The Boston Globe on the dead architect of the previous post —
"Mr. McKinnell, who was a fellow of the American Institute of Architects
and the American Academy of Arts and Sciences, and a member of the
Royal Institute of British Architects, taught for many years at the
Harvard Graduate School of Design and the Massachusetts Institute of
Technology School of Architecture and Planning."
Some ugly rhetoric to go with the ugly architecture —
The Boston Globe Saturday on Friday's death of one of
the two architects of Boston City Hall —
A gifted storyteller, Mr. McKinnell liked to recount
the response of renowned architect Philip Johnson to
City Hall. “ ‘Absolutely marvelous. … I think it’s wonderful.
… And it’s so ugly!’ ” Mr. McKinnell told Pasnik, adding:
“We thought that was the greatest praise we could get.”
See more ugliness from this journal on Friday —
See also this journal on the death of the other City Hall architect.
See also this journal on the date — February 19, 2009 —
of the above Ibsen opening, as well as today’s previous post.
From yesterday morning —
“Play the numbers, play the odds
Play ‘Cry Me a River’ for the Lord of the gods”
— Bob Dylan at
https://genius.com/Bob-dylan-murder-most-foul-lyrics
This suggests . . .
Polydor 2001 566 —
“Play the numbers, play the odds
Play ‘Cry Me a River’ for the Lord of the gods”
— Bob Dylan at
https://genius.com/Bob-dylan-murder-most-foul-lyrics
See also “Cry Me a River” in this journal.
Recent posts now tagged Paycheck suggest . . .
Related material —
See too “The Bond with Reality” in posts tagged Voids.
Log24 last Sunday:
Two years earlier —
Saturday Night Live on March 24, 2018 (a repeat) —
Related literature: The 1953 Philip K. Dick story
“Paycheck” —
A punchline for Saoirse —
“Manly, yes, but I like it too.”
Some notes suggested by recent posts now also tagged Three Days —
Sporkin in 1975, according to his obituary in this morning’s print edition
of The New York Times —
He reportedly died at 88 of natural causes on Monday, March 23.
See also, for a child of Hell’s Kitchen, a New York Times
quote from this morning’s print edition:
“A version of this article appears in print
on , Section SR, Page 6 of
the New York edition with the headline:
My Grandma on Art and Sex.” —
“Above all, she was unfailingly true to herself.”
An 1132 for James Joyce — (Click to enlarge)
A brief summary of the eightfold cube is now at octad.us.
Father Flynn in this morning’s post “Hollywood Interpretation
of Quantum Mechanics” suggests a flashback to Tron: Legacy —
A search for the above blogger “hilbertthm90”
yields some of his remarks from April 30, 2008
in his weblog “A Mind for Madness.” See as well
this journal on Walpurgisnacht 2008.
“After consulting with medical experts and receiving guidance from
the World Health Organization, CNN has determined that the term
‘Chinese virus’ is both inaccurate and considered stigmatizing.”
— March 19 coronavirus news
By Jessie Yeung, Helen Regan,
Adam Renton, Emma Reynolds and
Fernando Alfonso III, CNN,
Updated 10:42 p.m. ET, March 19, 2020
In memory of Stephen Schwartz, a member of
the Harvard College class of 1963 —
Synchronology check —
In memory of a University of Washington pathologist
who reportedly died on Tuesday, March 17 —
Cezanne’s Greetings.
See as well . . .
This morning’s online New York Times has news of Glastonbury:
Glastonbury Woo in this journal features the arch, not the pyramid.
For some personalities , see the previous post.
Philip Roth's 2004 paranoid classic premieres on TV tonight.
I prefer an alternative Lindbergh plot. See Peter Lindbergh in this journal.
At right below, a work of art that the fashion photographer Lindbergh
made when he was young and known as "Sultan."
". . . recognizing the bias in your models
and sharing it with clients, users, and engineers
is monumental . . . ."
— Made Lapuerta, Sept. 23, 2019, on AI
"Is this an obelisk I see before me?"
— m759, from a Log24 search for Obelisk
Mathematics: See Tetrahedron vs. Square in this journal
(Notes on two different models of schoolgirl space ).
Narrative: Replacing the square from the above posts by
a related cube …
… yields a merchandising inspiration —
Dueling Holocrons:
Jedi Cube vs. Sith Tetrahedron —
* See also earlier posts on Mathematics and Narrative.
