In memory of George F. Simmons, a mathematician
who reportedly died Aug. 6 at the age of 94 —
"It seems to me that a worthwhile distinction can be made
between two types of pure mathematics. The first …
centers attention on particular functions and theorems
which are rich in meaning and history…. The second is
concerned primarily with form and structure."
— George F. Simmons, Introduction to Topology and
Modern Analysis (1963)
" . . . Only by the form, the structure,
Can words or music reach
The stillness . . . ."
— Adapted from T. S. Eliot's Four Quartets
by replacing "pattern" with "structure."
Two posts related to Eliot's theological interests:
Form: Jan. 10, 2012.
Structure: June 6, 2016.
… Continued from previous posts now tagged Art Logos.
"Logos," a Greek word used in philosophy and theology,
is, in modern usage, also a brief form of "logotypes,"
a name for the branding symbols used by businesses.
For some less commercial aspects of the philosophical
concept, see Logo in this journal.
See also this morning's previous post, Peacock News.
"And all of the colors are black." — Paul Simon
* The title of course refers to the NBC logo.
See also other instances of "Peacock" in this journal.
* From earlier posts containing the title phrase.
Neil Montanus, a Kodak Colorama Photographer, Dies at 92
His colossal pictures, depicting an idealized American life,
greeted travelers at Grand Central Terminal for decades.
Katharine Q. Seelye in The New York Times —
Mr. Montanus was 92 when he died on Friday
under hospice care in Rochester, his son Jim said.
Robert Frank Dies; Pivotal Documentary Photographer Was 94
Mr. Frank, who was best known for his groundbreaking book,
“The Americans,” had a visually raw and personally expressive
style that made him one of the most influential photographers
of the 20th century.
Philip Gefter in The New York Times —
Robert Frank, one of the most influential photographers
of the 20th century, whose visually raw and personally
expressive style was pivotal in changing the course of
documentary photography, died on Monday in Inverness,
Nova Scotia. He was 94.
"And everything looks worse in black and white." — Paul Simon
For Harlan Kane
From this journal on Feb. 5, 2009:
"In the garden of Adding
live Even and Odd…
And the song of love's recision
is the music of the spheres."
— The Midrash Jazz Quartet in
City of God , by E. L. Doctorow (2000).
From this journal on the date of
the above post by Gavaler:
See as well an obituary for Mrs. Wertham from 1987.
Related art —
Friday, July 11, 2014
|
For further details, search the Web for "Wertham Professor" + Eck.
(For Harlan Kane)
"While digging in the grounds for the new foundation,
the broken fragments of a marble statue were unearthed."
— From Thomas Hardy, "Barbara of the House of Grebe,"
quoted in an epigraph to Paul de Man's "Shelley Disfigured,"
in turn quoted by Barbara Johnson on page 231 of Persons
and Things (Harvard paperback, 2010).
From "the world of the unintentional, the contingent, the minute,
and the particular" (Kovacevic, U. of Montenegro, 2011) —
Yes, we received your payment. No, it wasn't late, but it was for $78.13, and the bill was for $78.31. Okay, great. Read more: https://www.springfieldspringfield.co.uk/ movie_script.php?movie=the-circle
Another such transposition: Pages 213 and 231 in a search
for "gaps" in a 2010 paperback discussion of Lacan —
These pages are as follows —
(The above title was suggested by today's "Child-Resistant 4×4.")
* Specifically, resistant to the above revelation attributed to Barbara Johnson
by Harvard University Press —
"Deconstruction calls attention to gaps and reveals
that their claims upon us are fraudulent."
A related search at Amazon.com:
Barbara Johnson explains Lacan:
" The 'gap' in the real is the leap
from the empirical to
the signifying articulation
of the object of desire;
it cannot be perceived empirically.
It is 'nothing.' "
— Persons and Things , paperback (2010),
Harvard University Press, page 213
“By groping toward the light we are made to realize
how deep the darkness is around us.”
