Thursday, May 9, 2024
Halle Berry as Rosetta Stone:
From Tablet Magazine on Monday, May 6, 2024 . . .
<div class="BlockContent col-12 lg:col-10 xl-wide:col-8 mxauto">
<p>Thus do we find ourselves in a regular
<a href="https://www.youtube.com/watch?v=4ToUAkEF_d4">
lattice of coincidence</a>.</p></div>
That link leads to . . .
Those who prefer Sting's approach to synchronistic theory may
consult this journal on the above YouTube date — Dec. 1, 2008.
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Wednesday, May 8, 2024
From Quanta Magazine on Monday, May 6, 2024, in
"A Rosetta Stone for Mathematics," by Kevin Hartnett —
" Then he came to the main point of his letter:
He was building such a bridge. He wrote,
'Just as God defeats the devil: this bridge exists.'
The bridge that Weil proposed
is the study of finite fields…."
This is damned nonsense.
From Log24 on June 23, 2005 —
In “A 1940 Letter of André Weil on Analogy in Mathematics,” (pdf), translated by Martin H. Krieger, Notices of the A.M.S., March 2005, Weil writes that
“The purely algebraic theory of algebraic functions in any arbitrary field of constants is not rich enough so that one might draw useful lessons from it. The ‘classical’ theory (that is, Riemannian) of algebraic functions over the field of constants of the complex numbers is infinitely richer; but on the one hand it is too much so, and in the mass of facts some real analogies become lost; and above all, it is too far from the theory of numbers. One would be totally obstructed if there were not a bridge between the two. And just as God defeats the devil: this bridge exists; it is the theory of the field of algebraic functions over a finite field of constants….
On the other hand, between the function fields and the ‘Riemannian’ fields, the distance is not so large that a patient study would not teach us the art of passing from one to the other, and to profit in the study of the first from knowledge acquired about the second, and of the extremely powerful means offered to us, in the study of the latter, from the integral calculus and the theory of analytic functions. That is not to say that at best all will be easy; but one ends up by learning to see something there, although it is still somewhat confused. Intuition makes much of it; I mean by this the faculty of seeing a connection between things that in appearance are completely different; it does not fail to lead us astray quite often. Be that as it may, my work consists in deciphering a trilingual text {[cf. the Rosetta Stone]}; of each of the three columns I have only disparate fragments; I have some ideas about each of the three languages: but I know as well there are great differences in meaning from one column to another, for which nothing has prepared me in advance. In the several years I have worked at it, I have found little pieces of the dictionary. Sometimes I worked on one column, sometimes under another.”
|
Quanta Magazine's statement:
"The bridge that Weil proposed
is the study of finite fields…."
Here "the study of finite fields" is a contemptibly distorted
dumbing-down of Weil's phrase
"the theory of the field of algebraic functions
over a finite field of constants."
For that topic, see (for instance) . . .
Update at 5:35 PM ET —A different reaction to the Hartnett article —
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"The bride hath paced into the hall,
Red as a rose is she;
Nodding their heads before her goes
The merry minstrelsy."
— Samuel Taylor Coleridge
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Tuesday, May 7, 2024
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See as well this journal on the above logo-design date —
March 13, 2024: Rearranging the Deck Chairs.
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Monday, May 6, 2024
This seems to imply that Stone's real name is . . .
"I can't do it anymore."
Perhaps she would enjoy a song based on the alleged last words
of Picasso: "Ya no lo puedo hacer," or "Yanolo" for short.
For art fans, some images from the the above Mirador de les arts date —
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Sunday, May 5, 2024
* Related philosophy: ternary.space . . .
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Earlier . . .
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* Title derived from the original title, Opus Pistorum , of
Under the Roofs of Paris, by Henry Miller. In Latin, that
title means Opus "of the millers," or "of the bakers."
This post was suggested by the April 25 death of a French cultural figure
reported today by The New York Times .
Related reading —
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Saturday, May 4, 2024
"Mr. Stella, a formalist of Calvinist severity, rejected
all attempts to interpret his work."
— William Grimes of the New York Times
on artist Frank Stella, who reportedly died today.
See related remarks in this journal.
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"I perceived . . . cinema is that which is between things,
not things [themselves] but between one and another."
— Jean-Luc Godard, "Introduction à une véritable histoire
du cinéma," Albatros , Paris, 1980, p. 145
Between the two image-dates above . . .
