Other matching patterns . . .
Tuesday Weld in the 1972 film of Didion's Play It As It Lays :
Note the making of a matching pattern.
Other matching patterns . . .
Tuesday Weld in the 1972 film of Didion's Play It As It Lays :
Note the making of a matching pattern.
Illustration of "translate the input into
a language of your choice" —
Exploring bitspace via posts so tagged yields . . .
This, together with the acronym COS from Charlottesville, suggests
a look at what Princeton means by COS.
Why COS? . . . November 6, 2015 . . . Serena Zheng
(https://admission.princeton.edu/blogs/why-cos) —
Three years ago around this time, I was applying to Princeton,
and I had no idea what I wanted to study.
I was, however, pretty set against studying computer science,
or "COS," as we call it at Princeton.
"Three years ago around this time" translates to November 6, 2012.
Hence another Princeton-related tale . . .
Time of the most recent image post, at top left —
<time class="x1p4m5qa" datetime="2024-05-19T13:03:18.000Z"
title="May 19, 2024">9 hours ago</time> .
Cover illustration:
Spies returning from the land of
Canaan with a cluster of grapes.
Colored woodcut from
Biblia Sacra Germanica ,
Nuremberg, Anton Koberger, 1483.
Victoria and Albert Museum, London.
Related material —
The Faustus Square :
Design from 1514
From OSF . . . Among the positions that take this independence even further is Susanne Langer's approach towards meaning. Long before Derrida, she suggested in her chapter "The logic of signs and symbols" that we should understand meaning not as a relation to an author at all. Influenced by music and musical notation, she defines meaning instead as the function of a term from which a pattern emerges:
It is better, perhaps, to say: "Meaning is not a Reference: Langer, Susanne K., 1948 [1954]. Philosophy in a New Key: A Study in the Symbolism of Reason, Rite, and Art. Mentor Book. |
Related art . . .
Cover illustration:
Spies returning from the land of
Canaan with a cluster of grapes.
Colored woodcut from
Biblia Sacra Germanica ,
Nuremberg, Anton Koberger, 1483.
Victoria and Albert Museum, London.
For the ten steps of the OSF (Open Science Framework),
see other posts tagged OSF.
For the ten steps of St. John of the Cross, see . . .
https://www.catholictreasury.info/books/dark_night/dn34.php and
https://www.catholictreasury.info/books/dark_night/dn35.php.
"I've got a brand new pair of roller skates,
you've got a brand new key." — Song lyric
From OSF . . . "According to Derrida, to break with its original context and with its situation of production entirely is the ability of, and even a necessity for, the written. With this argument, Derrida moves the author and their communicative intent to the margins and frees up space to approach meaning from another side, stressing the independence of writing from its speaker. Among the positions that take this independence even further is Susanne Langer's approach towards meaning. Long before Derrida, she suggested in her chapter 'The logic of signs and symbols' that we should understand meaning not as a relation to an author at all. Influenced by music and musical notation, she defines meaning instead as the function of a term from which a pattern emerges:
It is better, perhaps, to say: 'Meaning is not a Langer's approach towards meaning as a function puts the relation to other terms in the foreground, the pattern a term is part of and linked to. From her perspective, strongly informed by thinking of meaning-making in music, this seems obvious. In music, no note holds meaning for itself. It is in the relation between notes that meaning emerges, and Large Language Models approach language in a similar manner." Reference: Langer, Susanne K., 1948 [1954]. Philosophy in a New Key: A Study in the Symbolism of Reason, Rite, and Art. Mentor Book. |
A post from the above date contained the following image —
Related material — Tonight's midnight post, which led to
a different circular image from the date Feb. 15, 2023 . . .
https://osf.io/preprints/mediarxiv/4th3x —
Thinking through generated writing Abstract – This article returns to the release of ChatGPT to study the mechanics of Large Language Models (LLMs) and to counterpose them against established theories of language and writing. Its aim is to explore the hypothesis that ‘generated writing’ is “the beginning of new writing”, a writing that has its own cultural logic and tendencies. To show this, the article revisits philosophical theories of writing, in particular those of Jacques Derrida and André Leroi-Gourhan, and reads them in light of the computational methods of LLMs to understand in what way ‘generated writing’ diverges from the writing we have known before. |
For Derrida as the serpent in Paradise Garden, see
"Derrida Serpent" in this journal —
From a search in this journal for Kochen —
Related material — Hitchcock in this journal and Mermin Pentagrams on the Web.