— Arthur Koestler, The Call Girls: A Tragi-Comedy ,
Random House, 1973, page 118
"Fury: OK. Your turn. Prove you're not a Skrull.
[Carol calmly blasts energy out of her fists towards a jukebox
on the opposite side of the room before resting her head
back on her fist. Fury continues to look towards the jukebox,
both concerned and confused]
Fury: And how is that supposed to prove to me that you're not a Skrull?
Carol: It's a photon blast.
Fury: And…?
Carol: A Skrull can't do that. So a full-bird colonel turned spy turned
SHIELD agent must have pretty high security clearance. Where's Pegasus?
[The scene changes to a black car driving through an empty highway
next to a mountain, before changing to the inside of the car showing Fury
driving and Carol in the passenger seat]
Fury: So the Skrulls are alien races which infiltrate and overtake alien planets.
And you're a Kree, a race of noble warriors.
Carol: Heroes. Noble warrior heroes."
* See also this morning's post in memory of guitarist Jimmy Johnson,
as well as . . .
"New York Fashion Week is scheduled Friday, September 6 through
Wednesday, September 11. View the preliminary schedule here. …
UPDATED AS OF: Thu 08/29/19"
— https://cfda.com/fashion-calendar/official-nyfw-schedule
View also a fashion photo from this journal on 08/29/19 —
I do not know where the above tank top can be purchased.
In memoriam: Guitarist, studio engineer Jimmy Johnson, 1943-2019 .
Johnson reportedly died on Thursday, Sept. 5.
See also, from the first of the seven posts of Thursday, August 29 —
* See a reference to that literary saloon from June 11, 2013.
The title, from Doreen St. Félix (previous post),
is irresistible. Details to flesh it out will follow.
Update of 12:41 PM – See Brosnan in Urge .
"Letting someone speak does not mean we condone
what they are saying, and it does not absolve that person
or group from consequences. And when we disagree,
we have an obligation to respond earnestly."
— Harvard College dean Rakesh Khurana in an undated
"Welcome Home" message to returning students (Fall, 2019)
An earnest response from this journal —
See as well a webpage from 2000,
"Symmetry from Plato to the
Four-Color Conjecture."
"When you come to a fork . . . ." — Yogi Berra (?)
The Observable site does not work in my Chrome browser.
To play with it, use Firefox. For a more straightforward
JavaScript program see the Diamond 16 Puzzle.
A link, observablehq.com/demo, (not functioning in my Chrome
browser at the present time but apparently OK in Firefox) in the
previous post suggests . . .
"Physically meaningful observables must also satisfy
transformation laws which relate observations
performed by different observers in different
frames of reference. These transformation laws are
automorphisms of the state space, that is
bijective transformations which preserve certain
mathematical properties of the space in question."
— Wikipedia, Observable
Those who prefer narrative to mathematics may read
"automorphisms" as "auto morphisms."
"Before time began . . . ." — "Transformers" first line, 2007
At present, the above Ajna page is not functioning in my Chrome browser
and is only partly functioning in Edge, but seems OK in Firefox.
Illustration from other posts now tagged
Cervantes Meets Pascal.
See as well Verhexung in this journal.
This post was suggested by . . .
Down the Up Ladder
From this journal on All Hallows' Eve 2007 —
"God demands scrutiny beyond his menacingly comic aspects."
— Harold Bloom on José Saramago's The Gospel According to
Jesus Christ (1991). Saramago was awarded the Nobel Prize
in Literature in 1998.
The Hamilton watch from "Interstellar" (2014) —
Those who prefer entertainment may consult Bright Club (August 4).
"From an early age she aspired to be a ballet dancer,
and, though never the sveltest girl en point, at 16
she landed a job in the corps de ballet at Radio City Music Hall."
— From a New York Times obituary this evening
The previous post displayed part of a page from
a newspaper published the day Olivia Newton-John
turned 21 — Friday, September 26, 1969.
A meditation, with apologies to Coleridge:
In Xanadu did Newton-John
A stately pleasure-square decree
Where Aleph the sacred symbol ran
Through subsquares measureless to man.