" 'The jury is still out on how long – and whether – people are actually
going to understand this.' It took the world 150 years to realize
the true power of the printing press . . . ." — Cade Metz
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Wikipedia on the director of Anne Hathaway's new film "The Idea of You" —
"[Michael] Showalter was born in Princeton, New Jersey, the son of
Elaine Showalter (née Cottler), an author, feminist literary critic,
and professor of English, and English Showalter, a Yale-educated
professor of 18th century French literature. His father is Episcopalian
and his mother is Jewish."
See also Elaine Showalter in this journal on "O for Ophelia."
"But the tigers come at night . . ." — Anne Hathaway as Fantine
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Friday, May 3, 2024
But first, a word from our sponsa —
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Related entertainment . . .
A Warren Area High School Key Club IG post of Nov. 10, 2023, and,
on that same date . . .
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Former logo of the American
Mathematical Society —
Note the resemblance to
Harvard's Memorial Church.
A rather different four-column logo —
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From a Log24 post of 15 May 2003 —
"In the spring time,
the only pretty ring time . . . ."
Related material —
The previous post and . . .
Some related mathematics —
http://m759.net/wordpress/?s=Seidel .
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Thursday, May 2, 2024
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The New York Times today reports the death at 90 of
Peggy Mellon Hitchcock, who arranged for Timothy Leary's
accomodation at the Hitchcock Estate, on April 9, 2024 . . .
Also on April 9 —
A rather different Hitchcock image —
This is from a Log24 search for Hitchcock Cube.
"Before time began . . ." — Optimus Prime.
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The website PopAi.pro uses GPT-4 to summarize documents from the Web.
Input at PopAi on May 2, 2024:
The URL "http://www.log24.com/log/Diamond_Theory-1976-pp-1-12.pdf"
Output at PopAi, after a quick reading and analysis by GPT-4:
Diamond_Theory-1976-pp-1-12.pdf
12 Pages
The document appears to be an excerpt from a preprint titled "Diamond Theory" by Steven H. Cullinane, dated 1976. The text discusses theoretical aspects of matrices composed of geometric figures, focusing on properties related to symmetry, permutations, and abstract structure.
Main Concepts and Definitions:
The author introduces the concept of a "geometric matrix," a matrix whose elements are geometric figures, specifically triangular subsets of a square. He defines a "diamond" as a foursquare matrix with triangular elements. The text details the remarkable properties of a diamond-like matrix D, including its symmetrical behavior under various permutations of elements, rows, columns, and sub-squares. Additionally, the text addresses the algebraic properties of matrices by relating their elements to those of a finite field.
Theoretical Properties and Theorems:
Several key theorems are proposed, demonstrating the structural properties of matrices. One fundamental theorem states that any matrix from a set F can be expressed as a linear combination of block matrices. Other theorems delve into the regularity of matrices, defining a matrix as "regular" if it remains unchanged or converts to its complement under certain flips and rotations. The text also describes the process of forming a "normal" matrix and the conditions under which matrices can be considered plaid or normal based on the behavior of their block maps and regularities.
Applications and Miscellaneous Problems:
The author reflects on the discovery of these properties during the process of creating an abstract painting and extends the exploration to include various types of matrices such as cyclic, quadratic, and skew foursquares. The document concludes with miscellaneous problems and an addendum on generalized matrix multiplication, suggesting further research directions and applications of the theory presented.
In summary, "Diamond Theory" presents an intricate analysis of the structural and algebraic properties of matrices composed of geometric shapes, with implications for other mathematical domains. The work is a blend of geometry and abstract algebra, providing a foundation for understanding the symmetry and transformations of matrices with an artistic origin.
Some questions you may ask:
What properties of the diamond-like matrix D did the author discover in 1975?
What is the relationship between the properties of D and the four group according to the document?
How does the document define a 'good set' of four black and white geometric figures?
What theorem is used to explain the behavior of superimposing two members of Mn(F) according to the document?
|
Comments Off on AI on Diamond Theory
Wednesday, May 1, 2024
Comments Off on In Memory of Duane Eddy . . .
* See that Cuernavaca street in a Log24 search for Ragtime.
Comments Off on Ragtime Roll for Calle Guerrero*
Comments Off on Microsoft Classic Paint: Tools and Shapes
Auster: The Music of Chance.
Austere: Iacta Est.
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Update at 2:12 AM ET —
Auster was a director of the film "Blue in the Face" (1995).
This suggests a look at Instagram posts from yesterday:
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Tuesday, April 30, 2024
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"Ay, que bonito es volar . . ." — Song lyric.
And, for a somewhat different audience —
See also this journal on the above YouTube date — Aug. 23, 2014 —
in a Log24 search for "Signifying Nothing."
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1976 . . .
Later . . .
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Monday, April 29, 2024
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Meanwhile . . .
