Images from posts tagged Fire Water —
Scholium —
". . . The last of the river diamonds . . . .
bright alluvial diamonds,
burnished clean by mountain torrents,
green and blue and yellow and red.
In the darkness, he could feel them burning,
like fire and water of the universe, distilled."
— At Play in the Fields of the Lord ,
by Peter Matthiessen (Random House, 1965)
Related Log24 posts are now tagged Fire Water.
See as well, from posts tagged Heartland Sutra —
♫ "Red and Yellow, Blue and Green"
— "Prism Song," 1964
From this journal on Dec. 3, 2011 —
Some Weinberger-related art —
See as well the prose of Peter Matthiessen —
The New York Times reports a Monday,
March 13, 2023, death:
This journal Monday —
Final image of the above "diamond theorem" penrose search on Monday —
From March 2 —
Previous posts have shown ChatGPT answering the question
"What is the diamond theorem?" with references to Thurston
and, later, to Conway. Today it is Penrose's turn.
Related search results (click to enlarge) —
Forbes magazine on April 1, 2022 —
* Title suggested by "Colossus: The Forbin Project" (1970)
Related material — 7/02, 2021.
From other posts tagged Tetrahedron vs. Square —
A Scholium for Chomsky —
The ABC of words —
A nutshell —
The name "Kilgore Trout" in the previous post suggests a passage in
Wikipedia on authors — two real, one imaginary —
"The 'Kilgore Trout' name was a transparent reference to
the older writer (substituting 'Kilgore' for 'Theodore' and
'Trout' for 'Sturgeon'), but since the characterization was
less than flattering (both Sturgeon and Trout were financially
unsuccessful and seemingly slipping into obscurity),
Vonnegut did not publicly state the connection, nor did
Sturgeon encourage the comparison."
See also, in this journal, Theodore Sturgeon's "The Dreaming Jewels."
In memory of film auteur Bert I. Gordon, who reportedly
died at 100 yesterday —
"Make me young again." — Attributed to Kilgore Trout
The previous post suggests a search in this journal for Netanyahu.
That search suggests a Wikipedia article on n+1 magazine.
* See Wikipedia for a definition.
On a reported Wednesday, March 8, death —
From Chomsky's remarks in The New York Times today —
"It is at once comic and tragic, as Borges might have noted,
that so much money and attention should be concentrated
on so little a thing — something so trivial when contrasted
with the human mind, which by dint of language, in the
words of Wilhelm von Humboldt, can make 'infinite use of
finite means,' creating ideas and theories with universal reach."
A search in this journal for Humboldt University yields . . .
"Cum grano salis" — Boris Karloff in "The Black Cat."
See Helen Mirren with a plastic 45-rpm record adapter.
Related Log24 posts — Galois Seals.
The name "Vrinda Madan" from the above book cover metadata
yields a webpage that may or may not have the same Madan as
an author — "… Howie Michels' Epic Dreamscapes."
The date of that webpage — Sept. 15, 2022 — seems of particular
interest. See as well this journal on that date for some other posts
that are also now tagged The Cavalier Date.
Wednesday may or may not want to play "Paint it Black" to honor
the cover of the above newly published book.
(Michels is reportedly married to Francine Prose,
author of Bigfoot Dreams and Mister Monkey .)
The response of ChatGPT to a question about my work
continues to evolve. It now credits Conway, not Thurston,*
for the diamond theorem.
The paragraph beginning "The theorem states" appears** to be based
on the following 24 patterns — which number only 8, if rotated or
reflected patterns are considered equivalent.
* For Thurston in an earlier ChatGPT response to the same question,
see a Log24 post of Feb. 25.
** The illustration above is based on the divison of a square into
four smaller subsquares. If the square is rotated by 45 degrees,
it becomes a diamond that can be, in the language of ChatGPT,
divided into "four smaller diamonds ."
* Continued from the previous post.
An actor's obituary in The New York Times today suggests
a review of the phrase "geometry and death" in this journal.