A related video —
Beware, beware, her flashing eyes, her floating hair:
Set design —
As opposed to block design —
"In real life, Sophia Lillis loves horror…."
"Spirits rise and their dance is unrehearsed…."
— A nightmare song by Barbra Streisand
But not, perhaps, horror in real life . . .
Continuing the themes of the last three posts, which
are now also tagged News Women . . .
"publishDate":"04-07-2017 01:48"
"date":"2019-08-21"
For some backstory, see
http://m759.net/wordpress/?s=”I+Ching”+48+well .
See as well “elegantly packaged” in this journal.
“Well” in written Chinese is the hashtag symbol,
i.e., the framework of a 3×3 array.
My own favorite 3×3 array is the ABC subsquare
at lower right in the figure below —
Influenz , by Paul Klee —
"One of the most influential of modern thinkers . . . ."
As is Stan Lee . . .
"Watch the trailer." — This journal on Eliza Doolittle Day, 2012 .
From Catherine Asaro’s The Spacetime Pool :
|
She gaped at him. “Do you mean a Riemann sheet? A branch cut from one Riemann sheet to another?” “That’s right.” He hesitated. “You know these words?” She laughed unsteadily. “It’s nonsense. Not the sheets, I mean, but they’re just mathematical constructs! They don’t actually exist. You can’t physically go through a branch cut any more than you could step into a square root sign.” |
A broken link found in the search results of
the previous post suggests a review . . .
Photo Opportunity , courtesy of Leni Riefenstahl — Click to enlarge.
From Paul Simon's dreaded Cartoon Graveyard —
The Riefenstahl publication above was suggested by . . .
See as well the firsts of Sophia Lillis (Saturday, August 24).
"Look at what you've done
Why, you've become a grown-up girl"
See also September Morn in this journal.
"Mein Führer… Steiner…"
See Hitler Plans and Quadruple System.
"There is such a thing as a quadruple system."
— Saying adapted from a 1962 young-adult novel
See as well posts now tagged Helsinki Math in this journal.
* See Kane in this journal.
Every picture tells a story .
The A Team —
The Z Team —
* See the previous post. Related material:
The Lolita Express and Magic Carpet Ride.
(The title refers to the previous post.)
"There is a house in New Orleans…
Not the one you've heard about,
I'm talking about another house.
They spoke of gold in the cellar
That a Spanish gentleman had left…"
— Song lyric by David Berman suggested by
his New Yorker elegy
"Reddington and Vesco are watching the opera,
and the plan begins."
In reply to a post by David Justice this afternoon,
"Wardrobe Malfunction."
From a three-part meditation on Sept. 30, 2008:
For less high-minded meditations, see Tony Stark in today's
previous post —
"Tony Stark: That's how I wished it happened.
Binarily Augmented Retro-Framing, or BARF.
God, I gotta work on that acronym.
An extremely costly method of hijacking the
hippocampus to . . . clear traumatic memories. Huh."
Working on that acronym . . .
The "Real Presences" title is from the Aug. 20 post "Inception."
See also the real presences in a recent book by J. D. Vance —
"Mom was, everyone told me, the smartest person
they knew. And I believed it. She was definitely the
smartest person I knew."
— Vance, J. D., Hillbilly Elegy (pp. 65-66).
Harper Paperbacks. Kindle Edition.
And not so real . . .
(Oneworld Publications, Jan. 3, 2011)
Compare and contrast with an illustration
from "Time Fold," a webpage of Oct. 10, 2003 —
See also the Squarespace logo:
From my reading Monday morning —
From the online New York Times this afternoon —
Related literature —
For the Church of Synchronology —
The Gigantomachia page above is dated September 20, 2003.
See as well my own webpage from that date: "The Form, the Pattern."
"The inception of critical thought, of a philosophic
anthropology, is contained in the archaic Greek definition
of man as a 'language-animal'…."
— George Steiner, Real Presences
A schoolgirl in 1961 —
"Non, rien de rien…"
— Edith Piaf
"I get a kick though it's clear to see,
You obviously don't adore me."
