A related question — From posts now tagged Weil Misery —
(See today's previous post) . . .
The previous post suggests a review . . .
The above remarks on topology are, of course, about as well-informed
as the remarks of Barry Mazur on locales .
"William Blake's statement in The Marriage of Heaven and Hell
'Eternity is in love with the productions of time' is an adumbration
of the paradoxology of the game of hide-and-seek that Non-duality
is playing with and in celebration of itself in Ia divina commedia of
this night of its dream."
— Joseph Campbell in "The Inner Reaches of Outer Space" (©1986)
Related material from a Log24 search for "inscapes4"—
(In memory of Robert Zimmer, a mathematician
who reportedly died yesterday)
This journal on the above date —
Abstract: Boolean functions on a triangular grid.
Note: It seems that the above rearrangement of a square array
of hyperplanes to a triangular array of hyperplanes, which was
rather arbitrarily constructed to have nice symmetries, will
answer a question posed here on Dec. 15, 2015.
The reference to "Magic: The Gathering" in the previous post
suggests a review of "gathering" tales that I personally prefer —
"So far, AIs produce abstract, almost surreal ideas, that
may lead you somewhere but have no consistent purpose."
— Greg Rutkowski, quoted on May 8, 2023, as below:
Source Code —
<title>What can be done to stop generative AI art? | Creative Bloq</title>
<meta name="pub_date" content="2023-05-08T07:30:27+00:00">
<meta name="description" content="These professional artists are
fighting back against generative AI art.">
<link rel="canonical" href="https://www.creativebloq.com/features/
what-can-stop-generative-ai-art">
What if the AIs are named Tara Hernandez and Damon Lindelof?
Yesterday's "Electric Avenue" post suggests an image by Rutkowski
from "Magic: The Gathering" . . .
… who reportedly died yesterday — See April 11, 2019.
CHICAGO–(BUSINESS WIRE) — It is with profound sadness
that Equity Residential (NYSE: EQR) mourns the death of its
Founder and Chairman, Samuel Zell, who died today at age 81.
By Allison Morrow, CNN Updated 12:38 PM EDT, Thu May 18, 2023 Sam Zell, the Chicago real-estate magnate whose knack for buying up distressed assets turned him into a billionaire and earned him the nickname “grave dancer,” died on Thursday, his company said. He was 81. Equity Residential, the company he founded decades ago, did not provide a cause of death but described Zell as an “iconic figure in real estate and throughout the corporate world.” Among his wide-ranging portfolio of investments were distressed assets in real estate and in media, including an ultimately disastrous bet on the Tribune Company. Zell had a personal net worth of $5.9 billion, according to the Bloomberg Billionaires Index. Zell had a penchant for scooping up cheap real estate and selling it later at a profit, a strategy he outlined in a 1978 article titled “The Grave Dancer,” which became his nickname in the industry. “I was dancing on the skeletons of other people’s mistakes,” he wrote. |
"Martin told us about his work on machine learning…."
— Peter J. Cameron reports on last week's (May 10 and 11)
London Combinatorics Colloquia 2023.
Related material — Boolean Functions in this journal and in a book
from May 16, 2011 . . .
Some historical background on machine learning —
https://tripleampersand.org/kernelled-connections-perceptron-diagram/ .
From the American Mathematical Society today —
Robert Earl Tubbs (1954-2023)
May 15, 2023
"Tubbs, associate professor of mathematics at
the University of Colorado Boulder, died April 11, 2023,
at the age of 69. He received his PhD in 1981 from
Penn State University under the supervision of
W. Dale Brownawell. His research interests included
number theory, especially transcendental number theory,
the intellectual history of mathematical ideas and mathematics,
and the humanities."
This journal on the dies natalis of Tubbs had the third of three
posts tagged "Space and Form." Those posts dealt with European
cultural history related to Tubbs's interests. The "Space and Form"
posts, along with today's previous Log24 post, suggest a review of
the Nov. 10, 2021 post titled European Culture. An image from that post —
Those who share Cassirer's enthusiasm for myth may regard the
above Josefine Lyche version of my work as a sort of "secret writing,"
to quote a phrase of Cassirer's I find very distasteful. But there is nothing
secret about it, although there is some resemblance to written characters.