In that review, the phrase, by J. G. Ballard in a 2006 article,
refers to German fortifications in World War II. Ballard had
earlier used the same phrase in connection with French
nuclear-test structures in the Pacific —
— From Rushing to Paradise by J. G. Ballard, 1994.
Those interested in the religious meaning of the phrase "Saint-Esprit"
may consult this journal on the date of Ballard's death.
The above phrase "interpellative assemblages" suggests . . .
See also this journal on the above Won Choi date —
A story from Variety on January 9, 2001 —
For Sean Carroll, author of . . .
See also Carroll in this journal.
Related humor for Doctor Strange —
Windows Lockscreen at 12:43 AM ET tonight —
I prefer the non-humor of Cold Mountain .
* See his post published at 10:00 pm on Monday 27 February 2023.
His categories and tags: Categories — Argentina Heraldry History Monarchy
Tags — Argentina, Chile, History, Latin America, Monarchy, Peru.
"Oh, would you like to swing on a star?" — Song lyric
"Depends on the star, baby." — Sinatra.
"What is the 16 puzzle?" . . . Good question.
"You show me your control panel and I'll show you mine."
See also this journal on what, according to IMDb, was the
release date of the film "Body/Antibody" — June 7, 2007.
Boston Globe AP story yesterday —
LOS ANGELES — Walter Mirisch, the astute and Oscar-winning
film producer who oversaw such classics as “Some Like It Hot,”
“West Side Story,” and “In the Heat of the Night,” died on Friday
of natural causes in Los Angeles, the Academy of Motion Picture
Arts and Sciences said Saturday. He was 101.
The part about tilings, group actions, and the diamond-shaped
pattern is more or less OK. The parts about Thurston and
applications are utterly false.
Compare and contrast . . .
"… based on true events, in much the same way that
'Pinocchio' is based on string theory. "
— Film review by Anthony Lane today
Related lyrics —
"Spread your wings and let me come inside."
— Rod Stewart, October 1976
Kristen, Rod . . . Rod, Kristen.
— Conrad Aiken, Great Circle
And the light shone in darkness and
Against the Word the unstilled world still whirled
About the centre of the silent Word.
— T. S. Eliot, "Ash Wednesday"
About the Centre:
See also Dorm Room.
* See this evening's online New York Times obituaries.
For Carr as dominant and
Boston University students
as submissive, see . . .
Carr's BU syllabus is dated Aug. 4, 2014.
For some other content from that date, see . . .
In memory of illustrator Istvan Banyai,
who reportedly died on Dec. 15, 2022 . . .
https://www.nytimes.com/2023/02/18/
arts/istvan-banyai-dead.html —
"US actor Stewart, who previously depicted Princess Diana
in Spencer, is president of the international jury at the 73rd
Berlin International Film Festival, where filming will begin for
the project." — Mona Tabbara at screendaily.com, 10 Feb. 2023
From an earlier Berlinale . . .
This post was suggested by Peter Woit's weblog today and by . . .
Update of 4:48 PM ET on Friday, Feb. 17, 2023 —
Other Norman-Yao-related reading —
In memory of a Harvard Corporation Senior Fellow
who reportedly died at 86 on December 20, 2022 —
See http://m759.net/wordpress/?s="Mac+Lane"+Boolean.
An image from that search —
.
A related image
for T. S. Eliot:
"And then there’s the ultimate unknown known:
the 'enlightenment' (satori, kensho) of Zen practice.
If my sense of it from accounts I have read is accurate,
it involves seeing the world and realizing that you always
knew its true nature, but you just didn’t know you knew…
because you were too busy putting it into boxes and
matrices and categories and words. Which reminds us
again that while logical deductions and categorizations
can lead us to discoveries, they can also lead us away
from them."
— James Harbeck on Groundhog Day, 2023
This post was suggested by a Log24 image from All Saints' Day, 2018 —
Related verbiage: Unthought Known.
Mathematics:
From Log24 "Pyramid Game" posts —
The letter labels, but not the tetrahedron, are from Whitehead’s
The Axioms of Projective Geometry (Cambridge U. Press, 1906), page 13.