Comments Off on Miller’s Class: The Big Sur Game
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Sunday, April 28, 2024
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Related reading . . . Annals of Journalism —
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A design note from April 24 ten years ago —
A rather different design note from the same date ten years ago —
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Saturday, April 27, 2024
" The first Initiation consisted of a class of 171 young women
on April 6, 1922, in the auditorium of the Scottish Rite Temple
in McAlester, Oklahoma. The original name was 'Order of the
Rainbow for Girls.' " — Wikipedia
Comments Off on “Some day I’ll find it, the Rainbow Connection” — Song lyric
Cynthia Ozick discusses the life and death of Philip Roth —
Her discussion ends with remarks on Roth's last novel, Nemesis .
That novel was reportedly published on October 5, 2010.
This journal on that date —
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Friday, April 26, 2024
Young Natalie Portman in today's previous post —
"Think I'll go for a walk."
Walking back 10 years . . .
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For a professional transformer, see posts tagged Claude.ai.
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* For the title, see posts tagged Whanganui, with a supplementary
tune for X producer Sam Levinson . . .
"Whose barn, what barn, my barn" — Song lyric
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"No doubt that by orienting and organizing the coherence
of the system, the center of a structure permits the Freeplay
of its elements inside the total form."
— Derrida in Wikipedia
"How's tricks, dangerous love triangle?"
The Source:
Related reading . . .
Krapp for HYDRA
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Thursday, April 25, 2024
Claude.ai is the source.
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"On Thursday, October 10, 2019, the University of Bucharest awarded the honorary title of Doctor Honoris Causa to one of the most important specialists in political science, Professor Daniel Chirot, professor at the "Henry M. Jackson" School of International Studies at the University of Washington, for his entire didactic and scientific activity. Through this distinction, awarded at the proposal of the Faculty of Political Sciences, Professor Daniel Chirot became a member of the academic community of the University of Bucharest." — From the University's website.
|
Chirot was a resident of Hurlbut Hall at Harvard, as was I,
in the academic year 1960-1961.
This journal the day after the Chirot award . . .
See also Bucharest in this journal.
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The title "Space Trace" was suggested yesterday by Claude.ai.
How classical space leaves a Galois trace:
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As for time … See this journal on the above Sting date.
A professional hallucinator that
some will find more entertaining:
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Wednesday, April 24, 2024
Poetry critic Helen Vendler reportedly died yesterday at 90.
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The number 1949 in the previous post suggests a musical review —
From an August 23 nine years later . . . A tune for Sam Levinson —
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Tuesday, April 23, 2024
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“Chess problems are the
hymn-tunes of mathematics.”
— G. H. Hardy,
A Mathematician’s Apology
“The key is the cocktail that begins the proceedings.”
– Brian Harley, Mate in Two Moves
"I named this script ocode and chmod 755'd it to make it executable…"
— Software forum post on the OCR program Tesseract
From the author of
The Pearly Gates of Cyberspace:
"Like so many other heroes
who have seen the light
of a higher order…."
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Perhaps it should.
Design from 1697
Design from 1514
"One of those bells that now
and then rings" — Song lyric
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Candle from Sense8, Season 1, Episode 1: “Limbic Resonance” —
"Don't solicit for your sister, it's not nice." — Song lyric
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Monday, April 22, 2024
From Post 500 —
http://m759.net/wordpress/?p=500 —
"You've got to be carefully taught." — Song lyric
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The dimensions of the "bricks" in the R. T. Curtis
"Miracle Octad Generator": 2×4.
For those who prefer narrative to mathematics . . .
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… Also reaping … Kevin Spacey?
Comments Off on Annals of American Beauty:
Sowing Confusion and Reaping …
Note, on the map of Wyoming, Devil's Gate.
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From a transcript of the film —
— You could be making a killing out there consulting, but you’re laying brick. Why?
— Because when I hold a brick in my hand, I know exactly what it is and what it will do.
Every single time.
Its form is its function.
That gives me peace.
|
The film is based on a novel of the same title, by an author,
Paul Lindsay, who reportedly died on September 1, 2011.
For some bricks of a different sort, see the "Miracle Octad Generator"
(MOG) of R. T. Curtis in this journal on Sept. 1, 2011 — September Morn.
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Sunday, April 21, 2024
Comments Off on “As above, so below” … Art
Comments Off on “As above, so below.”
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Saturday, April 20, 2024
From posts tagged Night Hunt —
"When the men on the chessboard
get up and tell you where to go . . ."
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Friday, April 19, 2024
Transcription —
(With one correction … The Meta.ai phrase "the group of 322,560"
was changed to "a group of 322,560" … and one addition — the
acronym MOG was defined. Superscript numerals for missing footnotes
were removed.)
