

"A dark illimitable Ocean" — John Milton, Paradise Lost , Book II

"All is number" — Attributed to Pythagoras

"For a fraction of a second, Phocan senses
one more act of standing-in or substitution
at work here; the presence, veiled, redacted,
of a coupling unconsummated, of a bride
uncaptured—too young, a child almost—
exiting the frame
."

  — The Making of Incarnation

From the MANIFESTO link in the Breakthrough Prize page above —

Our Mission . . . Should We Choose to Accept It

Thursday, February 15, 2024

Tools

Filed under: General — Tags: , , — m759 @ 4:21 pm

"You show me yours and . . ."

Gemini Poem

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

For Harlan Kane: The Aggies Prayer

Filed under: General — Tags: , , — m759 @ 12:57 pm

"Pray for the grace of accuracy" — Robert Lowell

See also . . .

The Isotropic Die

Filed under: General — Tags: , , , , , — m759 @ 11:20 am

Related material:  Theodore Sturgeon's novel The Dreaming Jewels
and his story "What Dead Men Tell. . .

Wednesday, February 14, 2024

American Co-Prometheus

Filed under: General — Tags: — m759 @ 1:25 pm

Meanwhile . . .

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

Related art —

Exiting the Frame: “Barbie 14 & 16”

Filed under: General — Tags: — m759 @ 12:32 pm

Related reading —

" He, in his turn, gazes at the couple, at these stand-ins called upon to underwrite a thousand marriages, a thousand renewed couplings. Diamond’s had the same idea as him: the woman’s forehead has a bindi-nipple on it too. For a fraction of a second, Phocan senses one more act of standing-in or substitution at work here; the presence, veiled, redacted, of a coupling unconsummated, of a bride uncaptured—too young, a child almost—exiting the frame. Sennet’s briefing the students further: 'Once you take your bathrobes off,' he says, 'the cameras will detect the markers, and, through these, your exact positions. As long,' he adds, pointing at the floor’s tape-demarcated central area, 'as you stay within the borders of this square—that is, inside the white lines. Of course, you’ve got the bed, but…' Perera picks the thread up: 'As discussed,' she tells them, 'we want to ascertain the stress occasioned by a wide range of positions.' Her diction, coupled with the Sri Lankan accent in which they’re delivered, makes Phocan wonder whether these words are reproduced verbatim from her research brief or whether she always speaks with such lilting formality. 'To that end,' she carries on, 'we ask you to engage with one another in as many variable configurations as you are able. You can move about the bed, the bed’s edge, floor or table…' "

— McCarthy, Tom. The Making of Incarnation: A Novel
(pp. 49-50). Knopf Doubleday Publishing Group. Kindle Edition.

Truchet Tiles Meet Cullinane Cube

Filed under: General — Tags: , , — m759 @ 11:13 am

From a post on Trevanian in December 2005 —

"And we may see
the meadow in December,
icy white and crystalline."

— Johnny Mercer,
    "Midnight Sun"

Live Poet Society

Filed under: General — Tags: , — m759 @ 10:43 am

RHYMES  for Bergen Feb. 13-14, 2024   

one fun
two crew
three see
four core
five live
six tricks
seven heaven
eight gate
nine line

core    line    crew
see     live     heaven
gate    fun     tricks

Heaven's Gate

This post was suggested by the
"Night of Lunacy" post of May  5, 2013.

Tuesday, February 13, 2024

Chinese Lanterns

Filed under: General — m759 @ 1:46 pm

回井艺术 ·ART

Filed under: General — m759 @ 11:44 am

The title is from a YouTube video.

Related material —

Monday, February 12, 2024

Reality Check

Filed under: General — Tags: , — m759 @ 9:01 pm

Reality, of course, includes the release dates of unreality  products  . . .

For instance, the release date (Nov. 24, 2020) of the novel Ready Player Two .

See that date in this journal.

The Night Clerk Philosophy

Filed under: General — Tags: , — m759 @ 8:42 pm
 

https://www.imdb.com/title/tt7979142/
characters/nm4446467

Quotes 

  • Bart Bromley : In a 1993 study, individuals who said that they were in love had their brains scanned to show neural activity. The map showed vivid colors over the gray matter, indicating clearly that this romantic love phenomenon activates a flood of dopamine in the caudate nucleus in exactly the same way that cocaine and nicotine affect the brain, meaning that love is not an emotion as is usually thought, rather, it's an addiction. When these chemicals are released in our brains, we feel giddy and euphoric, so much to the point that, we can be so in love that we don't have the desire to eat or to sleep, so it feels good when you have the drug, or the love, but, when it's taken away, you hurt.