From posts tagged Schoolgirl Space —
"The bride hath paced into the hall,
Red as a rose is she;
Nodding their heads before her goes
The merry minstrelsy."
* The title is from the following passage . . .
August 26, 2022, was the opening date of
the Nathalie Emmanuel film "The Invitation."
See as well Emmanuel here on Walpurgisnacht 2024
in "The Invitation" (2022) —
Wednesday, May 1, 2024
|
From the end credits for "The Invitation" —
<img src="http://www.log24.com/log/pix24/
240514-Previs_Pro-storyboard-software.jpg" width="500" />
Earlier in this journal (March 1, 2023) —
"Say the secret word and divide a hundred dollars."
Saxophonist David Sanborn reportedly died Sunday at 78.
He appears in this journal in a search for "Tequila."
* For a Hollywood version of this name, see the May 6 post
"Game for a Language Animal."
#modellife
“We know that these models are getting more and more complex, but we want the experience of interaction to actually become more natural, easy, and for you not to focus on the UI at all, but just focus on the collaboration with ChatGPT,” Murati said. “For the past couple of years, we’ve been very focused on improving the intelligence of these models … But this is the first time that we are really making a huge step forward when it comes to the ease of use.” — TechCrunch today, |
"… we want the experience of interaction to actually become
more natural, easy, and for you not to focus on the UI at all,
but just focus on the collaboration…."
UI:
UX:
Art from Marcelanowak.com
For the significance of the date "February 20," see . . .
Google One: Gemini Advanced AI on 13 May 2024. Prompt: How can Weyl's 1946 remarks on coordinatization in "The Classical Groups" be applied to models of finite geometries? Response (after several drafts): In "The Classical Groups," Hermann Weyl discusses the concept of coordinatization, which is the process of assigning numerical coordinates to points in a geometric space. This process is fundamental in connecting abstract geometric concepts with concrete numerical representations, allowing for algebraic manipulation and analysis. Weyl's remarks on coordinatization have significant implications for models of finite geometries. Finite geometries are geometric systems with a finite number of points and lines, and they often exhibit different properties compared to traditional Euclidean geometry. Here's how Weyl's ideas can be applied to finite geometries: 1. **Relativity of Coordinatization:** Weyl emphasizes that the choice of coordinate system is arbitrary and that different coordinate systems can be used to describe the same geometric object. This relativity of coordinatization is particularly relevant in finite geometries, where multiple coordinate systems may exist, each with its own advantages and disadvantages. 2. **Equivalent Coordinatizations:** Weyl introduces the concept of "equivalent coordinatizations," which are different coordinate systems that can be transformed into one another through a group of transformations. In finite geometries, identifying and understanding these equivalent coordinatizations can provide deeper insights into the underlying structure and symmetries of the geometry. 3. **Objective Class of Coordinatizations:** Weyl discusses the problem of fixing an "objective class" of coordinatizations that capture essential features of the geometry while being independent of arbitrary choices. In finite geometries, this could involve identifying coordinatizations that best reflect the specific properties and relationships within the geometry. 4. **Group of Transformations:** Weyl emphasizes the role of the "group of transformations" that mediates between equivalent coordinatizations. In finite geometries, understanding these transformation groups can help classify different types of finite geometries and reveal their underlying symmetries. By applying Weyl's insights, researchers can gain a deeper understanding of finite geometries, including their classification, properties, and relationships. Additionally, exploring different coordinatization schemes can lead to new algebraic and geometric tools for studying finite geometries. For further exploration, you can delve into the works of other mathematicians like Steven H. Cullinane, who has written extensively on finite geometry and its connections to relativity and other areas of mathematics. I hope this explanation is helpful! Please let me know if you have any further questions. |
Update at about 5 PM ET the same day . . .