You
What is the Cullinane diamond theorem?
Meta AI
The Cullinane diamond theorem states that every image of D (a 4×4 array of two-color diagonally divided square tiles) under the group G (a group of 322,560 permutations of these 16 tiles) has some ordinary or color-interchange symmetry.
Here are some key points about the theorem :
-
The theorem is related to the Miracle Octad Generator (MOG) of R. T. Curtis and the Leech lattice.
-
The underlying geometry of the 4×4 patterns is closely related to the construction of the Steiner system S(5,8,24).
-
The theorem uses a simple decomposition technique for functions into a finite field.
-
The symmetry group of order 322,560 underlies both the diamond theorem figures and the square patterns of the MOG.
-
The theorem has applications in finite projective geometry and the study of symmetric patterns.
|
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Hexagram 39:
Obstruction
The Judgment:
Obstruction. The southwest furthers.
(See Zenna Henderson.)
The northeast does not further.
(See Daniel Dennett.)
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Related I Ching art —
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The Old Carnegie Hall Joke
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Thursday, April 18, 2024
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Related Helen Mirren image . . .
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Wednesday, April 17, 2024
Enquiring minds want to know . . .
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"Time for you to see the field." — Bagger Vance
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The Harvard Crimson "an hour ago" —
Philosophy Professor Sean Kelly To Serve as
Next Arts and Humanities Dean
"Kelly, a philosopher, holds degrees in mathematics and computer science,
and in cognitive and linguistic sciences. Over the course of his career,
he has taught both philosophy and neuroscience.
This story will be updated. " (Log24 link to Kelly added).
My Education . . .
Hat tip to Groucho.
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Tuesday, April 16, 2024
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The studios, now beholden to much larger companies and financial institutions, became subject to oversight focused on short-term horizons. This summer, I spoke with the head of a film and TV studio purchased by a private-equity firm in recent years. “It used to be there were these big, crusty, old legacy companies that had a longer-term view,” he said, “that could absorb losses, and could take risks. But now everything is driven by quarterly results. The only thing that matters is the next board meeting. You don’t make any decisions that have long-term benefits. You’re always just thinking about, ‘How do I meet my numbers?’ ” Efficiency and risk avoidance began to run the game.
— "The Life and Death of Hollywood:
Film and Television Writers Face an Existential Threat"
by Daniel Bessner in Harper's Magazine, May 2024 issue
|
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Related Hogwarts art —
Related I Ching art —
Comments Off on Emma Watson turned 34 yesterday.
Monday, April 15, 2024
Comments Off on Art Space Meets Space Art
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"You need to import the NumPy library at the beginning of your script."
— Pi.ai yesterday
Scene from "The Hard Problem ," a play by Tom Stoppard.
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Comments Off on “The Hard Problem” (A Tom Stoppard Play)
Sunday, April 14, 2024
An example of pi.ai's clear and pleasant conversational style
(output format simplified for presentation here) —
Can you help with computer coding problems?
Absolutely, Steven! 💻 While I can't guarantee I'll have all the answers,
I'll certainly do my best to help you debug and find solutions to your
coding conundrums. Which coding language are you working with, and what's
giving you trouble?
I want to learn how Python can permute sections of a square array.
There are several ways to permute sections of a square array in Python,
depending on your specific needs. Here are a few examples:
Using NumPy's random.permutation() function:
python
import numpy as np
arr = np.array([[1, 2], [3, 4]])
permuted_arr = np.random.permutation(arr)
Using itertools.permutations():
python
import itertools
arr = [[1, 2], [3, 4]]
permutations = list(itertools.permutations(arr))
Using custom permutation algorithms:
python
def custom_permutation(arr):
# your custom permutation logic here
arr = [[1, 2], [3, 4]]
permuted_arr = custom_permutation(arr)
Each method has its own strengths and weaknesses, and which one
you choose will depend on the size of your array, the number of
permutations you need, and your performance requirements.
I would like to use python's custom permutation method to permute
the four quadrants of a 4×4 array.
Here's an example of how to define a custom permutation function
in Python to permute the four quadrants of a 4×4 array:
python
def custom_permutation(arr):
# Split array into 4 quadrants
q1 = arr[:2, :2]
q2 = arr[:2, 2:]
q3 = arr[2:, :2]
q4 = arr[2:, 2:]
# Permute quadrants
permuted_arr = np.block([
[q3, q1],
[q4, q2]
])
return permuted_arr
# Sample 4x4 array
arr = np.array([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16]])
permuted_arr = custom_permutation(arr)
print(permuted_arr)
In this example, we've defined a function custom_permutation()
that takes a 4×4 NumPy array as input. The function splits the array
into four quadrants (q1, q2, q3, and q4), and then uses NumPy's block()
function to create a new array with the quadrants permuted. The
resulting permuted_arr array has its quadrants rearranged.