The phrase “octad group” discussed here in a post
of March 7 is now a domain name, “octad.group,”
that leads to that post. Remarks by Conway and
Sloane now quoted there indicate how the group
that I defined in 1979 is embedded in the large
Mathieu group M24.
Related literary notes — Watson + Embedding.
In memory of mathematician Richard K. Guy
and of songwriter Eric Taylor,
who each reportedly died on March 9.
For Guy, some small numbers:
For Taylor, a link to the lyrics of his song "Dean Moriarty."
See as well this journal on March 9.
(More backstory — Posts on Nanci Griffith.)
Related material in this journal — Posts tagged Berlekamp's Game.
Artnet.com yesterday on "previously unsung or undersung
female artists working in esoteric or occult traditions" —
Click the above image for details.
There was, however, a challenge by Cozzens himself:
The apparent source:
In memory of a composer who reportedly died on Wednesday,
March 11, 2020 —
From a synchronology check —
Today's 4:02 AM ET post, "Steinfeld as Rose the Hat,"
suggests a review —
A more impressive woman in white —
Update of 8 PM ET —
Beckinsale gives Oct. 5, 2001, as the date of the New York
premiere of the film "Serendipity." Synchronology check:
Beckinsale's premiere date — Oct. 5, 2001 — is incorrect.
The film was released on that date, but its New York premiere
was actually on Oct. 3, 2001. See Getty Images.
The conclusion of an elegy for George Steiner
in th Times Literary Supplement issue dated
March 13, 2020 —
"What distinguishes humans from other animals, Johann Gottfried Herder
suggested in his essay On the Origin of Language (1772), is not so much
their capacity for language as their capacity for arriving at general reflection
(Besonnenheit ) through language. Few thinkers of the postwar era can be
said to have pursued this reflection with as much range and rigour as George
Steiner.
Ben Hutchinson is Professor of European Literature at the University of Kent
and Director of the Paris School of Arts and Culture. His most recent book is
Comparative Literature: A very short introduction, 2018 ."
See as well . . .
"A hunger to be more serious"
— Arts & Letters Daily on the late
George Steiner, who reportedly
died on February 3, 2020
The New York Times on a Sunday death —
A Midrash —
Serious —
Update of March 17, 2020 —
The graphic images illustrate nicely Conder's six 4-cycles, but
their relationship, if any, to his eight 2-cycles is a mystery —
The Conder paper is at
https://core.ac.uk/download/pdf/82622574.pdf.
The above arrangement of graphic images on cube faces is purely
decorative and static, and of little mathematical interest.
(A less static, but structurally chaotic, artifact might be made by
pasting the above 24 graphic images in the "Cosets in S4" picture
above onto the 24 faces of a 2x2x2 Rubik cube. This suggests the
reflection below on the poet Wallace Stevens, whose "Connoisseur
of Chaos" first appeared on page 90 of Twentieth Century Verse ,
Numbers 12-13, October 1938.)
If mathematically interesting permutations of the graphic images
are to be done, the images should be imagined as situated on
parallel planes, as in the permutahedron below —
Click the above permutahedron for an analysis of its structure.
The title is from a post of January 10, 2019.
A figure from this journal on June 1, 2019 —
The following figure may help relate labelings of the
truncated octahedron ("permutahedron") to labelings
of its fellow Archimedean solid, the cuboctahedron.
See as well other posts tagged Aitchison.
From the Bucharest author in last night's 12:12 AM post —
From this journal on the above date, Feb. 16, 2011 —
For fans of "The Zero Theorem" —
The 24 permutations of S4 arranged on a cube
by Cristi Stoica of Bucharest at
http://www.unitaryflow.com/2009/06/polyhedra-and-groups.html:
"Hello! Kinch here. Put me on to Edenville.
Aleph, alpha: nought, nought, one."
"A very short space of time through very short times of space….
Am I walking into eternity along Sandymount strand?"
— James Joyce, Ulysses , Proteus chapter
See also the previous post and Masks of the Illuminati .
From "Mathieu Moonshine and Symmetry Surfing" —
(Submitted on 29 Sep 2016, last revised 22 Jan 2018)
by Matthias R. Gaberdiel (1), Christoph A. Keller (2),
and Hynek Paul (1)
(1) Institute for Theoretical Physics, ETH Zurich
(2) Department of Mathematics, ETH Zurich
https://arxiv.org/abs/1609.09302v2 —
"This presentation of the symmetry groups Gi is
particularly well-adapted for the symmetry surfing
philosophy. In particular it is straightforward to
combine them into an overarching symmetry group G
by combining all the generators. The resulting group is
the so-called octad group
G = (Z2)4 ⋊ A8 .
