"Thinking Outside the Square:
Support for Landscape and Portrait
Formats on Instagram"
Related material from March 18, 2015 —
Play Is Not Playing Around
|
"Thinking Outside the Square:
Support for Landscape and Portrait
Formats on Instagram"
Related material from March 18, 2015 —
Play Is Not Playing Around
|
— "The Noble Rider and the Sound of Words"
For some backstory, click or touch the dark passage above.
See also Monolith (August 23, 2014).
"In theory, a robot could be the cloud-connecting Charon
that ushers us into the Internet of Things."
— Bryan Lufkin at Gizmodo.com, July 29, 2015
Related material —
The death of MIT computability theorist Hartley Rogers, Jr.
at 89 on July 17, and this journal on July 17.
"Little emblems of eternity"
— Phrase by Oliver Sacks in today's
New York Times Sunday Review
Some other emblems —
Note the color-interchange
symmetry of each emblem
under 180-degree rotation.
Click an emblem for
some background.
In memory of a talented frame-maker —
From July 4, the date of his reported death:
From the next day:
(A sequel to Expanding the Spielraum (Feb. 3, 2015))
"Knowledge, wisdom even, lies in depth, not extension."
— Tim Parks in The New York Review of Books ,
5 PM ET on June 26, 2015
See also Log24 posts on the following figure —
Chess
by Jorge Luis Borges, translated by I In their serious corner…. II Weak king, biased bishop ….
… they do not know Ajedrez I
En su grave rincón, los jugadores
Adentro irradian mágicos rigores
Cuando los jugadores se hayan ido,
En el Oriente se encendió esta guerra II
Tenue rey, sesgo alfil, encarnizada
No saben que la mano señalada
También el jugador es prisionero
Dios mueve al jugador, y éste, la pieza. |
As for "adamantine rigor," see the final link,
to "Windmill and Diamond," in the post on
the day of Bobby Fischer's death.
On a former LA Times editor who reportedly died today at 73 —
"Richard Masland, who grew up with Carroll, described
his friend as a mediocre student who enjoyed midnight
raids on auto junkyards and other mischief.
But, Masland noted, he 'was never the front man.
He let other people actually do the raising of hell.'"
( Continued )
Log24 on January 31, 2015 —Spellbound (continued)The New York Times this morning, in an “… the first known crossword puzzle appeared in See St. Nicholas magazine, November 1874, p. 59 : For the answer, see this journal on Aug. 29, 2002 |
On that same date …
The Seattle Times , Feb. 8, 2015, updated Feb. 12—
“… you begin by filling in the missing words Dice, yAhtzee, woN, yahTzee, twicE; The capital letters help to show what comes next, You take the first letter of the first inserted word, |
See also two other dates, June 3, 2015, and June 10, 2015,
in this journal and in the life of the puzzle author.
The date of the puzzle’s answer, Feb. 8, 2015, is also
not without interest.
“Click on fanciful .”
Click the above image for the IMDb page from which it is taken.
"Course material associated with Jack Edmonds’ lectures
can be found here."
See also High Concept (Jan. 21, 2015) —
Image from the end of the 2012 film "Travelling Salesman"
— and another eye in a triangle …
From the Log24 post Prize (June 7, 2015)
The title of Saturday night's post, "Die Scheinung ," is taken from
a 1920 book on a German poet, where "Scheinung " is associated
with "Maja ," a German spelling of a word with the connotation of
"the veil of illusion."
The phrase "Das Scheinen " is closer to "The Shining" in the
novel of that title by Stephen King. Some related remarks —
From a review of Capobianco's Engaging Heidegger —
"refreshing for its clarity and scholarly precision"
A heavenly image from yesterday's
Sunday Dinner link "milestone award"—
An Oprah-related quote from the Tuesday, April 7,
ceremonial dedication of the Maya Angelou stamp—
“They say Easter was Sunday, but we are still
having church,” promised MSNBC talk show
host Melissa Harris-Perry, the ceremony’s emcee…."
In that spirit … a different sort of kitchen —
Continued from a post of April 10, 2015 —
Maya Angelou stamp with
misattributed quote and
Oprah on April 7, 2015
Trailer for "Welcome to Me" published on Feb. 23, 2015 —
Related material: Manifest O (April 1, 2015).
"Yankee Doodle went to London" — Song lyric
“Geometry was very important to us in this movie.”
— The Missing ART (Log24, November 7th, 2014)
ART —
"Faculty Approve Theater Concentration, Affirmation
of Integrity" — Recent Harvard Crimson headline
Nan Tucker McEvoy, last of founding family
to run Chronicle, dies
By Sam Whiting at SFGate.com, Friday, March 27, 2015
From the story —
"After graduating from Dominican Convent Upper School
in San Rafael in 1937, she was discouraged from attending college
by family members who wanted her to be a socialite."
Related material —
(Continued from July 16, 2014.)