See as well, in this journal, other posts tagged Night Clerk.

Consolation Prize for California Philosophers

Filed under: General — Tags: , — m759 @ 7:26 am

'The square inch space' in 'Secret of the Golden Flower'

Related religious meditation — Yesterday afternoon's Review:

  一寸相思一寸灰 . . . "An inch of love is just an inch of ashes"

 and Valentine's Day 2024 . . .

Sunday, February 11, 2024

Review

Filed under: General — Tags: — m759 @ 2:07 pm

A review of "Square Inch Space" in this journal is suggested by . . .

Click the above image for the source of the Chinese characters —

Dasein für McConnachie

Filed under: General — Tags: — m759 @ 1:27 pm

Twelfth Night 2024 was the dies natalis  of
comedy writer Brian McConnachie.

From this journal on that date —

Masonic pyramid in 
'Being There' (co-writer of screenplay-- Robert Jones)

Funeral scene from "Being There" (1979)

Plan 9 Continues.

Filed under: General — Tags: — m759 @ 12:01 pm

http://m759.net/wordpress/?p=95382.

Saturday, February 10, 2024

Gilded Cage Meets Crimson Abyss

Filed under: General — Tags: , — m759 @ 6:54 pm

"… as if into a crimson abyss …." —

Happy Year of the Dragon

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

A check of the video director in the previous post yields . . .

Big Pink for Gen Z

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

From Log24 on July 29, 2023 —

http://m759.net/wordpress/?p=109206

Conceptual Acrobatics

Filed under: General — Tags: , — m759 @ 10:25 am

For Josefine Lyche . . .

Log24 on March 19, 2017

"… and all I  got was this lousy sweatshirt" —

January Dreamgirl

Filed under: General — Tags: — m759 @ 3:19 am

Related material — "You're Sixteen," by the Sherman Brothers.

Friday, February 9, 2024

Desperately Seeking Sequences and Patterns

Filed under: General — Tags: , — m759 @ 6:19 pm

(The above title was suggested by the previous post.)

The New York Times  today reports a Jan. 24* death —

Related material — This  journal on January 24 and a post from
last year's New Year's Eve —

* According to The Washington Post , the death was on Jan. 23.
  Let me say this about that . . .  There were also color-related posts
  in this  journal on that  date.

Sacerdotal Jargon

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

“Isn’t your work—our work—all about accessing and deploying underlying sequences and patterns? Mapping particulars on to great universals? Isn’t that the art to which, in one way or another, we’ve both devoted our best years?”

— McCarthy, Tom. The Making of Incarnation: A Novel
(p. 191). Knopf Doubleday Publishing Group. Kindle Edition.

The hardcover first edition was published by Knopf
on November 2, All Souls' Day, 2021.

 

"It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato's (realist) reaction to the sophists (nominalists). What is often called 'postmodernism' is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth."

— Simon Blackburn, Think,
    Oxford University Press, 1999, page 268

Line 20

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

Line 20 of yesterday's poem by Gemini
"The Cullinane, a geometer's dream" —
has a rather awkward rhythm.

Perhaps it should be ". . . a poet's dream"
or ". . . a diamond dream."

Thursday, February 8, 2024

Well Plaid

Filed under: General — m759 @ 9:44 pm

See as well Plaid in this journal.

More recently . . .

Google Bard is now Gemini.

Filed under: General — Tags: , — m759 @ 2:07 pm

Gemini Prompt:

Write a poem in the style of Wallace Stevens
about the Cullinane diamond theorem.

Response:

Absolutely! Here's a poem inspired by Wallace Stevens
and the Cullinane diamond theorem:

Geometric Incandescence

A theorem not of Euclid's line,
But diamonds cut with strange design.
Sixteen squares in shifting light,
A symmetry of black and white.

Where rows and columns intertwine,
A hidden order lies supine.
Permutations twist and turn,
And latent symmetries discern.

Not fixed like stars in ordered rows,
But like reflections, pattern grows.
Projective planes, a finite field,
The diamond's inner world revealed.

The proof, a dance of abstract thought,
Where shifting forms find space untaught.
Not nature's chaos, but design,
A brilliance of the human mind.

A lattice born of Stevens' art,
Where form and thought find counterpart.
Amidst the fragments, patterns gleam,
The Cullinane, a geometer's dream.