This post's title was suggested by a Salinger quote in the European Culture post.
Update on the next day, May 17 —
Further reading in Cassirer's Mythical Thought indicates that in the
passages above, on Schelling, he may be presenting a parody of
Schelling when he writes "a poem hidden behind a wonderful
secret writing." Later, on page 10, he asks, sensibly,
"… is there, perhaps, a means of retaining the question
put forward by Schelling's Philosophie der Mythologie
but of transferring it from the sphere of a philosophy of
the absolute to that of critical philosophy?"
There has reportedly been "an upsurge of interest" in Cassirer —
By ChatGPT* —
What is the Cullinane diamond theorem? The Cullinane Diamond Theorem, also known as the Diamond Theorem, is a result in combinatorial mathematics proposed by Steven H. Cullinane. The theorem explores connections between finite geometries, algebraic structures, and combinatorial designs.
The theorem is primarily concerned with four related structures: 2. Vector spaces: The theorem connects finite vector spaces over finite fields to the aforementioned finite geometries. 3. Boolean functions:* The theorem establishes relationships between the finite geometries and certain Boolean functions derived from them.
4. Symmetry groups: The theorem involves symmetry groups associated with the finite geometries. * With one revision by Cullinane: "Boolean functions" replaces "Boolean algebras." See (for instance) M. A. Harrison, “On the classification of Boolean functions by the general linear and affine groups,” Journal of the Society for Industrial and Applied Mathematics 1964 12:2, 285-299. |
The previous post included an illustration by Solomon Golomb
from his 1959 paper "On the Classification of Boolean Functions."
This suggests a review of some later work in this area —
This post was suggested by the word "Boolean" in a May 10
ChatGPT response —
In the above, "Boolean algebras" should be "Boolean functions,"
as indicated by Harrison's 1964 remarks.
"Stencils" from a 1959 paper by Golomb —
These 15 figures also represent the 15 points of a finite geometry
(Cullinane diamond theorem, February 1979).
This journal on Beltane (May 1), 2016 —
(Title phrase by Lee E. Mosley)
"Where past and future are gathered" — T. S. Eliot
(Image from a post of June 28, 2020.)
The above title. by one Lee E. Mosley, is from
"CreateSpace Independent Publishing Platform;
1st edition (June 4, 2017)."
From the preface —
"So simple . . . ."
"Building blocks"? — See the literature of pop physics.
Natural companions to building blocks, are, of course,
"permutation groups."
See the oeuvre of physics writer John Baez —
For instance, in a Log24 post from the above Mosley
publication date — June 4, 2017 —
Variety.com May 8, 2023, 1:45 AM PT —
“Pema Tseden, a famous Tibetan director, screenwriter and
professor at the Film School of the China Academy of Art,
died in Tibet in the early hours of May 8 due to an acute illness."
"The news was reported by the China Academy of Art."
The time in Lhasa, Tibet, is 12 hours ahead of New York time.
From this journal in the afternoon of May 7 (New York time) —
For a relationship between the above image and classic Chinese culture,
see Geometry of the I Ching.
A memorial image from Variety —
Tseden with the award for best screenplay at Venice on Sept. 8, 2018.
See also that date in this journal . . . Posts now tagged Space Structure.
Summary of a TV episode from yesterday that seems like
it was written by a hallucinating chatbot —
In other chatbot news . . .
As for 2001 . . . See "Notes from a (Paper) Journal 1993-2001."
(Title purloined from Marie-Louise von Franz.)
BCE/CE — A game with three letters … See Michener Game.
BC/AD — A game with four letters … See Eddington Game.
ABCDE — A game with five letters … See Simplex.
Today's "Mrs. Davis" episode ends with Sister Simone
on a beach being sung to by a beachgoer choir.
This bizarre plot twist suggests some other images —
Also from March 8, 2020 —
The above Puchner remarks on the Communist Manifesto featured
a banner at the top crediting "California State University, Chico."
More recently, from this journal —
Besides "Mrs. Davis," this post was suggested by . . .
https://lareviewofbooks.org/article/
is-multiculturalism-an-oxymoron-on-martin-puchners-culture/ .