It can be described as a maximal subgroup of M24
obtained by the setwise stabilizer of a particular
'reference octad' in the Golay code, which we take
to be O9 = {3,5,6,9,15,19,23,24} ∈ 𝒢24. The octad
subgroup is of order 322560, and its index in M24
is 759, which is precisely the number of
different reference octads one can choose."
This "octad group" is in fact the symmetry group of the affine 4-space over GF(2),
so described in 1979 in connection not with the Golay code but with the geometry
of the 4×4 square.* Its nature as an affine group acting on the Golay code was
known long before 1979, but its description as an affine group acting on
the 4×4 square may first have been published in connection with the
Cullinane diamond theorem and Abstract 79T-A37, "Symmetry invariance in a
diamond ring," by Steven H. Cullinane in Notices of the American Mathematical
Society , February 1979, pages A-193, 194.
* The Galois tesseract .
Update of March 15, 2020 —
Conway and Sloane on the "octad group" in 1993 —
See the title in this journal.
Such generation occurs both in Euclidean space …
… and in some Galois spaces —
.
In Galois spaces, some care must be taken in defining "reflection."
Suggested by the previous post: "Garland is an architect of complicated stories and actual spaces."
— Adam Rogers, 7 AM March 4th, 2020,
https://www.wired.com/story/
inside-devs-dreamy-silicon-valley-quantum-thriller/.
See also The Reality Blocks.
Friday, July 11, 2014Spiegel-Spiel des GeviertsFiled under: Uncategorized — m759 @ 12:00 PM See Cube Symbology.
|
The previous post addressed the "N" part.
For the "O" part, see Juliette Binoche in "High Life,"
a sequel to Kristen Stewart as bait in "Clouds of
Sils Maria" (2014) —
The Tackle —
The minute in the previous post's timestamp
suggests a review —
See also Post-It Aesthetics
and posts tagged Story of N.
On Boston's Hancock Tower:
"I reflect that all art, all beauty, is reflection."
— Fictional character by John Updike (July 1976)
The architect of the tower reportedly died Monday.
See as well "Reflections: Disturbing the Universe I"
by the late Freeman Dyson in The New Yorker
issue dated August 6, 1979.
A reflection I prefer:
Last night's 11:59 PM post linked to some news from Slovenia —
"Ulay, the performance artist whose provocative collaborations with
Marina Abramovic often led them to push each other to extremes,
died on Monday at his home in Ljubljana, Slovenia. He was 76."
— Alex Marshall in The New York Times
Ljubljana last appeared in this journal on August 10, 2011, in a post
titled "Objectivity."
A number related to that concept —
Less objectively —
— Performance artist who reportedly died today. See . . .
See also https://www.li-ma.nl/lima/sites/default/files/
Concept%20programme%20Transformation%20Digital%20Art%20Symposium
%2019%2620%20March%2C%202020%20-%20LIMA%20%283%29.pdf.
What are you, 12?
I'm 8. What are you reading?
Just a Western.
What does that mean? Is it good?
Pretty good.
What's the story?
I haven't finished it yet.
[Link added.]
Read more: https://www.springfieldspringfield.co.uk/
movie_script.php?movie=once-upon-a-time-in-hollywood
Freeman Dyson on his staircase at Trinity College
(University of Cambridge) and on Ludwig Wittgenstein:
“I held him in the highest respect and was delighted
to find him living in a room above mine on the same
staircase. I frequently met him walking up or down
the stairs, but I was too shy to start a conversation.”
Frank Close on Ron Shaw:
“Shaw arrived there in 1949 and moved into room K9,
overlooking Jesus Lane. There is nothing particularly
special about this room other than the coincidence that
its previous occupant was Freeman Dyson.”
— Close, Frank. The Infinity Puzzle (p. 78).
Basic Books. Kindle Edition.
See also other posts now tagged Trinity Staircase.