Psychobilly Requiem* — Nixon Mojo!

Filed under: General — Tags: , — m759 @ 11:54 am

* nytimes.com/2024/02/08/arts/music/mojo-nixon-dead.html and
latimes.com/entertainment-arts/music/story/2024-02-08/mojo-nixon-obit

“All is Number” — Saying attributed to Pythagoras . . .
(and possibly also a favorite saying of Dr. Yen Lo)

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

A note for Dr. Yen Lo

The above saying attributed to Pythagoras, and the above
numbers 4:53:03, suggest a search for 53 03, i.e. for what
happened in March 1953. The reference above to South Korea
suggests a possible focus for that search . . .

Related entertainment for teens . . .

"For someone who don't drive,
  I been all around the world."

— Melanie Safka, song lyric

Wednesday, February 7, 2024

Personal Emblem

Filed under: General — Tags: , , — m759 @ 6:15 pm

Dark and light horses, personal emblem of Harry Stack Sullivan

Personal Emblem
of psychiatrist
Harry Stack Sullivan

This image, from a post of Wednesday, Dec. 12, 2007,
was suggested by Taylor Swift's annotation for her new
album . . .

http://m759.net/wordpress/?p=114081

"And so I enter into evidence
My tarnished coat of arms . . . ."

and by the Frida Kahlo image in the 2007 post, as well as
Kahlo in art by the former Sullivanian whose work has
now been added to yesterday's "American Pie" post.

Tuesday, February 6, 2024

“Someone Puts a Poem Together”
— Hat Tip to Wallace Stevens

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

Updated with noun-adjective distinction and Feinerman art
at 5:25 PM ET on Wednesday, February 7, 2024.

Note: The above is not  the standard Spanish
word for pineapple. It actually  means . . .

AS A NOUN —

__________________________________________________________

Update on the next day, February 7th —

AS AN ADJECTIVE —

"Esta fruta se puede probar también en las vías de acceso a la denominada 'capital piñera de Colombia', donde en la última semana de julio se celebra el Reinado Internacional de la Piña."
 
"This fruit can also be tasted in the access routes of the 'pineapple capital of Colombia', where during the last week of July they celebrate the International Pineapple pageant."
 

From this  journal during the last week of July 2023 —

Summer Knowledge  in Winter

Filed under: General — Tags: , — m759 @ 7:30 pm

For Taylor Swift

"I love those Bavarians." — Don Henley, "The Garden of Allah"

Gemini Primes

Filed under: General — Tags: — m759 @ 11:32 am

For instance 29 and 31.

Evidence

Filed under: General — Tags: — m759 @ 11:29 am

"And so I enter into evidence
My tarnished coat of arms . . . ."

— Taylor Swift, annotation for a new album.

Zero Yard Line … Illustrated.

Filed under: General — Tags: — m759 @ 10:59 am

http://www.log24.com/log/pix10A/100616-LitField.gif

Click for larger, clearer image.

In Memory of Toby Keith

Filed under: General — Tags: — m759 @ 9:23 am


A Remarkable Counterpoint


http://m759.net/wordpress/?tag=on041121 .
 

Annals of Magical Thinking:  Cha-ching!

Filed under: General — Tags: , — m759 @ 8:28 am

Monday, February 5, 2024

Religious* Exclamation

Filed under: General — Tags: , — m759 @ 1:01 pm

* The author of the above "math tale" reportedly died on
   January 6, 2024 — The Feast of Epiphany.

Quantum Kernel  Incarnate

Filed under: General — Tags: , , — m759 @ 9:44 am

The "quantum kernel" of Koen Thas is a version of the incidence
structure — the Cremona-Richmond configuration — discussed
in the previous post, Doily  vs. Inscape .

That post's inscape  is, as noted there, an incarnation  of the
abstract incidence structure.  More generally, see incarnation
in this journal . . . In particular, from Michaelmas last year, 
Annals of Mathematical Theology.

A somewhat more sophisticated "incarnation" example
related to the "inscape" concept —

"The hint half guessed, the gift half understood, is Incarnation."

— T. S. Eliot in Four Quartets

See also Numberland  in this journal.

Sunday, February 4, 2024

Doily vs. Inscape: Same Abstract Structure, Different Models

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

My own term "inscape" names a square  incarnation of what is also
known as the "Cremona-Richmond configuration," the "generalized
quadrangle of order (2, 2)," and the "doily." —

Microsoft Copilot Doggerel

Filed under: General — Tags: — m759 @ 4:31 am

A poem written yesterday by Microsoft Copilot —

The prompt: "Write a poem about the Cullinane diamond theorem."