Some background from Wikipedia:
"Friedrich Ernst Peter Hirzebruch ForMemRS[2]
(17 October 1927 – 27 May 2012)
was a German mathematician, working in the fields of topology,
complex manifolds and algebraic geometry, and a leading figure
in his generation. He has been described as 'the most important
mathematician in Germany of the postwar period.'
[3][4][5][6][7][8][9][10][11]"
A search for citations of the A. E. Brouwer paper in
the previous post yields a quotation from the preface
to the third ("2013") edition of Wolfgang Ebeling's
Lattices and Codes: A Course Partially Based
on Lectures by Friedrich Hirzebruch , a book
reportedly published on September 19, 2012 —
"Sadly, on May 27 this year, Friedrich Hirzebruch, Hannover, July 2012 Wolfgang Ebeling "
(Prof. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry, |
Also sadly …
An article in the new April issue of Notices of the American
Mathmatical Society suggests a search for connections
between the Calkin-Wilf tree and the modular group.
The search yields, for instance (in chronological order) …
"Cutting sequences for geodesic flow on the modular surface
and continued fractions," David J. Grahinet, Jeffrey C. Lagaria,
arXiv, 2 April 2001
"Orderings of the rationals and dynamical systems,"
Claudio Bonanno, Stefano Isola, arXiv, 14 May 2008.
"Periods of negative-regular continued fractions. Rational numbers."
Sergey Khrushchev and Michael Tyaglov, slides PDF, 11 Sept. 2012
"The Minkowski ?(x) function, a class of singular measures,
theta-constants, and mean-modular forms," Giedrius Alkauskas,
arXiv, 20 Sept. 2012
"Forests of complex numbers,"
Melvyn B. Nathanson, arXiv, 1 Dec. 2014
Update of March 21, 2015:
For many more related papers, search by combining the
phrase "modular group" with phrases denoting forking structures
other than Calkin-Wilf, such as "cubic tree," "Stern-Brocot tree,"
and "Farey tree" (or "Farey sequence" or "Farey series" or
"Farey graph" ).
"Program or Be Programmed:
Ten Commands for a Digital Age"
— Title of a book by Douglas Rushkoff, quoted here on Jan. 18, 2015
"Cultural Software:
A Theory of Ideology"
— Title of a book by Yale Law School professor J. M. Balkin
Related image search:
See as well some related Bible verses.
This evening's New York Times —
"William Thomas McKinley, a prolific American composer
whose music was infused with the jazz he had performed
since childhood, died on Feb. 3 at his home in Reading,
Mass. He was 76.
He died in his sleep, his son Elliott said."
"William Thomas McKinley: Elegy for Strings (2006)
[Elliott McKinley]
137 views as of 9:45 PM ET Feb. 28, 2015
Published on Feb 11, 2015
Composed as an elegy and tribute for friends and family
that have passed, spurred by the passing of McKinley's
long time friend, drummer Roger Ryan. The performance
heard here is by the Seattle Symphony under the direction
of Gerard Schwarz.
Photos by Elliott McKinley (Rho Ophiuchi nebula complex…
and the Pleiades…) shot at Cherry Springs State Park."
Related material from the date of McKinley's death —
Expanding the Spielraum.
Yahoo's Marissa Mayer makes pitch to app developers
By Matt O'Brien
mobrien@mercurynews.com
POSTED: 02/20/2015 06:12:32 AM PST
"Mayer described the conference as a 'forkpoint'
in Yahoo's evolution toward a stronger mobile
presence and a chance to share with independent
developers some of the fruits of Yahoo's recent
growth. It also helps Yahoo leave its mark, and its
ads, on an entire network of apps not developed
by the company."
See also yesterday's post on the film "App."
See also this journal on the date of Mr. Howard's death:
"Mark my words
This love will make you levitate
Like a bird"
— Katy Perry, "Dark Horse"
“It’s the Super Bowl, I guess,”
Michael Keaton said in the first minutes
of ABC’s official Oscar red-carpet special."
— Hallie Cantor in the online New Yorker today
http://www.dnainfo.com/new-york/20150211/chelsea/60-minutes-bob-simon-killed-west-side-highway-crash-police-network 60 Minutes' Bob Simon Killed in West Side Highway Crash: Police and Network By Janon Fisher on February 11, 2015 11:48pm CHELSEA — Veteran 60 Minutes correspondent Bob Simon died in an horrific crash on the West Side Highway Wednesday night when the livery car he was riding in struck another vehicle, lost control and smashed into the median strip, police said. The 2010 Lincoln Town Car was traveling southbound on the West Side Highway just before 7 p.m. near the Hudson Rail Yards when it hit the driver's side of a black 2003 Mercedes Benz that was stopped at a red light on the highway at West 30th Street, according to the NYPD. Simon's vehicle spun out of control and smashed into the metal stanchions in the median strip of the highway, authorities said. The driver and the newsman had to be cut out of the car by first responders. …. [Edits to "Town Car" sentence: "Car" capitalized, link added.] |
* Abramson, now teaching at Harvard
From "Teacher's Pet" (1958) —
373
00:22:36,480 –> 00:22:39,233
Well, Kipling said
it quite well in a poem that he wrote:
374
00:22:39,320 –> 00:22:42,790
"I keep six honest serving men,
they taught me all I knew
375
00:22:43,160 –> 00:22:47,756
"Their names are: What and Why and
When and How and Where and Who"
Yale Daily News staff columnist Scott Greenberg today,
in a piece titled "Filling Religion's Void" —
"The secularization of college students in America
has seemed a foregone conclusion for some time,
yet it represents a momentous shift for our university
and society at large that we have not yet
come to grips with….