Illuminati enthusiasts may enjoy the following image:
See as well "Up the Trinity Staircase" (yesterday afternoon)
and "British Pottery" (Log24 , December 22, 2018).
|
Roberta Smith on Donald Judd’s BY ALEX GREENBERGER February 28, 2020 1:04pm If Minimalist artist Donald Judd is known as a writer at all, it’s likely for one important text— his 1965 essay “Specific Objects,” in which he observed the rise of a new kind of art that collapsed divisions between painting, sculpture, and other mediums. But Judd was a prolific critic, penning shrewd reviews for various publications throughout his career—including ARTnews . With a Judd retrospective going on view this Sunday at the Museum of Modern Art in New York, ARTnews asked New York Times co-chief art critic Roberta Smith— who, early in her career, worked for Judd as his assistant— to comment on a few of Judd’s ARTnews reviews. How would she describe his critical style? “In a word,” she said, “great.” . . . . |
And then there is Temple Eight, or Ex Fano Apollinis —
Cicero, In Verrem II. 1. 46 —
He reached Delos. There one night he secretly 46 carried off, from the much-revered sanctuary of Apollo, several ancient and beautiful statues, and had them put on board his own transport. Next day, when the inhabitants of Delos saw their sanc- tuary stripped of its treasures, they were much distressed . . . .
Delum venit. Ibi ex fano Apollinis religiosissimo noctu clam sustulit signa pulcherrima atque anti- quissima, eaque in onerariam navem suam conicienda curavit. Postridie cum fanum spoliatum viderent ii qui Delum incolebant, graviter ferebant . . . .
"I know then that the story is there, buried in what I call
my magma. It’s absolute chaos but the novel is in there,
lost in a mass of dead elements, superfluous scenes
that will disappear or scenes that are repeated several
times from different perspectives, with different characters.
It’s very chaotic and makes sense only to me. But the story
is born under there."
— Mario Vargas Llosa, interviewed in The Paris Review ,
Issue 116, Fall 1990
Vargas Llosa is the author of "Aunt Julia and the Scriptwriter."
See also a Log24 search for "Seix Barral."
For scriptwriter-related remarks by one Julia Carmel in yesterday's online
New York Times , see an obituary about a Tuesday, Feb. 25, death.
See also Log24 posts from Tuesday, Feb. 25, now tagged Deutsche Schule .
https://www.spectator.co.uk/2020/02/
the-restless-spirit-of-the-enlightenment/
See as well instances of "to and fro" in this journal.
Or: The Newman Prize Continues.
Freeman Dyson reportedly died today. In memoriam ,
some remarks by Dyson from Hiroshima Day 1979 —
(Click to enlarge.)
From the author who in 2001 described "God's fingerprint"
(see the previous post) —
From the same publisher —
From other posts tagged Triskele in this journal —
Other geometry for enthusiasts of the esoteric —
|
Monday, November 4, 2019
As Above, So Below*
|
|
|
Usage example —
(Click to enlarge.)
See also the previous post as well as PG(3,2),
Schoolgirl Space, and Tetrahedron vs. Square.
"Dirk Pitt is a fictional character created by American novelist Clive Cussler
and featured in a series of novels published from 1976 to 2009. Pitt is a
larger-than-life hero reminiscent of pulp magazine icon Doc Savage."
"Algebra is the offer made by the devil to the mathematician."
— Sir Michael Atiyah, quoted here in Two Views of Finite Space.
Author Clive Cussler, who reportedly died Monday at 88 —
“I detested school,” he told Publishers Weekly in 1994.
“I was always the kid who was staring out the window.
While the teacher was lecturing on algebra, I was on
the deck of a pirate ship or in an airplane shooting down
the Red Baron.”
Related material —
An image I saved on Oct. 26, 2016 —
Related New York Times opinion from that
same date —
"Every political movement in a democracy is
shaped like a pyramid — elite actors on the top,
the masses underneath."
The Sternheim Portrait (For Harlan Kane)
From last night's 1:01 AM post —
Detail —
This portrait is of German playwright Carl Sternheim.
Steve Martin's version of Sternheim's 1910 play "The Underpants"
reportedly opened on November 3, 2006.
My own interests on that date lay elsewhere . . .
Related abstract art —
"Although art is fundamentally everywhere and always the same,
nevertheless two main human inclinations, diametrically opposed
to each other, appear in its many and varied expressions. ….
The first aims at representing reality objectively, the second subjectively."
— Mondrian, 1936 [Links added.]
An image search today (click to enlarge) —
"Remembering speechlessly we seek
the great forgotten language . . . ."
|
"At the point of convergence by Octavio Paz, translated by Helen Lane
|
See also other posts now tagged Transparent Things.
Also on January 27, 2017 . . .
For other appearances of John Hurt here,
see 1984 Cubes.