Narrative:
The above title is a commercial slogan from Westinghouse Studio One —
in particular, from its "June Moon" broadcast on June 22, 1949.
The date August 4, 2011, from the previous post suggests a review . . .
Related search results —
From a different Adelson, in a Log24 post from 2003 —
Related geometric entertainment —
"Zwei Seelen wohnen, ach! in meiner Brust,
die eine will sich von der andern trennen:
Die eine hält in derber Liebeslust
sich an die Welt mit klammernden Organen;
die andre hebt gewaltsam sich vom Dust
zu den Gefilden hoher Ahnen."
— Faust 1, Vers 1112 – 1117; Vor dem Tor. (Faust),
according to www.gutzitiert.de.
A version in English: "In me there are two souls."
This post was suggested by a New York Times obituary today.
"These are not the examples most of us want to follow."
The New York Times on a set designer who
reportedly died at 83 on Monday (Feb. 6, 2023) —
"Adrian Hall, the founding artistic director,
brought him in as resident designer.
(Mr. Hall died on Feb. 4 in Van, Texas.)"
Hall was the founding artistic director of
Trinity Repertory Company, Providence, R.I.
Not-so-holy writ ….
Panthers — "Dimensions," Log24, Feb. 5, 2023.
Beast Belly — Tonight's previous post, "Gutter Mathematics."
From the Feb. 7 post "The Graduate School of Design" —
Related material —
Illustrations — From The previous post . . .
From Google —
Call a 4×4 array labeled with 4 copies each
of 4 different symbols a foursquare.
The symmetries of foursquares are governed
by the symmetries of their 24 interstices —
(Cullinane, Diamond Theory, 1976.)
From Log24 posts tagged Mathieu Cube —
A similar exercise might involve the above 24 interstices of a 4×4 array.
See "Two Approaches to Local-Global Symmetry"
(this journal, Jan. 19, 2023), which discusses
local group actions on plane and solid graphic
patterns that induce global group actions.
See also local and global group actions of a different sort in
the July 11, 1986, note "Inner and Outer Group Actions."
This post was suggested by some remarks of Barry Mazur,
quoted in the previous post, on " Wittgenstein's 'language game,' "
Grothendieck, global views, local views and "locales."
Further reading on "locales" — Wikipedia, Pointless topology.
The word "locale" in mathematics was apparently* introduced by Isbell —
ISBELL, JOHN R. “ATOMLESS PARTS OF SPACES.”
Mathematica Scandinavica, vol. 31, no. 1, 1972, pp. 5–32.
JSTOR, http://www.jstor.org/stable/24490585.
* According to page 841 of . . .
Johnstone, P. (2001). "Elements of the History of Locale Theory."
Pp. 835–851 in: Aull, C.E., Lowen, R. (eds) Handbook of the
History of General Topology, Vol 3. Springer, Dordrecht.
The epigraph to Chapter 2 of Category Theory in Context by Emily Riehl —
[Maz16] Barry Mazur. Thinking about Grothendieck.
Notices of the AMS, 63(4):404–405, 2016.
The above epigraph in context, in a paper dated
January 6, 2016 (Epiphany) —
Also on Epiphany 2016 —
Wednesday, January 6, 2016
|
The above cubic equation may also be written as
x3 – x – 1 = 0.
The equation occurred in my own work in 1985:
An architects' equation that appears also in Galois geometry.
For further details on the plastic number, see an article by
Siobhan Roberts on John Baez in The New York Times —
Perhaps Crossan should have consulted Galois, not Piaget . . .
From Hermann Weyl's 1952 classic Symmetry —
"Galois' ideas, which for several decades remained
a book with seven seals but later exerted a more
and more profound influence upon the whole
development of mathematics, are contained in
a farewell letter written to a friend on the eve of
his death, which he met in a silly duel at the age of
twenty-one. This letter, if judged by the novelty and
profundity of ideas it contains, is perhaps the most
substantial piece of writing in the whole literature
of mankind."