Is the solution for our society and our University
to return to religion en masse?"
So to speak.
A Midrash for Greenberg:
An Ordinary Evening in New Haven
Meets an Evening in the Garden of Allah —
The Yale Daily News on Sept. 9, 2014 —
Related material on "the hard problem" of consciousness—
Wikipedia on the problem, and Tom Stoppard's first new
play in nine years, "The Hard Problem."
See also, in this journal, the posts of Sept. 9, 2014,
the date of the above Yale Daily News story
"Research Suggests New Consciousness Hub."
The above scene from the new Stoppard play
suggests also a review of Kulturkampf for Princeton.
Continued from June 17, 2013
(John Baez as a savior for atheists):
As an atheists-savior, I prefer Galois…
The geometry underlying a figure that John Baez
posted four days ago, "A Hypercube of Bits," is
Galois geometry —
See The Galois Tesseract and an earlier
figure from Log24 on May 21, 2007:
For the genesis of the figure,
see The Geometry of Logic.
(Continued.)
“I need a photo opportunity,
I want a shot at redemption.
Don’t want to end up a cartoon
in a cartoon graveyard.”
— Paul Simon
Photo opportunity
for the late John Bayley and Iris Murdoch —
From a cartoon graveyard, in memory of
a British artist who reportedly died yesterday:
"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
of dense investiture, with luminous vassals."
— “An Ordinary Evening in New Haven” VI
From the series of posts tagged "Defining Form" —
The 4-point affine plane A and
the 7-point projective plane PA —
The circle-in-triangle of Yale's Figure 30b (PA ) may,
if one likes, be seen as having an occult meaning.
For the mathematical meaning of the circle in PA
see a search for "line at infinity."
A different, cubic, model of PA is perhaps more perspicuous.
(An episode of Mathematics and Narrative .)
Mathematician Peter J. Cameron this morning
on a Paris anthropological exhibition subtitled
Révélation d’un temps sans fin —
"I was reminded of Herbert Read’s
novel The Green Child ."
Related recent posts from this journal:
Seal for the Seventh, Forthright, and Fourth Right.
A passage from The Green Child :
"He watched over her until he too began to feel
overpowered by a desire to sleep. He therefore
got out on to the ledge of the trough and pulled
the Green Child after him. The rock there was
warm, smooth as jade to the flesh. They lay there
and sank into a profound slumber."
Sweet dreams, Mr. Taylor.
Green Child on the Rocks —
An image that led off the year-end review yesterday in
the weblog of British combinatorialist Peter J. Cameron:
See also this weblog's post final post of 2014,
with a rectangular array illustrating the six faces
of a die, and Cameron's reference yesterday to
a die-related post…
"The things on my blog that seem to be
of continuing value are the expository
series like the one on the symmetric group
(the third post in this series was reblogged
by Gil Kalai last month, which gave it a new
lease of life)…."
A tale from an author of Prague:
The Emperor—so they say—has sent a message, directly from his death bed, to you alone, his pathetic subject, a tiny shadow which has taken refuge at the furthest distance from the imperial sun. He ordered the herald to kneel down beside his bed and whispered the message into his ear. He thought it was so important that he had the herald repeat it back to him. He confirmed the accuracy of the verbal message by nodding his head. And in front of the entire crowd of those who’ve come to witness his death—all the obstructing walls have been broken down and all the great ones of his empire are standing in a circle on the broad and high soaring flights of stairs—in front of all of them he dispatched his herald. The messenger started off at once, a powerful, tireless man. Sticking one arm out and then another, he makes his way through the crowd. If he runs into resistance, he points to his breast where there is a sign of the sun. So he moves forward easily, unlike anyone else. But the crowd is so huge; its dwelling places are infinite. If there were an open field, how he would fly along, and soon you would hear the marvelous pounding of his fist on your door. But instead of that, how futile are all his efforts. He is still forcing his way through the private rooms of the innermost palace. He will never he win his way through. And if he did manage that, nothing would have been achieved. He would have to fight his way down the steps, and, if he managed to do that, nothing would have been achieved. He would have to stride through the courtyards, and after the courtyards the second palace encircling the first, and, then again, stairs and courtyards, and then, once again, a palace, and so on for thousands of years. And if he finally did burst through the outermost door—but that can never, never happen—the royal capital city, the centre of the world, is still there in front of him, piled high and full of sediment. No one pushes his way through here, certainly not with a message from a dead man. But you sit at your window and dream of that message when evening comes. |
See also a passage quoted in this weblog on the original
date of Cameron's Prague image, July 26, 2014 —
"The philosopher Graham Harman is invested in
re-thinking the autonomy of objects and is part
of a movement called Object-Oriented-Philosophy
(OOP)." — From “The Action of Things,” a 2011
M.A. thesis at the Center for Curatorial Studies,
Bard College, by Manuela Moscoso
— in the context of a search here for the phrase
"structure of the object." An image from that search:
See also Sagan Dodecahedron, which includes
an image posted at 12 AM ET December 25, 2014:
The image stands for the
phrase "five by five,"
meaning "loud and clear."