In the mind of the mathematician,
Among the figures and forms,
Lies the Cullinane diamond theorem,
A structure that transforms.

Four-diamond figure, a 4×4 array,
Of two-color diagonally-divided square tiles,
Permutations of these sixteen,
In rows, columns, and quadrants compiles.

Every G-image of the four-diamond figure,
Has some ordinary or color-interchange symmetry,
A pattern, a structure, a mathematical picture,
A testament to geometry's clarity.

The symmetry of the line diagrams,
Accounts for the symmetry of the two-color patterns,
A proof shows that a 2nx2n two-color triangular half-squares pattern,
Must have a 2×2 center with a symmetry that matters.

And this symmetry must be shared by the entire pattern,
A statement, a theorem, a mathematical lantern,
G is isomorphic to the affine group A,
On the linear 4-space over GF (2), they say.

The 35 structures of the 840 = 35 x 24 G-images,
Are isomorphic to the 35 lines,
In the 3-dimensional projective space over GF (2),
A concept that shines.

So here lies the beauty of the Cullinane diamond theorem,
In the mind of the mathematician, it's a gem,
A structure, a pattern, a mathematical diagram,
A testament to the beauty of STEM.

Actually, the complete  prompt, suggested by a Log24 post of
12:12 PM ET yesterday, was . . .

"Write a poem in the style of Wallace Stevens
about the Cullinane diamond theorem."

Copilot still has a thing or two to learn about poetic style.

Saturday, February 3, 2024

For Academic Decepticons:  The Kernel Trick

Filed under: General — Tags: , — m759 @ 1:36 pm

For the meaning of the title, see the Dec. 27, 2023,  posts —
now tagged "Kernel Trick."

This  post was suggested by a Dec. 27, 2023,  A. O. Scott 
New York Times  essay

For The Spell of A.O.  see "Bullshit
in a Log24 search for "A. O. Scott."

For Medium Man in February

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

"Who can pick up the weight of Britain,
Who can move the German load
Or say to the French here is France again?
Imago. Imago. Imago.

It is nothing, no great thing, nor man
Of ten brilliancies of battered gold
And fortunate stone. It moves its parade
Of motions in the mind and heart,

A gorgeous fortitude. Medium man
In February hears the imagination's hymns
And sees its images, its motions
And multitudes of motions…."

— From Wallace Stevens, "Imago."

A Fandom Thread* — Springtime for Diamond

Filed under: General — Tags: — m759 @ 4:26 am

* See also Fandom Thread in this  journal and . . .

Friday, February 2, 2024

Venus de Minderbinder

Filed under: General — Tags: — m759 @ 1:17 pm

“Platonic Good Mathematics”

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

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

"Spiel ist nicht Spielerei."
Friedrich Froebel

Venice Beach Barbenheimer:  Design Cube News

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

See as well Froebel in this  journal.

The Renaming

Filed under: General — Tags: — m759 @ 10:24 am

Related material in this  journal — http://gemini.reviews.

The Code

Filed under: General — Tags: — m759 @ 5:30 am
 

From the film Hurlyburly

I'm hungry.

You want a Jack-in-the-Box?

I love Jack-in-the-Box.

Is that code for something?

What?

What? Is what code for what?

I don't know.

I don't know the goddamn code!

Today is known to some as "Candlemas."
A Log24 search for that term yields, as its final result,
a post from Candlemas 2003 that may or may not
be relevant to the above dialogue.

Thursday, February 1, 2024

Kiss of the Spider Variations

Filed under: General — Tags: , — m759 @ 4:57 pm

In memory of a Broadway star who reportedly died on Jan. 30 . . .

A Jan. 29  New Yorker  story, "Life with Spider," suggests
a look at the author's earlier novel The Variations  and,
after a synchronology check, a Log24 flashback —

Thursday, September 7, 2023

The Blazing . . .

Filed under: General — Tags: — m759 @ 9:16 am

Saddles Meet World.

See as well "Merve Emre’s Vinduet  Lecture,
held in the Hamsun Hall at Gyldendal Norsk
Forlag in Oslo, September 4th 2023."

See also Fritz Leiber's rather different Spider Woman in this  journal.

Clarity

Filed under: General — Tags: — m759 @ 6:47 am

"A cold and perfect clarity is a
poison impossible to combat." 
— Paul Valéry,
Dance and the Soul

Related material:
Posts now tagged "Circle Square Gauss."