Epigraph to The Dark Interval , by John Dominic Crossan —
“I am the pause between two notes that fall
into a real accordance scarce at all:
for Death’s note tends to dominate—
Both, though, are reconciled in the dark interval,
tremblingly.
And the song remains immaculate.”
—Rilke, The Book of Hours , I
"What we do may be small, but it has
a certain character of permanence."
— G. H. Hardy in A Mathematician's Apology
For Bill Irwin —
<meta property="article:published_time"
content="2023-02-06T11:00:00.000Z"/>
The Source —
view-source:https://www.newyorker.com/magazine/2023/02/13/
finding-laughs-amid-the-gray-in-becketts-endgame
See as well the previous post and . . .
You, Xi-lin; Zhang, Peter. "Interality in Heidegger."
The term "interology" is meant as an interventional alternative to traditional Western ontology. The idea is to help shift people's attention and preoccupation from subjects, objects, and entities to the interzones, intervals, voids, constitutive grounds, relational fields, interpellative assemblages, rhizomes, and nothingness that lie between, outside, or beyond the so-called subjects, objects, and entities; from being to nothing, interbeing, and becoming; from self-identicalness to relationality, chance encounters, and new possibilities of life; from "to be" to "and … and … and …" (to borrow Deleuze's language); from the actual to the virtual; and so on. As such, the term wills nothing short of a paradigm shift. Unlike other "logoi," which have their "objects of study," interology studies interality, which is a non-object, a no-thing that in-forms and constitutes the objects and things studied by other logoi. |
Some remarks from this journal on April 1, 2015 —
Manifest O
|
83-06-21 | An invariance of symmetry The diamond theorem on a 4x4x4 cube, and a sketch of the proof. |
83-10-01 | Portrait of O A table of the octahedral group O using the 24 patterns from the 2×2 case of the diamond theorem. |
83-10-16 | Study of O A different way of looking at the octahedral group, using cubes that illustrate the 2x2x2 case of the diamond theorem. |
84-09-15 | Diamonds and whirls Block designs of a different sort — graphic figures on cubes. See also the University of Exeter page on the octahedral group O. |
The above site, finitegeometry.org/sc, illustrates how the symmetry
of various visual patterns is explained by what Zhang calls "interality."
Patterns in the space
between subsquares —
Figures in the space
between fingers —
A different NAM that some will prefer —
Experiential Events in this journal
on the above DC program date —
A Logo for Riri —
The above Nick Romano passage is from Knock on Any Door,
a 1947 novel by Willard Motley. Another Motley novel about
Chicago, from 1958 . . .
Page 41 The city was a blue-black panther that slunk along beside them. The tall, skyscraper night-grass hemmed them in. The thousand neon animal eyes watched their going. Page 67 The blue-black panther of a city watched their going. The un- blinking neon animal eyes watched their going. Thousands of neon signs lit their way. In an alley behind West Madison Street half an Page 68 hour before, a bum, drunk, had frozen to death lying in the back doorway of a pawnshop. The blue-black panther crouched over him. Page 70 First the creak of ice as an automobile goes by. Then the frown into your room of the red brick building across the street, its windows frosted over like cold, unfriendly eyes. Then a bum stumbling along trying to keep warm. Now a drunk, unevenly. And the wind like the howling voice of the blue-black panther, hunting, finding. And the clanging of impersonal streetcars. And each bar of neon, cold, dead. No message. The clown takes his bow and it is Christmas Day. Page 79 The blue-black panther followed them, sniffing at their heels. Page 106 Above them the blue-black panther lay on the roof of a tenement house, its feline chin on the cornice, its yellow-green eyes staring down onto the black night street of Maxwell. Its tail, wagging slowly back and forth, was like a lasso, a noose, sending little shivers of pebbles rolling loosely across the roof. Page 154 Then he went down to the Shillelagh Club. Through the pane, in the crowded, noisy place, he saw her. She was sitting at a table near the back, alone. Her cigarette had fallen from her lips and rolled away from her on the table top. It had burned itself to a long gray ash. Her head hung loosely on her neck as if she was asleep. A half-empty glass of beer was in front of her. Please, Mother, please come out, he prayed to her. And he stood next door to the tavern, waiting, his small shoulders drawn in, his head down in shame. And often he walked to the window and stood on tiptoe. She was still there. In the same position. He waited. He would be late to school tomorrow. He waited, keeping the long vigil. He waited. Twelve years old. And the thousand neon-animal eyes stared at him savagely. He waited. The blue-black panther lashed out its tail, flicking its furry tip against his ankles. He waited. Page 250 Alongside the blue-black patrol wagon the blue-black panther walks majestically. Page 262 Outside the door the blue-black panther rubs its back like a house cat. Page 409 Nick held the cigarette listlessly. The smoke curled up his wrist and arm like a snake. The blue-black panther licked his hand. |
("Miniaturist of Modernism" → "Windows on World")
(Women's Center → Central Intelligence)
This post was inspired by eBay —
On a concert at Carnegie Hall
on Saturday, Jan. 28, 2023 —
"The ravished NYT reviewer offers
some nice writing …."