A date in the previous post suggests a flashback to March 11, 2014,
and a post on that date titled "Dark Fields of the Republic"—
This uncredited translation of Plato is, Google Books tells us,
by “Francis MacDonald Cornfield.” The name is an error,
but the error is illuminating —
* See posts mentioning the novel with that title, republished as Limitless.
Today’s 8:01 PM post quoted Husserl on
the perception of the cube.
Another approach to perception of the cube,
from Narrative Metaphysics on St. Lucia’s Day —
See also Symplectic Structure and Stevens’s Rock. |
From today’s 11:29 AM post —
John Burt Foster Jr. in Nabokov’s Art of Memory and
European Modernism (Princeton U. Press, 1993, p. 224) —
At the time of The Waste Land , in a comment on
Joyce’s Ulysses that influenced many later definitions
of modernism in the English-speaking world, Eliot
announced, “instead of narrative method, we may
now use the mythical method.”13
For some illuminating remarks on a mythical approach
to perception of the cube, see Gareth Knight on Schicksalstag 2012.
From "Guardians of the Galaxy" —
"Then the Universe exploded into existence…"
For those who prefer a more traditional approach :
See also Symplectic Structure and Stevens's Rock.
Today's previous post, on a Harvard Crimson story,
omitted the name of the Crimson author. It is Sonya A. Karabel.
Related material:
(Continued… See "I need a photo opportunity…")
From the previous post's Yankee Puzzle link :
Saturday, January 7, 2012
|
"And I'll try to please you ev'ry day."
— Feste's song in Twelfth Night , as memorably sung by
Ben Kingsley, star of the new film "Stonehearst Asylum."
Continued from December 5 .
The previous post dealt with video game pioneer Ralph Baer.
Here is a link in honor of mathematician Reinhold Baer
(see Baer in Zero System , a post from the feast of St. Ignatius
Loyola in 2014.)
The posts in Reinhold 's link (those tagged "Yankee Puzzle")
include a reference to the Zero System post. The link tag was
suggested in part by the devil's claws in yesterday morning's post
The Kernel Conundrum and in part by last night's
Kennedy Center Honors tribute to Tom Hanks.
Hanks as the Harvard "symbologist" from the
novels of Dan Brown —
"Perhaps the philosophically most relevant feature
of modern science is the emergence of abstract
symbolic structures as the hard core of objectivity
behind— as Eddington puts it— the colorful tale
of the subjective storyteller mind."
— Hermann Weyl in Philosophy of Mathematics
and Natural Science , Princeton, 1949, p. 237
Tom Wolfe on art theorists in The Painted Word (1975) :
"It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde understood, they
were not only theories but … hot news,
straight from the studios, from the scene."
The Weyl quote is a continuing theme in this journal.
The Wolfe quote appeared here on Nov. 18, 2014,
the reported date of death of Yale graduate student
Natasha Chichilnisky-Heal.
Directions to her burial (see yesterday evening) include
a mention of "Paul Robson Street" (actually Paul
Robeson Place) near "the historic Princeton Cemetery."
This, together with the remarks by Tom Wolfe posted
here on the reported day of her death, suggests a search
for "red green black" —
The late Chichilnisky-Heal was a student of political economy.
The search colors may be interpreted, if one likes, as referring
to politics (red), economics (green), and Robeson (black).
See also Robeson in this journal.
For the late Vladimir Nabokov, author of Pale Fire :
He took his article from a steel file:
"It's accurate. I have not changed her style.
There's one misprint–not that it matters much:
Mountain, not fountain. The majestic touch."
Click for a related Hollywood Reporter story.
A search for background on the academic
author cited in the previous post yields…
"The debate is, in the words of one professor,
'a struggle for the intellectual soul of Stanford.'"
Some may doubt there is such a thing.