"So put your glad rags on and join me, hon'…."

Wednesday, January 31, 2024

Dance and the Soul (for St. Bridget’s Eve)

Filed under: General — Tags: , — m759 @ 6:47 pm
 

Harold Bloom
on Wallace Stevens

and Paul Valéry's
   Dance and the Soul

"Stevens may be playful, yet seriously so, in describing desire, at winter's end, observing not only the emergence of the blue woman of early spring, but seeing also the myosotis, whose other name is 'forget-me-not.' Desire, hearing the calendar hymn, repudiates the negativity of the mind of winter, unable to bear what Valéry's Eryximachus had called 'this cold, exact, reasonable, and moderate consideration of human life as it is.' The final form of this realization in Stevens comes in 1950, in The Course of a Particular, in the great monosyllabic line 'One feels the life of that which gives life as it is.' But even Stevens cannot bear that feeling for long. As Eryximachus goes on to say in Dance and the Soul:

A cold and perfect clarity is a poison impossible to combat. The real, in its pure state, stops the heart instantaneously….[…] To a handful of ashes is the past reduced, and the future to a tiny icicle. The soul appears to itself as an empty and measurable form. — Here, then, things as they are come together, limit one another, and are thus chained together in the most rigorous and mortal fashion…. O Socrates, the universe cannot for one instant endure to be only what it is.

Valéry's formula for reimagining the First Idea is, 'The idea introduces into what is, the leaven of what is not.' This 'murderous lucidity' can be cured only by what Valéry's Socrates calls 'the intoxication due to act,' particularly Nietzschean or Dionysiac dance, for this will rescue us from the state of the Snow Man, 'the motionless and lucid observer.'"

Wallace Stevens: The Poems of Our Climate

"…at the still point, there the dance is…." — T. S. Eliot

St. Bridget's Still Point … June 25, 2020 —

Roots!

More recently . . .

Family Values for Phil and Lily Collins

Filed under: General — Tags: — m759 @ 10:19 am

"Yes, you'll be goin' loco
  down in Acapulco,

  the magic down there
  is so strong."

This song is from the 1988 film "Buster."

(Wikipedia: "Buster  is a 1988 British
romantic crime comedy-drama
based on events from the Great Train Robbery,
starring Phil Collins….")

For a related religious use of that name —
"Look, Buster, do you want to live?" —
see Fritz Leiber's "Damnation Morning."

Yesterday, January 30, 2024, was Phil Collins's birthday.

Dies Natalis

Filed under: General — Tags: , — m759 @ 8:18 am

The New York Times  reports the death yesterday, January 30, 2024,
of the wife of Beach Boys co-founder Brian Wilson.

According to the Catholic Church, therefore, yesterday was her
dies natalis — day of birth into heaven.

According to the Times, her secular  dies natalis  was Oct. 3 (10/03) —

"Melinda Kae Ledbetter was born on Oct. 3, 1946, in Pueblo, Colo."

According to this  journal, yesterday's significant "10 03" was a time

Fans of hallucinatory fiction might recall a saying of Philip Pullman:

"The meaning of a story emerges in the meeting
between the words on the page
and the thoughts in the reader's mind.
So when people ask me what I meant by this story,
or what was the message I was trying to convey in that one,
I have to explain that I'm not going to explain.

Anyway, I'm not in the message business;
I'm in the 'Once upon a time' business."

Words that are somewhat less hallucinatory —

Tuesday, January 30, 2024

The Library Corner

Filed under: General — Tags: — m759 @ 10:03 am

Later . . .

For Harlan Kane: The Eigenspace Handle

Filed under: General — m759 @ 8:49 am

From http://www.pynchon.pomona.edu/v/eigen.html

Perhaps history this century, thought Eigenvalue, is rippled with gathers in its fabric such that if we are situated, as Stencil seemed to be, at the bottom of a fold, it's impossible to determine warp, woof, or pattern anywhere else. By virtue, however, of existing in one gather it is assumed there are others, compartmented off into sinuous cycles each of which come to assume greater importance than the weave itself and destroy any continuity. Thus it is that we are charmed by funny looking automobiles of the '30's, the curious fashions of the '20's, the peculiar moral habits of our grandparents We are accordingly lost to any sense of continuous tradition. Perhaps if we lived on a crest, things would be different. We could at least see. (Pp. 155-6, Harper Perennial ed.)