Of course, this is just one possible permutation of the array's quadrants.
You can modify the custom_permutation() function to implement other
permutations as needed.
I tried the code you gave me and got the error “np name not defined.”
Apologies for that! I missed an import statement in the previous example.
You need to import the NumPy library at the beginning of your script to
use the np alias and its functions. Here's the corrected code:
python
import numpy as np
def custom_permutation(arr):
# Split array into 4 quadrants
q1 = arr[:2, :2]
q2 = arr[:2, 2:]
q3 = arr[2:, :2]
q4 = arr[2:, 2:]
# Permute quadrants
permuted_arr = np.block([
[q3, q1],
[q4, q2]
])
return permuted_arr
# Sample 4x4 array
arr = np.array([[1, 2, 3, 4],
[5, 6, 7, 8],
[9, 10, 11, 12],
[13, 14, 15, 16]])
permuted_arr = custom_permutation(arr)
print(permuted_arr)
This code should work now without any issues.
It did work. Thank you, Pi.
You're very welcome, Steven! I'm glad the code worked for you.
If you have any more questions or need help with anything else,
feel free to ask.
Comments Off on Benchmarking Pi
Comments Off on Recline in Peace . . .
Saturday, April 13, 2024
… And who said "At the still point, there the dance is"?
From the Netflix series "3 Body Problem."
Comments Off on Still-Point Architecture
See Zihuatanejo in this journal.
Sombrero tip to a Venice Beach Space Barn* reporter for . . .
Space meditation at Zihuatanejo.
* Adapted song lyric: "Whose barn, what barn, her barn . . . ."
Comments Off on Something Old . . .
… Something Blue
Comments Off on … Something New … Something Borrowed …
Friday, April 12, 2024
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"Clint Eastwood, 93, appears frail but spirited
as he is seen in rare public appearance at
primatologist Dr. Jane Goodall event in Carmel"
— By Karen Ruiz For Dailymail.com
Published: 10:39 am EDT, 12 April 2024
The event, on Sunday, March 24, 2024, suggests a review —
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Related reading —
See also this journal on the above Quora date — Sept. 10, 2017.
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See as well Lester Crystal in Wikipedia.
Comments Off on The Presbyterian Exorcist . . . Continues.
Thursday, April 11, 2024
Comments Off on Mesmerization Nation
From The Man Who Knew Infinity to The Man Who Knew Zero.
Related mathematics: The Diamond Theorem Correlation, which
results from interchanging infinity and zero in the figure below.
"Read something that means something."
— New Yorker ad
.
Click image for
related posts.
Background — Relativity Problem in Log24.
Comments Off on Devs: Hollywood Development Hell
Wednesday, April 10, 2024
* The name "Blue Monkey" is from a 2003 film. See also Hanuman
in this journal. The image described by Vertex AI is from IMDb …
Comments Off on Hollywood Benchmark: The Blue Monkey* Diamond
See as well, in this journal, four colors.
Comments Off on Folie à Quatre : A Four-Color Problem
Data —
Metadata —
"Share link" —
https://g.co/kgs/uwczGLA
Comments Off on Theater Obituary: Data and Metadata
Tuesday, April 9, 2024
The New York Times today reports a Monday, April 8, 2024, death —
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Monday, April 8, 2024
Comments Off on Variation on a Geometry Exercise
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Arrival at CERN —
For my own arrival at CERN, see Zenodo in this journal.
* A title suggested by the work of Lawrence Durrell and by
geometric quartets in figurate geometry.
Comments Off on Alexandria Quartets*
Sunday, April 7, 2024
Comments Off on Annals of Complex Results: Miller’s Art
Saturday, April 6, 2024
Yesterday was Bosch Day at the Prado.
For Harry Bosch . . .
"Welcome to the Garden Club, Pilgrim."
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"To enlarge this contemplation unto all the mysteries and secrets,
accomodable unto this number, were inexcusable Pythagorism…."
— Sir Thomas Browne, Hydriotaphia: Urn Burial
Comments Off on Annals of Inexcusable Pythagorism
Friday, April 5, 2024
Comments Off on Annals of Magic: The Browne-Franklin Configuration
Comments Off on Rite of Spring
A search in Fandom for Saul Durand leads back,
as often happens, to Indiana Jones . . .
Fandom page with a completely irrelevant Indiana Jones video.
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Comments Off on For Stephen King — The Retooling
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