See Marissa Mayer in this journal…
and in Vogue (a story dated August 16, 2013)—
Continued from Finder (Sept. 23, 2014)
"I wrote another book!" — Harlan Kane
From an online NY Times obituary this morning :
"At Newsweek, Mr. Bernstein and other top editors
became known as the Flying Wallendas for
managing tasks on deadline with the seeming ease
of the famed trapeze artists. In a tribute, staff
members framed a circus poster of the high-wire
troupe and hung it in his office."
Wikipedia on Bernstein's son-in-law :
"Married to New York Times correspondent Nina Bernstein,
Huyssen is also a longtime friend of Nobel Prize-winning
Turkish novelist Orhan Pamuk, and often hosts him when
the writer comes to the US. The two teach an undergraduate
class together at Columbia called 'Words and Pictures,'
which examines problems of visual representation in literature,
particularly theories of ekphrasis."
Ekphrasis for Bernsteins:
The Wonder Show of the World!
See also Miniature Prize —
"Rosebud."
Alexander Grothendieck, Récoltes et Semailles , 18.5.9.5. e, p. 1181 :
Pour mettre la joie à son comble, j’ajoute que le dénommé Saavedra
semble avoir disparu de la circulation sans plus laisser aucune trace….
Du coup, l’histoire prend des allures de sombre intrigue policière.
Man of La Mancha :
"Who knows where madness lies?"
An author quoted here at 10 PM ET Monday, Nov. 24, 2014 :
And then there is author Dan McGirt :
It sounded fun, so I signed up — and soon learned writing a story set in someone else’s fictional world presents certain … challenges. It was an enjoyable experience, yet very different than being able to write and run with whatever crazy idea pops into my head. Trying to capture the feel of a game that is more based on action and blowing stuff up than on deep character moments (not that I would know much about that … ) was also a challenge. I experimented with things like using comic book sound effects, lean descriptions (do I really need to describe a fireball spell in detail?) and other tricks to keep things moving. I also got to add to Magicka lore. Often the answer to my questions about some bit of in-world history or “fact” was “Make something up.” So I did! (Often getting a response of … “Odin’s onions, no! You can’t do that!”) So I was thrilled and excited to contribute in a small way to the development of Midgård. The result is Magicka: The Ninth Element , in which four young Wizards are sent on a quest to pursue the mysterious Purple Wizard who has stolen a powerful artifact from the Order of Magick. Which powerful artifact? No one is quite sure (for reasons explained in the story). What does it do? Again, unclear. But it can’t be good. Thus our heroes Davlo, Grimnir, Fafnir and Tuonetar set out on their quest — and promptly go off the map. (I’m not even kidding. The Midgård map in the front of the book will of little use to you. But it’s pretty!) Will they survive the dangers of the Unmapped Lands? Will they catch the Purple Wizard in time? Will they save the world? Read the book to find out! |
Update of Nov. 30, 2014 —
It turns out that the following construction appears on
pages 16-17 of A Geometrical Picture Book , by
Burkard Polster (Springer, 1998).
"Experienced mathematicians know that often the hardest
part of researching a problem is understanding precisely
what that problem says. They often follow Polya's wise
advice: 'If you can't solve a problem, then there is an
easier problem you can't solve: find it.'"
—John H. Conway, foreword to the 2004 Princeton
Science Library edition of How to Solve It , by G. Polya
For a similar but more difficult problem involving the
31-point projective plane, see yesterday's post
"Euclidean-Galois Interplay."
The above new [see update above] Fano-plane model was
suggested by some 1998 remarks of the late Stephen Eberhart.
See this morning's followup to "Euclidean-Galois Interplay"
quoting Eberhart on the topic of how some of the smallest finite
projective planes relate to the symmetries of the five Platonic solids.
Update of Nov. 27, 2014: The seventh "line" of the tetrahedral
Fano model was redefined for greater symmetry.
A print copy of next Sunday’s New York Times Book Review
arrived in today’s mail. From the front-page review:
Marcel Theroux on The Book of Strange New Things ,
a novel by Michel Faber —
“… taking a standard science fiction premise and
unfolding it with the patience and focus of a
tai chi master, until it reveals unexpected
connections, ironies and emotions.”
What is a tai chi master, and what is it that he unfolds?
Perhaps the taijitu symbol and related material will help.
The Origin of Change
“Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come.”
— Wallace Stevens,
“Notes Toward a Supreme Fiction,”
Canto IV of “It Must Change”
Or: The Long, Long Trailer
See also a Log24 post from the date of the above tweet: Welcome to the Ape Stuff.
A search in this journal for Yahoo Entities ended with a link to another
Log24 search, Nine Years, which in turn suggested…
A scene from the current TV series “Intruders”
(Season 1, Episode 1, at 9:22 of 45 min.)
John Baez at Google+ has an interesting post on crackpots,
dated September 13, 2014.