— Cole Porter
The title is from the post "Child's Play" of May 21, 2012 . . .
"It seems that only one course is open to the philosopher
who values knowledge and truth above all else. He must
refuse to accept from the champions of the forms the
doctrine that all reality is changeless [and exclusively
immaterial], and he must turn a deaf ear to the other party
who represent reality as everywhere changing [and as only
material]. Like a child begging for 'both', he must declare
that reality or the sum of things is both at once [το όν τε και
το παν συναμφότερα] (Sophist 246a-249d)."
Related material —
"Schoolgirl Space: 1984 Revisited" (July 9, 2019) and
posts tagged Tetrahedron vs. Square.
Some background for The Epstein Chronicles —
|
“What modern painters — James J. Gibson, Leonardo, |
See also Robert Maxwell,
Frank Oppenheimer,
and the history of Leonardo .
Click the above Pergamon Press image
for Pergamon-related material.
Burroway on Hustvedt in The New York Times ,
Sunday, March 9, 2003 —
See as well "Putting the Structure in Structuralism."
For those who prefer greater clarity than is offered by Stevens . . .
The A section —
The B section —
"A paper from Helsinki in 2005 says there are more than a million
3-(16,4,1) block designs, of which only one has an automorphism
group of order 322,560. This is the affine 4-space over GF(2)."
A revision of the above diagram showing
the Galois-addition-table structure —
Related tables from August 10 —
See "Schoolgirl Space Revisited."
The exercise in the previous post was suggested by a passage
purporting to "use standard block design theory" that was written
by some anonymous author at Wikipedia on March 1, 2019:
Here "rm OR" apparently means "remove original research."
Before the March 1 revision . . .
The "original research" objected to and removed was the paragraph
beginning "To explain this further." That paragraph was put into the
article earlier on Feb. 28 by yet another anonymous author (not by me).
An account of my own (1976 and later) original research on this subject
is pictured below, in a note from Feb. 20, 1986 —
An image from a Log24 post of March 5, 2019 —
The following paragraph from the above image remains unchanged
as of this morning at Wikipedia:
"A 3-(16,4,1) block design has 140 blocks of size 4 on 16 points,
such that each triplet of points is covered exactly once. Pick any
single point, take only the 35 blocks containing that point, and
delete that point. The 35 blocks of size 3 that remain comprise
a PG(3,2) on the 15 remaining points."
Exercise —
Prove or disprove the above assertion about a general "3-(16,4,1)
block design," a structure also known as a Steiner quadruple system
(as I pointed out in the March 5 post).
Relevant literature —
A paper from Helsinki in 2005* says there are more than a million
3-(16,4,1) block designs, of which only one has an automorphism
group of order 322,560. This is the affine 4-space over GF(2),
from which PG(3,2) can be derived using the well-known process
from finite geometry described in the above Wikipedia paragraph.
* "The Steiner quadruple systems of order 16," by Kaski et al.,
Journal of Combinatorial Theory Series A Volume 113, Issue 8,
November 2006, pages 1764-1770.
* The title refers to The Institute , by Stephen King, a novel
to be published on September 10, 2019.
"If you want to win, you need to know just one thing and not to waste your time
on anything else: the pleasures of erudition are reserved for losers. The more
a person knows, the more things have gone wrong."
— Eco, Umberto. Numero Zero (p. 9). HMH Books. Kindle Edition.
"All this notwithstanding, I dreamed what all losers dream, about one day writing
a book that would bring me fame and fortune. To learn how to become a great
writer, I became what in the last century was called the nègre (or ghostwriter,
as they say today, to be politically correct) for an author of detective stories who
gave himself an American name to improve sales, like the actors in spaghetti
westerns. But I enjoyed working in the shadows, hidden behind a double veil
(the Other’s and the Other’s other name)."
— Eco, Umberto. Numero Zero (pp. 9-10). HMH Books. Kindle Edition.