Update of 12:45 AM Feb. 22 —
A check of later obituaries reveals that Hurt may well
have died on January 25, 2017, not January 27 as above.
Thus the following remarks may be more appropriate:
Not to mention what, why, who, and how.
… An abstract artist who reportedly died at 93 yesterday.
A search in this journal for Shubnikov yields…
"Raiders of the Lost Stone" (December 26, 2017).
“Continue to exercise caution with stories that can only be
corroborated by dead guys."
— Intelligence officer Frank Anderson in the previous post.
“Continue to exercise caution with stories that can only be
corroborated by dead guys. Fabricated stories are almost
never made up out of whole cloth, but are made by stitching
together generally known facts with bits of uncheckable fantasy.”
— Intelligence officer Frank Anderson, who reportedly
died on January 27, 2020.
This journal on that date —
The 759 octads of the Steiner system S(5,8,24) are displayed
rather neatly in the Miracle Octad Generator of R. T. Curtis.
A March 9, 2018, construction by Iain Aitchison* pictures the
759 octads on the faces of a cube , with octad elements the
24 edges of a cuboctahedron :
The Curtis octads are related to symmetries of the square.
See my webpage "Geometry of the 4×4 square" from March 2004.
Aitchison's p. 42 slide includes an illustration from that page —
Aitchison's octads are instead related to symmetries of the cube.
Note that essentially the same model as Aitchison's can be pictured
by using, instead of the 24 edges of a cuboctahedron, the 24 outer
faces of subcubes in the eightfold cube .
Image from Christmas Day 2005.
* http://www.math.sci.hiroshima-u.ac.jp/branched/files/2018/
presentations/Aitchison-Hiroshima-2-2018.pdf.
See also Aitchison in this journal.
"Nothing opens up new spaces…."
— Book description from the University of Chicago Press,
shown here on February Ninth, 2020:
See as well the Roman Polanski film "The Ninth Gate" and
an obituary reporting a death on February Ninth.
"… while at the end I didn't yearn for spectacular special effects,
I did wish for spectacular information–something awesome,
not just a fade to white." — Roger Ebert, March 10, 2000
Remarks by Rosalind Krauss in the previous post suggest a look at …
Then there is the universal beauty of oneself :
Jung's Four-Diamond Figure from Aion—
This figure was devised by Jung
to represent the Self.
See also "True Grid " in this journal.
|
Rosalind Krauss "If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World , for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit. From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete. Or, to take a more up-to-date example…."
"He was looking at the nine engravings and at the circle,
"And it's whispered that soon if we all call the tune
The nine engravings of The Club Dumas
An example of the universal— or, according to Krauss,
"This is the garden of Apollo, the field of Reason…." |
See as well . . .
"… And the song of love's recision . . . ." — E. L. Doctorow
The title is a phrase by Einstein (see previous post).
Related material — Posts now tagged Declamation.
“Pure mathematics is, in its way, the poetry of logical ideas.
One seeks the most general ideas of operation which will
bring together in simple, logical and unified form the largest
possible circle of formal relationships. In this effort toward
logical beauty spiritual formulas are discovered necessary
for the deeper penetration into the laws of nature.”
— Albert Einstein, May 1, 1935, obituary for Emmy Noether
(Quoted in part, without source, in Quanta Magazine yesterday.)
Once Upon a Time in New Hampshire
See as well this journal on the above date,
in posts tagged "Semiotic Watchman."
The novel Zero Sum Game by S. L. Huang is reviewed in the
March 2020 Notices of the American Mathematical Society .
For the same novel in this journal, see posts tagged Berlekamp’s Game.
On Feb. 11, Christian Lawson-Perfect posed an interesting question
about mappings between square and triangular grids:
For the same question posed about non -continuous bijections,
see "Triangles are Square."
I posed the related non– continuous question in correspondence in
the 1980's, and later online in 2012. Naturally, I wondered in the
1980's about the continuous question and conformal mappings,
but didn't follow up that line of thought.
Perfect last appeared in this journal on May 20, 2014,
in the HTML title line for the link "offensive."
"So ist das Selbst auch das Ziel des Lebens…."
"The Self is our life's goal…."
— Carl Jung, as quoted and translated by Paul Bishop in
The Dionysian Self (de Gruyter, 1995, p. 344).
His goal, perhaps.
Happy birthday to Sophia Lillis, who turns 18 today.
The plane at left is modeled naturally by
seven types of “cuts” in the cube at right.
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