Related Log24 posts —
"Just 17," Dec. 17, 2020, and
"Just 17," June 17, 2022.
"The child is father of the man." — Wordsworth
"Suck any sense from that who can." — Hopkins
Illustration —
See as well Expanding the Spielraum.
From Wednesday, St. Bridget's Day, 2023 —
Poetic meditation from The New Yorker today —
"If the tendency of rhyme, like that of desire,
is to pull distant things together
and force their boundaries to blur,
then the countervailing force in this book,
the one that makes it go, is the impulse
toward narrative, toward making sense of
the passage of time."
"Intended for a white European male audience, the sensual
reclining nude belongs to a long artistic tradition."
— The Courtauld Gallery on Gaugin's "Nevermore" (1897)
"After decades abroad, Mr Doig has returned again to London.
On February 10th he opens a new exhibition at the Courtauld Gallery ….
The Courtauld is also the home of Britain’s finest Impressionist collection,
and some of the paintings in the new show recall and respond to those works.
A depiction of an alpinist by Mr Doig speaks to Paul Cézanne’s view of
Lake Annecy, a tropical bather . . . gestures at Paul Gauguin’s nude
'Nevermore'."
— https://www.economist.com/culture/2023/02/02/
look-closely-at-peter-doigs-paintings-then-look-again
The London School of Economics has a more direct approach to art —
"When the Washington Post unveiled the slogan
'Democracy Dies in Darkness,' on February 17, 2017,
people in the news business made fun of it.
'Sounds like the next Batman movie,' the New York Times’
executive editor, Dean Baquet, said."
— Louis Menand in The New Yorker ,
"When Americans Lost Faith in the News," Jan. 30, 2023.
See also Darkness in this journal.
Not so dark:
A Log24 post from February 17, 2017
regarding that year's Groundhog Day — The dies natalis
(in the Catholic sense) of St. Bertram Kostant.
From tonight's previous post —
"here I come again . . . the square root of minus one,
having terminated my humanities" —
Samuel Beckett, Stories and Texts for Nothing
(New York: Grove, 1967), 128.
From The French Mathematician 0
I had foreseen it all in precise detail. i = an imaginary being
Here, on this complex space, |
Related reading . . .
See also "William Lawvere, Category Theory, Hegel, Mao, and Code."
( https://www.reddit.com/r/socialistprogrammers/comments/m1oe88/
william_lawvere_category_theory_hegel_mao_and_code/ )
Also relating category theory and computation —
the interests of Lawvere and those of Davis — is
an article at something called The Topos Institute (topos.site) —
"Computation and Category Theory," by Joshua Meyers,
Wednesday, 10 Aug., 2022.
Meyers on Davis —
Last updated at 22:46 PM ET on 1 February 2023.
Click for a designer's obituary.
Paraphrase for a road-sign collector:
See as well … Today's New York Times obituary
of the Harvard Business School Publishing
Director of Intellectual Property.
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