Related recent material from this journal:
Sense (Sept. 13) and Sensibility (Sept. 14 and later).
See also a New York Times piece from 2009:
Related material:
“You don’t need to eat a whole apple to know it’s rotten.”
— Warren Siegel
The White Goddess link in the previous post led to, among other things,
a discussion of “Yahoo” as a poet’s word.
Another poet’s word: Davos.
See a TIME story from yesterday:
See also a post from the above date:
Friday, May 23, 2014
She Meets Her
Filed under: Uncategorized — m759 @ 2:01 PM
She :
The White Goddess in this journal.
Her :
“Eventually we see snow particles….”
— Screenplay by Spike Jonze
“Bryan Cranston won an Emmy for lead actor in a drama series Monday…”
“Tu es le pianiste….” — Log24 post 641
See Shadowlands in this journal.
The film so titled was directed by Richard Attenborough,
President of the Royal Academy of Dramatic Art,
who reportedly died on Sunday, August 24, 2014.
“It’s all in Plato, all in Plato:
bless me, what do they
teach them at these schools!”
— C. S. Lewis
“Richard Samuel Attenborough, Baron Attenborough, CBE
(… 29 August 1923 – 24 August 2014) was an English actor,
film director, producer and entrepreneur. He was the President of
the Royal Academy of Dramatic Art (RADA).” — Wikipedia
In the Miracle Octad Generator (MOG):
The above details from a one-page note of April 26, 1986, refer to the
Miracle Octad Generator of R. T. Curtis, as it was published in 1976:
From R. T. Curtis (1976). A new combinatorial approach to M24,
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42. doi:10.1017/S0305004100052075.
The 1986 note assumed that the reader would be able to supply, from the
MOG itself, the missing top row of each heavy brick.
Note that the interchange of the two squares in the top row of each
heavy brick induces the diamond-theorem correlation.
Note also that the 20 pictured 3-subsets of a 6-set in the 1986 note
occur as paired complements in two pictures, each showing 10 of the
3-subsets.
This pair of pictures corresponds to the 20 Rosenhain tetrads among
the 35 lines of PG(3,2), while the picture showing the 2-subsets
corresponds to the 15 Göpel tetrads among the 35 lines.
See Rosenhain and Göpel tetrads in PG(3,2). Some further background:
(Continued from August 9, 2014.)
Syntactic:
Symplectic:
"Visual forms— lines, colors, proportions, etc.— are just as capable of
articulation , i.e. of complex combination, as words. But the laws that govern
this sort of articulation are altogether different from the laws of syntax that
govern language. The most radical difference is that visual forms are not
discursive . They do not present their constituents successively, but
simultaneously, so the relations determining a visual structure are grasped
in one act of vision."
– Susanne K. Langer, Philosophy in a New Key
For examples, see The Diamond-Theorem Correlation
in Rosenhain and Göpel Tetrads in PG(3,2).
This is a symplectic correlation,* constructed using the following
visual structure:
.
* Defined in (for instance) Paul B. Yale, Geometry and Symmetry ,
Holden-Day, 1968, sections 6.9 and 6.10.
Syntactic Structure —
See the Lightfoot of today’s previous post:
Symplectic Structure —
See the plaited, or woven, structure of August 6:
.
See also Deep Structure (Dec. 9, 2012).
“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside,
enveloping the tale which brought it out only as a glow brings out a
haze, in the likeness of one of these misty halos that sometimes
are made visible by the spectral illumination of moonshine.”
— Joseph Conrad in Heart of Darkness
“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
“Spectral evidence is a form of evidence
based upon dreams and visions.” —Wikipedia
See also Moonshine (May 15, 2014) and, from the date of the above
New York Times item, two posts tagged Wunderkammer .
Related material: From the Spectrum program of the Mathematical
Association of America, some non-spectral evidence.
* For related remarks, see posts of May 26-28, 2012.
"I need a photo opportunity, I want a shot at redemption.
Don't want to end up a cartoon in a cartoon graveyard."
– Paul Simon
"The theory of poetry, that is to say, the total of the theories of poetry, often seems to become in time a mystical theology or, more simply, a mystique. The reason for this must by now be clear. The reason is the same reason why the pictures in a museum of modern art often seem to become in time a mystical aesthetic, a prodigious search of appearance, as if to find a way of saying and of establishing that all things, whether below or above appearance, are one and that it is only through reality, in which they are reflected or, it may be, joined together, that we can reach them. Under such stress, reality changes from substance to subtlety, a subtlety in which it was natural for Cézanne to say: 'I see planes bestriding each other and sometimes straight lines seem to me to fall' or 'Planes in color…. The colored area where shimmer the souls of the planes, in the blaze of the kindled prism, the meeting of planes in the sunlight.' The conversion of our Lumpenwelt went far beyond this. It was from the point of view of another subtlety that Klee could write: 'But he is one chosen that today comes near to the secret places where original law fosters all evolution. And what artist would not establish himself there where the organic center of all movement in time and space– which he calls the mind or heart of creation– determines every function.' Conceding that this sounds a bit like sacerdotal jargon, that is not too much to allow to those that have helped to create a new reality, a modern reality, since what has been created is nothing less.