Prompt: Correction: Cullinane has NOT written on finite geometry's "connections to relativity." He has, instead, quoted Weyl's remarks on what Weyl himself called "the relativity problem," but what was in fact his own term for problems involving coordinatization. Such problems are of interest both in physics and in finite geometry, but the latter is a field of pure mathematics, NOT of physics. Response: You are absolutely correct. I apologize for the error in my previous response. Steven H. Cullinane has indeed quoted Weyl's remarks on "the relativity problem" in the context of finite geometry. However, as you rightly pointed out, this term refers to Weyl's own terminology for problems involving coordinatization and not the theory of relativity in physics. Finite geometry is a field of pure mathematics and does not directly connect to the physical theories of relativity. While both areas involve concepts of space and transformations, they operate in fundamentally different domains. Cullinane's work focuses on applying Weyl's insights on coordinatization to the specific challenges and structures within finite geometries. This involves exploring different coordinatization schemes, understanding their equivalences, and identifying transformation groups that reveal the underlying symmetries of finite geometries. Thank you for pointing out this important distinction. It highlights the importance of precise language and accurate attribution when discussing complex mathematical concepts. |
"That year the rich came led by the pilot fish.
A year before they would never have come.
There was no certainty then.
The work was as good and the happiness was greater
but no novel had been written, so they could not be sure.
They never wasted their time nor their charm
on something that was not sure. Why should they?"
This journal on the above Bridge date — July 10, 2013 —
"…des carreaux mi-partis de deux couleurs
par une ligne diagonale…."
See also Josefine Lyche in Vril Chick
and Bowling in Diagon Alley.
* The Brolin of "No Country for Old Men" and "Sicario."
The title is a Log24 tag for posts of April 13, 2024.
See also a death on that date.
In memory of a woman advertising pioneer who
reportedly died at 95 today in London —
"And so I had an idea, which turned out to be
related to that question, and so it was a little theorem
that I proved and I showed it to my thesis advisor, and
then he said, 'Oh, that could maybe help with this question.'
And he told me the question. And I said, 'Oh that's right,
maybe it could.' But he said, 'But don't work on that.'
He says, 'Borel has worked on that, Singer has worked
on that, a lot of people have tried to do this without success.'
But that has just got me fired up. And so I solved that problem…."
— The late James H. Simons, on his thesis advisor Bertram Kostant.
The thesis advisor reportedly died on Groundhog Day, 2017.
See as well, in this journal, Facets for Snorri.
A relevant author (click to enlarge) —
For a related tune, see the concepts of space in the previous post.
See also this journal on the above YouTube date — April 4, 2010.
New teaser trailer . . .
Earlier teaser trailer . . . October 7, 2023 . . .
This journal on the above 2023 trailer date . . .
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.
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 —
"The bride hath paced into the hall,
Red as a rose is she;
Nodding their heads before her goes
The merry minstrelsy."
See as well this journal on the above logo-design date —
March 13, 2024: Rearranging the Deck Chairs.
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 —
* 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 —
"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.
"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
Log24 on 10 Dec. 2008 — |
Log24 on 12 Dec. 2008 —
|
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
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
But first, a word from our sponsa —
Related entertainment . . .
A Warren Area High School Key Club IG post of Nov. 10, 2023, and,
on that same date . . .
Former logo of the American
Mathematical Society —
Note the resemblance to
Harvard's Memorial Church.
A rather different four-column logo —
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 —
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.
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? |
* See that Cuernavaca street in a Log24 search for Ragtime.
Auster: The Music of Chance.
Austere: Iacta Est.
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:
Wednesday, April 30, 2014
|
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