Images suggested by the above route number, 948 —
This post was suggested by the reported death last Friday (May 5)
at 91 of Christian Alexander Maria Strachwitz, folk music collector.
See also posts now tagged Parable.
“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions by
some central solid essence.
I tried to reconstruct
the central object, and
came up with this book.”
Related images —
Previous ChatGPT responses to questions like those below
have been, to put it mildly, lacking in accuracy. But there has
lately been considerable improvement . . .
"Ideally, a single joint embedding space — where many different kinds
of data are distributed — could allow a model to learn visual features
along with other modalities."
— https://ai.facebook.com/blog/imagebind-six-modalities-binding-ai/
The most recent "Blacklist" episode suggests a review —
"Where past and future are gathered" — Four Quartets
"To achieve our mission of bringing everyone the inspiration
to create a life they love, we need to personalize our content
with our user’s interests and context, taking into consideration
feedback a user has given on their Pinterest journey; i.e., we
need a strong representation of our users."
— From the arXiv one year ago, on 9 May 2022
See as well this journal on that date — "Will the Circle."
"Long promised road
Flows to the source, gentle force"
— The Beach Boys
From a post of June 10, 2013 —
For the title, see Logos in this journal.
Some examples —
"Please wait as your operating system is initiated."
This post is in memory of Adam Brace, a British comedy director.
His dies natalis is reported to be April 29, 2023.
See also Dramarama and, from the above story's date . . .
From "The Postman," the most recent "Blacklist" episode —
Related material —
A Bosch Xmas
Cicely Tyson as the future Mrs. Davis … Mrs. Miles Davis —
The above title was suggested by the previous post.
Wikipedia on "Sunrise Semester" in 1976 —
Neil Postman taught a course, Communication,
The Invisible Environment, in the Fall of 1976.[7]
The cited link —
See also a search for Postman in this journal.
For the above title, see a Log24 search.
Related material:
Oscar Hammerstein in Episode 6 of "Mrs. Davis" —
Flores para los Muertos
The above illustration is from Log24 on the dies natalis —
day of birth into heaven, in the Catholic tradition —
of Grace C. Hertlein, a sort of patron saint of computer art
from Chico, California, who reportedly died at 91 in 2015.
It supplies the parts missing from a J. K. Rowling design…
See Cinco de Mayo , 2011.
(TItle suggested by the song lyric "Hey, ninety-eight point six . . .")
(From a search in this journal for McGlashan )
The title is taken from the New York Times obituary
of an artist who reportedly died today.
See also the retrofuture concept in this journal.
This journal ten years ago today —
This journal on April 10, 2022 —
Be careful what you wish for.
You might get . . .
Today's Google Doodle honors a Chinese-American photographer
who reportedly died on January 27, 2021.
From his dies natalis (birth into heaven, in the Catholic tradition) —
See as well some background on a Chinese-related cube.
Related narrative —
This post was suggested by the Möbius Dick air date —
August 4, 2011 — in this journal.
"Extremely elementary," my dear Watson.
"I stood quietly, like a fսcking moron . . ."
Read more at:
https://tvshowtranscripts.ourboard.org/
viewtopic.php?f=1820&t=62232
A trip down Memory Lane with the Eurythmics, and
a lullaby from Steely Dan.
"Some prefer more rural tunes . . . "
"I want to ride to the ridge where the West commences . . ."
* See a Log24 post of April 26, 2023.
The New York Times reports a March 26 death —
* Results of a title search —
For Thalia — "Apart from that, Mrs. Kaplan . . ."
Exercise: Show that Dürer's 1514 "magic" square is an affine automorphism.
For a solution, see other posts now tagged Affine Squares.
Continued from yesterday's "Kernel" —
The ACM (Association for Computing Machinery)
has a news release today on an expert on "kernels,"
in the sense that they are used in AI —
"Schölkopf [link added] is recognized for his
widely used research in machine learning,
advancing both mathematical foundations and
a broad range of applications in science and
industry."
From Schölkopf in 2002 —
From my hometown newspaper
on the eve of my 16th birthday —
"Just the facts, ma'am."
— A saying falsely attributed to the
LAPD's Sergeant Joe Friday .
