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.
One of a Kind Malfunction
Related literary remarks —
See also "Circle in the Square" and Fulcrum.
*For the title phrase, vide Wikipedia.
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.
Continuing the Ojo de Dios theme from recent Delving posts . . .
. . . and from posts now tagged Tepoztlan Dance . . .
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 . . .
*
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by Google Gemini AI Monday, March 4, 2024
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: 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:
Proof: 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!
1. www.hellenicaworld.com/Science/Mathematics/en/MathieuGroup.html
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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
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 —
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.
"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."
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 —
See also this journal on February 24, 2024: Wittenborn.
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."
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."
“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 . . .
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" —
"Right through hell there is a path…" — Under the Volcano
Some Context:
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:
|
According to Chu Hsi [Zhu Xi],
“Li” is
— Smith, Bol, Adler, and Wyatt, |
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.
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.
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New from Harlan Kane: The Wittenborn Date
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"Always with a little humor." — Dr. Yen Lo
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." |
For Focillon's "immobility" that "sparkles with metamorphoses,"
see Theodore Sturgeon's imagined "Dreaming Jewels ."
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.
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
"Looking for what was, where it used to be" — Wallace Stevens
— "Is this your business?"
— "No, but this is."
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…
Reading suggested by a phrase in The New York Times today —
Vocabulary for some combinatorial arts . . .
SEXadecimal and HEXadecimal —
Related entertainment — "Mathematical Possibilities"
At https://shc759.wordpress.com today —
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.
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
The previous post, and Wednesday's roommate, suggested the above title.
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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." |
From a post of August 17, 2023 —
Color of the diamond shape —
"Blue jean baby, L.A. lady…" — Song lyric
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):
"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.
From Log24 on September 19, 2023 —
Adapted image —
Related reading —
Related art — Square Round and Round Square.
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 . . .
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."
The "bride's chair" is the figure illustrating Euclid's proof
of the Pythagorean theorem (click image to enlarge) —
A somewhat simpler approach —
"Drop me a line" — Request attributed to Emma Stone
Detail of a February 16 illustration from The Harvard Crimson .
The URLs powerset.space and powerset.group are now operative.
Related vocabulary: See Boolean Functions Review (Log24, May 15, 2023).
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.
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.
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KESQ-TV News, Channel 3, Palm Springs, California
Modernism Week gears up to host thousands 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 —
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
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 dark illimitable Ocean" — John Milton, Paradise Lost , Book II
"All is number" — Attributed to Pythagoras
|
"For a fraction of a second, Phocan senses |
From the MANIFESTO link in the Breakthrough Prize page above —
Our Mission . . . Should We Choose to Accept It
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
Related material: Theodore Sturgeon's novel The Dreaming Jewels
and his story "What Dead Men Tell" . . .
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 |
From a post on Trevanian in December 2005 —
"And we may see
the meadow in December,
icy white and crystalline."
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
This post was suggested by the
"Night of Lunacy" post of May 5, 2013.
Reality, of course, includes the release dates of unreality products . . .
For instance, the release date (Nov. 24, 2020) of the novel Ready Player Two .
https://www.imdb.com/title/tt7979142/
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See as well, in this journal, other posts tagged Night Clerk.
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 . . .
A review of "Square Inch Space" in this journal is suggested by . . .
Click the above image for the source of the Chinese characters —
Twelfth Night 2024 was the dies natalis of
comedy writer Brian McConnachie.
From this journal on that date —
Funeral scene from "Being There" (1979)
Related material — "You're Sixteen," by the Sherman Brothers.
(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.
|
“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
The hardcover first edition was published by Knopf |
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"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, |
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."
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:
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.
* nytimes.com/2024/02/08/arts/music/mojo-nixon-dead.html and
latimes.com/entertainment-arts/music/story/2024-02-08/mojo-nixon-obit
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
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.
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 —
"And so I enter into evidence
My tarnished coat of arms . . . ."
— Taylor Swift, annotation for a new album.
* The author of the above "math tale" reportedly died on
January 6, 2024 — The Feast of Epiphany.
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.
-Thas-2020.jpg)
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." —
A poem written yesterday by Microsoft Copilot —
The prompt: "Write a poem … about the Cullinane diamond theorem."
|
In the mind of the mathematician,
Four-diamond figure, a 4×4 array,
Every G-image of the four-diamond figure,
The symmetry of the line diagrams,
And this symmetry must be shared by the entire pattern,
The 35 structures of the 840 = 35 x 24 G-images,
So here lies the beauty of the Cullinane diamond theorem, |
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.
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."
"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."
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