I prefer the NCS colors of Wednesday's "Exploring Color Space"
to the pastel shades in today's noon post. An illustration:
I prefer the NCS colors of Wednesday's "Exploring Color Space"
to the pastel shades in today's noon post. An illustration:
Related literature —
"The Birds Who Flew Beyond Time
is inspired by the great Persian poet
Farid ud-Din Attar's classic
twelfth-century allegory
The Conference of the Birds."
— Front jacket of The Birds Who Flew Beyond Time ,
by Anne Baring, with pictures by Thetis Blacker, first
published by Barefoot Books Ltd. in Bristol, 1993.
Anna Friel and Pierce Brosnan in "I.T." (2016).
* Title suggested by Sean Connery's well-known
remark to Nicolas Cage in "The Rock" (1996).
Related note for film fans —
I prefer the less stressful TV series “GLOW,” starring Alison Brie —
“In the bluish light emanating from the TV,
EE looked at him, her eyes veiled.”
— Being There , by Jerzy Kosinski
Mank, Baez, Collins — A trip back to Christmas Eve, 2021.
Related art (via Baez) for Josefine Lyche —
See also Lyche in Log24 posts tagged Star Cube.
Kitty in Uncanny X-Men #168 (April 1983)
"Try Bing Chat, Kitty."
* A Harvard phrase for a process analogous to that of the Hogwarts Sorting Hat.
From last night's update to the previous post —
The use of binary coordinate systems
Natural physical transformations of square or cubical arrays See "The Thing and I." |
From a post of May 1, 2016 —
Mathematische Appetithäppchen: Autor: Erickson, Martin —
"Weitere Informationen zu diesem Themenkreis finden sich |
Update at 9 PM ET March 17: A related observation by SHC —
The use of binary coordinate systems as a conceptual tool
Natural physical transformations of square or cubical arrays
of actual physical cubes (i.e., building blocks) correspond to
natural algebraic transformations of vector spaces over GF(2).
This was apparently not previously known.
See "The Thing and I."
Some related mathematics: https://m759.github.io .
Lurking in the background: Zurbarán's "Doctor of Law."
Some more-recent art — "Law Play," by Cullinane.
". . . 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 —
Powered by WordPress