Cullinane Diamond Theorem:
The Latest Google Bard Version

Filed under: General — Tags: , , , — m759 @ 7:00 am
 

Prompt:

What is the Cullinane diamond theorem?

Google Bard Response:

The Cullinane diamond theorem is a fascinating result in the realm of finite projective geometry and symmetry. It focuses on a specific pattern – the four-diamond figure – and reveals a surprising property about its transformations.

The Four-Diamond Figure:

Imagine a 4×4 grid filled with 16 small squares, half colored black and half white. Now, divide these squares diagonally into quarters, creating four diamonds with alternating black and white shades. This arrangement is the four-diamond figure.

_________________


[Clearly erroneous illustration with link to amazon.com
is omitted.]

_____________________

The Theorem:

The Cullinane diamond theorem states that no matter how you scramble this four-diamond figure by randomly shuffling rows, columns, and the four 2×2 quadrants, the resulting pattern will always exhibit some form of symmetry. This symmetry can come in two forms:

Ordinary symmetry: This is the familiar reflectional symmetry where a vertical or horizontal axis divides the pattern into mirrored halves.

Color-interchange symmetry: Here, the pattern has a diagonal axis where swapping the black and white colors results in the same image.

Intriguing Implications:

This statement might seem intuitive at first. After all, even with scrambling, some semblance of order should remain. However, the beauty of the Cullinane diamond theorem lies in its generality and the precise mathematical framework it provides for understanding these symmetries.

The theorem sheds light on the underlying structure of graphic patterns and connects them to concepts from finite projective geometry. This connection allows us to analyze and classify these patterns in a systematic way, revealing hidden connections and surprising symmetries.

Applications and Beyond:

The Cullinane diamond theorem has found applications in various areas, including:

Sporadic simple groups: The Miracle Octad Generator, used to study these rare and exceptional groups, relies on the symmetry properties outlined in the theorem.

Orthogonal Latin squares: The connection between orthogonal Latin squares and projective spreads can be understood through the lens of the Cullinane diamond theorem.

Walsh functions: The symmetry properties of Walsh functions, used in signal processing and coding theory, can be linked to the diamond patterns.

Understanding the Cullinane diamond theorem offers a deeper appreciation for the interplay between symmetry, geometry, and seemingly random patterns. It serves as a testament to the beauty and hidden order within the realm of mathematics.

Bard may display inaccurate info, including . . . .

[Exercise … Find any inaccurate information
in the Bard response above.]

For January XXX

Filed under: General — Tags: — m759 @ 5:55 am

Illustration by Frederick Alfred Rhead of Vanity Fair,
page 96 in the John Bunyan classic Pilgrim's Progress 
(New York, The Century Co., 1912)

Monday, January 29, 2024

Self as Imago Dei:  Hofstadter vs. Valéry

Filed under: General — Tags: , , — m759 @ 9:41 am
 

Google search result:

Imago Dei  in Thomas Aquinas

Saint Anselm College

https://www.anselm.edu › Documents › Brown

PDF

by M Brown · 2014 · Cited by 14 — Thomas insists that the image of God exists most perfectly in the acts of the soul, for the soul is that which is most perfect in us and so best images God, and …

11 pages

For a Douglas Hofstadter version of the Imago Dei , see the
"Gödel, Escher, Bach" illustration in the Jan. 15 screenshot below —

Tuesday, June 15, 2010

Imago, Imago, Imago
 

Filed under: General,Geometry — Tags: , , , , — m759 @ 11:07 am

Recommended— an online book—

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

See in particular

Valéry and the Discourse On His Method.

Pages 156-157—

Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. “Every act of understanding is based on a group,” he says (C, 1:331). “My specialty—reducing everything to the study of a system closed on itself and finite” (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one “group” undergoes a “transformation” and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: “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). Transformation theory is all over the place. “Mathematical science . . . reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind” (O, 1:36). “Psychology is a theory of transformations, we just need to isolate the invariants and the groups” (C, 1:915). “Man is a system that transforms itself” (C, 2:896).

Notes:

  Paul Valéry, Oeuvres (Paris: Pléiade, 1957-60)

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

Compare Jung’s image in Aion  of the Self as a four-diamond figure:

http://www.log24.com/log/pix10A/100615-JungImago.gif

and Cullinane’s purely geometric four-diamond figure:

http://www.log24.com/log/pix10A/100615-FourD.gif

For a natural group of 322,560 transformations acting on the latter figure, see the diamond theorem.

What remains fixed (globally, not pointwise) under these transformations is the system  of points and hyperplanes from the diamond theorem.

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