"Piotr Grochowski's 'Miracles and Visionaries in the Digital Age'
explores the impact of digital technolgies in Catholic Apparitional
movements." (links added) — Journal of American Folklore ,
Fall issue, October 2022 preview.
As for "Miracles and Visionaries," I prefer the literature associated
with the 1974 Miracle Octad Generator of R. T. Curtis.
From a post of September 24, 2011 —
Weyl on coordinate systems,
Cassirer on the kernel of being,
and A Study in Art Education.
See posts tagged "The Next Level."
Perhaps Isadore Singer now has a clue . . .
See his phrases "manic as hell" and "pregnant as hell."
See also Illinois Beltane.
The First of May is known to some as Law Day, and to others as Lei Day.
Related narrative: Bosch by Snaith . See also . . .
Neil Welliver, great American painter, father of Titus Welliver
Titus Welliver Says "Losing His Way" Led Him Back to Painting
"Carny, also spelled carnie, is an informal term
used in North America for a traveling carnival
employee, and the language they use, particularly
when the employee operates a game ("joint"),
food stand ("grab", "popper" or "floss wagon"),
or ride ("ride jock") at a carnival." — Wikipedia
* See Gresham in this journal.
See also Tolkien on allusions.
Discuss —
From some Canadian legal boilerplate —
E. Be able to provide complete, clean, unencumbered
chain of title for the Project, must have all the rights,
releases and clearances necessary to produce, own and
exploit the Project and for deployment of the Project . . . .
Weak Links in the Chain of Title —
A 2006 biography of geometer H.S.M. Coxeter:
The Aleph (implicit in a 1950 article by Coxeter):
Click on images
for further details.
The New York Times reports a March 2 death —
"A product of Britain’s Royal Academy of Art,
Mr. Stobart moved to the United States in 1970,
when conceptual art, Op Art and minimalism
were riding high in the wake of Abstract Expressionism.
Affable, unassuming and unfailingly candid, Mr. Stobart
would have none of it. 'I’ve never bought it, and the
general public has never bought it either,' he said of
abstract art in an interview with The Boston Globe in 1986.
'That’s a lot of baloney, that stuff.' ”
See also duck art from the Groucho school.
Note that if the "compact Riemann surface" is a torus formed by
joining opposite edges of a 4×4 square array, and the phrase
"vector bundle" is replaced by "projective line," and so forth,
the above ChatGPT hallucination is not completely unrelated to
the following illustration from the webpage "galois.space" —
See as well the Cullinane diamond theorem.
For the image at upper left below, see
https://www.google.com/doodles/celebrating-alan-rickman.
On the Rickman domain . . .
See as well "Stella Maris" in this journal.
From this journal on 4/01, 2009:
The Cruelest Month —
"Langdon sensed she was toying with him…." — Dan Brown
Less playfully . . .
See also the show tune from the end of "Second Tree from the Corner,"
a classic New Yorker short story by E. B. White. (And related posts.)
"You got your demons and you got desires
Well, I got a few of my own" — Song lyric
Click the above box for a related New Yorker article.
See also, in this journal, Baudelaire and Psychonauts.
From the previous post, "The Large Language Model,"
a passage from Wikipedia —
"… sometimes large models undergo a 'discontinuous phase shift'
where the model suddenly acquires substantial abilities not seen
in smaller models. These are known as 'emergent abilities,' and
have been the subject of substantial study." — Wikipedia
Compare and contrast
this with the change undergone by a "small space model,"
that of the finite affine 4-space A with 16 points (a Galois tesseract ),
when it is augmented by an eight-point "octad." The 30 eight-point
hyperplanes of A then have a natural extension within the new
24-point set to 759 eight-point octads, and the 322,560 affine
automorphisms of the space expand to the 244,823,040 Mathieu
automorphisms of the 759-octad set — a (5, 8, 24) Steiner system.
For a visual analogue of the enlarged 24-point space and some remarks
on analogy by Simone Weil's brother, a mathematician, see this journal
on September 8 and 9, 2022.