How's this for a double veil, Umberto? —
Boeing/Being Meets the Flying Spaghetti Monster . . .
For the title, see Zero: Both Real and Imaginary (a Log24 search).
The title was suggested by the previous post, by Zorro Ranch,
by the classic 1967 film The Producers , and by . . .
Related material —
Vanity Fair on Sept. 8, 2017, celebrated the young actress
who played Beverly Marsh in the 2017 film version of
Stephen King's IT . See a post from her 12th birthday —
"Winter's Game" — that touches upon Maori themes.
More generally, see Bester + Deceivers in this journal.
And for the Church of Synchronology . . .
See posts related to the above Vanity Fair date.
(From his “Structure and Form: Reflections on a Work by Vladimir Propp.”
Translated from a 1960 work in French. It appeared in English as
Chapter VIII of Structural Anthropology, Volume 2 (U. of Chicago Press, 1976).
Chapter VIII was originally published in Cahiers de l’Institut de Science
Économique Appliquée , No. 9 (Series M, No. 7) (Paris: ISEA, March 1960).)
The structure of the matrix of Lévi-Strauss —
Illustration from Diamond Theory , by Steven H. Cullinane (1976).
The relevant field of mathematics is not Boolean algebra, but rather
Galois geometry.
The article below suggests a review of other posts now tagged E-Girls.
* The title is that of a 1958 novel by John O'Hara.
See as well other instances of the title in this journal.
Wikipedia on film producer Lorenzo di Bonaventura
(Harvard AB (1980) in Intellectual History*) —
“His tenure at Warner Bros. included discovering and
shepherding The Matrix into production, and the
purchase of the rights to the Harry Potter books by
J. K. Rowling.”
From the previous post —
“But he enters into the central myth of
this book at another, higher level as well;
for he is an artist, a potter . . . .“
— Wendy Doniger O’Flaherty on
Claude Lévi-Strauss, author of
The Jealous Potter
* See as well “What is Intellectual History?” and
Magic for Liars .
" … this beautiful love story . . . ."
An image from the previous post:
The above line "From the producer of Transformers " suggests
a story from March 18, 2019 . . .
Misreading the words of di Bonaventura
yields a phrase that might be applied to
the Church of Rome . . .
"A franchise based on release dates."
See dies natalis in this journal.
For the Church of Synchronology, see
the above di Bonaventura date, March 18.
Then there is the Church of Cubism . . .
"Before time began, there was the Cube."
— Optimus Prime, Transformers , 2007
An illustration (slightly revised) from All Souls' Day 2010 —
Click to enlarge.
An illustration from a post of January 11, 2019 —
Advertisement for another January 11, 2019, event —
For related cinematic remarks, see Dabbling in this journal.
American Songwriters (the Petrusich versions)
The New Yorker Culture Desk online yesterday —
The New Yorker Culture Desk onine July 16 —
Related aesthetic meditation from this journal on July 16 —
(From the post "Schoolgirl Space for Quantum Mystics")
The Square "Inscape" Model of
the Generalized Quadrangle W(2)
Click image to enlarge.
-embedding-in-PG(3,2)-Planat-Saniga-1000w.jpg)
* The title refers to the role of PG (3,2) in Kirkman's schoolgirl problem.
For some backstory, see my post Anticommuting Dirac Matrices as Skew Lines
and, more generally, posts tagged Dirac and Geometry.
From posts tagged The Next Thing —
|
… an apt illustration can be found on the cover of
See also Stevens's use of the phrase "heaven-haven"
… Todo lo sé por el lucero puro – Rubén Darío
An academic work from 2003 discusses Stevens's "Notes" Note that "perfect" means "complete, finished, done." |
That university, in Dayton, Ohio, appeared in the previous post.
A curious recent wardrobe choice in Dayton suggests a review
of posts tagged Mathmagic Land.
Bylsma reportedly died on July 25. This journal on that date —
* See an article dated 11 April 2014 in Physics Today .
Representing Hellfire — CNN, as above.
Representing Truth —
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