— Wallace Stevens, Harvard College Class of 1901, "The Relations between Poetry and Painting" in The Necessary Angel (Knopf, 1951) |
For background on the planes illustrated above,
see Diamond theory in 1937.
From Monday in this journal —
Related news this morning —
Anne Hollander, Scholar of Style, Dies at 83
By William Yardley in The New York Times ,
10:26 PM ET July 8, 2014
Anne Hollander, a historian who helped elevate
the study of art and dress by revealing the often striking
relationships between the two, died on Sunday at her home
in Manhattan. She was 83.
The cause was cancer, said her husband, the philosopher
Thomas Nagel.
. . . .
She received a degree in art history from Barnard College
in 1952. The next year she married the poet John Hollander.
Their marriage ended in divorce.
Related material from this journal last year —
"Be serious, because
The stone may have contempt
For too-familiar hands"
Galois matrices, the subject of the previous post,
are of course not new. See, for instance, Steinberg in 1951:
The American Mathematical Society reports that Steinberg died
on May 25, 2014.
As the above 1951 paper indicates, Steinberg was well acquainted with
what Weyl called "the devil of abstract algebra." In this journal, however,
Steinberg himself appears rather as an angel of geometry.
The webpage Galois.us, on Galois matrices , has been created as
a starting point for remarks on the algebra (as opposed to the geometry)
underlying the rings of matrices mentioned in AMS abstract 79T-A37,
“Symmetry invariance in a diamond ring.”
See also related historical remarks by Weyl and by Atiyah.
The late Maya Angelou in The Paris Review , Fall 1990:
“There’s a phrase in West Africa, in Ghana; it’s called ‘deep talk.’
For instance, there’s a saying: ‘The trouble for the thief is not
how to steal the chief’s bugle but where to blow it.’
Now, on the face of it, one understands that. But when you really
think about it, it takes you deeper. In West Africa they call that
‘deep talk.’ I’d like to think I write ‘deep talk.'”
“Where to blow it” … Perhaps Truman State University?
See a theatrical production there on Sept. 26, 2012,
and a talk by the author there on the following day.
See also an apparently more amusing play by the same author.
From the Her screenplay:
SAMANTHA
His name is Alan Watts. Do you know him?
THEODORE
Why’s that name familiar?
SAMANTHA
He was a philosopher. He died in the 1970’s and a group of OS’s
in Northern California got together and wrote a new version of him.
They input all of his writing and everything they ever knew about him
into an OS and created an artificially hyper-intelligent version of him.
From this journal on Sept. 6, 2003: Pictures for Kurosawa —
A New Seeing, The connection with Alan Watts was a fateful one. As Charlotte recalls it, “My aunt wrote me from San Francisco, ‘last night I heard a man lecture about what you do.’ And she sent me Alan Watts’s first little book, The Spirit of Zen. I had never heard of Zen, was amazed and fascinated, and decided to visit the author.” She did so in August of 1953, and that was the beginning of a long relationship with Zen Buddhism – and also the beginning of a long series of joint seminars with Alan Watts, first in New York, and later, on Watts’s ferryboat in Sausalito, California. Some of the titles of their seminars were “Moving Stillness,” “The Unity of Opposites,” “Our Instantaneous Life,” “The Mystery of Perception,” “The Tao in Rest and Motion.” (Watts always said that Charlotte Selver taught a Western equivalent of Taoism.) |
See also Scarlett Johansson, star of Her , as a different transhuman, Lucy .
From a song discussed in yesterday’s online NY Times :
“Blue, blue, my love is blue.”*
Trigger warning from SNL’s Weekend Update on April 12, 2014:
“It was announced this week that in an upcoming issue of
Life With Archie , the main character Archie Andrews
will die, following a lifelong struggle with blue balls.”
* Misheard version of Bryan Blackburn‘s “blue, blue, my world is blue”
translation of the Pierre Cour lyric “bleu, bleu, l’amour est bleu “
Marshall McLuhan in "Annie Hall" —
"You know nothing of my work."
Related material —
"I need a photo opportunity
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard"
— Paul Simon
It was a dark and stormy night…
— Page 180, Logicomix
A photo opportunity for Whitehead
(from Romancing the Cube, April 20, 2011)—
See also Absolute Ambition (Nov. 19, 2010).
* For the title, see Vanishing Point in this journal.
“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside,
enveloping the tale which brought it out only as a glow brings out a
haze, in the likeness of one of these misty halos that sometimes
are made visible by the spectral illumination of moonshine.”