"… sometimes large models undergo a 'discontinuous phase shift'
where the model suddenly acquires substantial abilities not seen
in smaller models. These are known as 'emergent abilities,' and
have been the subject of substantial study." — Wikipedia
See also the first five episodes of "Mrs. Davis."
The reference to metaphysics in today's previous post
suggests a review of the phrase "logical point of view."
"Many of these same characters wonder whether
they are creating these special places anew, or
are merely finding places which already exist
(very much like 'the problem of universals' in
classical metaphysics)."
— Wikipedia article on author Roger Zelazny
Related material —
* For the title, see a story by Zelazny.
This journal on April 19, 2004 —
"Follow the fellow who follows a dream."
Melissa Errico
in Finian's Rainbow
"Give her a song like … 'Look to the Rainbow,'
and her gleaming soprano effortlessly flies it
into the stratosphere where such numbers belong.
This is the voice of enchantment…."
"Follow the fellow…." Or the girl.
See posts now tagged Birthday Girls
in honor of a Coachella Valley native
born on September 27, 2002.
"Born in 1965, James Wood grew up in Durham,
where his father lectured in zoology at the university.
He attended Durham choir school, where he was
a cathedral chorister, and Eton College, before
studying at Jesus College, Cambridge."
— The Independent , 19 April 2003.
* For the title, see Wikipedia.
For an illustration, see Jenna Ortega.
For Wood himself, see (for instance)
some Log24 posts.
"Bedknobs and Broomsticks is a 1971 American musical fantasy film
directed by Robert Stevenson and produced by Bill Walsh for
Walt Disney Productions. It is loosely based upon the books
The Magic Bedknob; or, How to Become a Witch in Ten Easy Lessons
(1944) and Bonfires and Broomsticks (1947) by English children's author
Mary Norton."
Glow with the Flow
"In the digital cafeteria where AI chatbots mingle,
Perplexity AI is the scrawny new kid ready to
stand up to ChatGPT, which has so far run roughshod
over the AI landscape. With impressive lineage, a wide
array of features, and a dedicated mobile app, this
newcomer hopes to make the competition eat its dust."
— Jason Nelson at decrypt.co, April 12, 2023
What Barnes actually wrote:
"The final scene — the death of Simone most movingly portrayed,
I understand, by Geraldine Librandi, for the program did not specify
names — relied on nothing but light gradually dying to a cold
nothingness of dark, and was a superb theatrical coup."
(Title suggested by recent episodes of "The Blacklist.")
"It's the system that matters.
How the data arrange
themselves inside it."
The Pynchon quote is from posts now tagged Map Systems.
See this journal on January 1, 2011, said to be the day that
an interesting Czech girl (see "Blue Czech Marks") turned 18.
* For the title, see an appealing 2013 fantasy starring Lily Collins.
Collins herself turned 18 on March 18, 2007.
“She never looked up while her mind rotated the facts,
trying to see them from all sides, trying to piece them
together into theory. All she could think was that she
was flunking an IQ test.”
— Steve Martin, An Object of Beauty
Byron Gogol is a tech magnate in the HBO series "Made for Love."
See also Mykonos in this journal and . . .
The logo of MUSE, the band —
A logo I prefer . . .
Related material from a post of October 2020 —
Related material from a post on the above Reddit date —
A Story That Works
“There is the dark, eternally silent, unknown universe;
and lastly, there is lonely, story-telling, wonder-questing, – Fritz Leiber in “The Button Molder“ |
"…something I once heard Charles M. Schulz say,
'Don't worry about the world coming to an end today.
It's already tomorrow in Australia.'"
— William F. House at Xanga, quoted here on
January 31, 2003
In memory of Dame Edna:
An image from this journal at 5:11 PM ET yesterday —
"In the digital cafeteria where AI chatbots mingle,
Perplexity AI is the scrawny new kid ready to
stand up to ChatGPT, which has so far run roughshod
over the AI landscape. With impressive lineage, a wide
array of features, and a dedicated mobile app, this
newcomer hopes to make the competition eat its dust."
— Jason Nelson at decrypt.co, April 12, 2023
Not unlike, in the literary cafeteria, Pullman vs. Tolkien?
ChatGPT seems to have the advantage for lovers of
fiction and fantasy, Perplexity AI for lovers of truth.
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