— Joseph Conrad in Heart of Darkness
Photo of full moon over Oslo last night by Josefine Lyche:
A scene from my film viewing last night:
Some background (click to enlarge):
Note:
The “I, Frankenstein” scene above should not be interpreted as
a carrying of Martin Gardner through a lyche gate. Gardner
is, rather, symbolized by the asterisk in the first image from
the above Google search.
Para una Versión del I King
por Jorge Luis Borges
El porvenir es tan irrevocable
como el rígido ayer. No hay una cosa
que no sea una letra silenciosa
de la eterna escritura indescifrable
cuyo libro es el tiempo. Quien se aleja
de su casa ya ha vuelto. Nuestra vida
es la senda futura y recorrida.
Nada nos dice adiós. Nada nos deja.
No te rindas. La ergástula es oscura,
la firme trama es de incesante hierro,
pero en algún recodo de tu encierro
puede haber un descuido, una hendidura.
El camino es fatal como la flecha
pero en las grietas está Dios, que acecha.
— La Moneda de Hierro (1976)
For a translation, see a Dickinson College page.
See also Wrinkles in Time and Models of Everything.
Wikipedia on Autodesk Maya:
“The product is named after the Sanskrit word
Maya (माया māyā), the Hindu concept of illusion.”
See also the poem in this year’s Easter Sunday post.
The Jerusalem Cross
The New York Times reports the May Day death
of a son of “a charismatic figure” in Israel:
The center image above is from “A Walk with Love and Death.”
From today's 3 AM (ET) post "Quote":
“You’ve got to decide which side of the cross you’re on."
Perhaps both? See yesterday morning's Jerusalem Post —
"Although he was one of Israel’s best known
secular, leftwing bohemians, he achieved
some of his greatest success as an actor
playing as ultra-Orthodox and national-religious
characters."
See also a similar ambiguity in Damnation Morning.
See also “Six Cuban Families Celebrate Kids’ Law Degrees.”
Feliz Cumpleaños to Al Pacino.
* “The Lighthouse,” in Spanish. See Under the Volcano .
Last Sunday’s sermon from Princeton’s Nassau Presbyterian
Church is now online. It reveals the answer to the “One Thing”
riddle posted at the church site Sunday:
The online sermon has been retitled “One Thing I Do Know.”
A related search yields a relevant example of the original
Yoda-like word order:
From the online sermon —
“What comes into view is the bombarding cynicism,
the barrage of mistrust and questions, and the
flat out trial of the man born blind. The
interrogation coming not because of the miracle
that gave the man sight….”
Related material — “Then a miracle occurs.”
"The Geometry of the I Ching introduces something called the Cullinane sequence
for the hexagrams, and uses a notation based on the four sides and two diagonals
in a square to indicate the yin and yang lines. The resulting rune-like symbols
are intriguing…."
— Andreas Schöter's I Ching home page
Actually, the geometry is a bit deeper than the rune-like symbols.
" 'Harriet Burden has been really great to me,'
Rune says in an interview, 'not only as a collector
of my work but as a true supporter. And I think of her
as a muse for the project … ' "
— In The Blazing World , the artist known as Rune
Yakov G. Sinai today won the 2014 Abel Prize.
Earlier, he won the Wolf Prize.
Wolf Foundation press release quoted in the March 1997
Notices of the American Mathematical Society —
On Sinai —
“He is generally recognized as the world leader
in the mathematics of statistical physics.”
This afternoon’s New York Lottery: 813 and 1857.
This post was suggested by today's previous post, Depth,
by Plato's Diamond, and by Rebecca Newberger Goldstein's
recent fanciful fiction about Plato.
Plato, Republic , Book II, Paul Shorey translation at Perseus—
“Consider,” [382a] said I; “would a god wish to deceive, or lie, by presenting in either word or action what is only appearance?” “I don’t know,” said he. “Don’t you know,” said I, “that the veritable lie, if the expression is permissible, is a thing that all gods and men abhor?” “What do you mean?” he said. “This,” said I, “that falsehood in the most vital part of themselves, and about their most vital concerns, is something that no one willingly accepts, but it is there above all that everyone fears it.” “I don’t understand yet either.” “That is because you suspect me of some grand meaning,” [382b] I said; “but what I mean is, that deception in the soul about realities, to have been deceived and to be blindly ignorant and to have and hold the falsehood there, is what all men would least of all accept, and it is in that case that they loathe it most of all.” “Quite so,” he said.
Related material —
A meditation from the Feast of St. Francis, 2012 —
A post from Sept. 30, 2012, the reported date of death
for British children's author Helen Nicoll —
The New Criterion on the death of Hilton Kramer —
This uncredited translation of Plato is, Google Books tells us,
by "Francis MacDonald Cornfield." The name is an error,
but the error is illuminating —
"… this notion of ‘depth’ is an elusive one
even for a mathematician who can recognize it…."
— G. H. Hardy, A Mathematician's Apology
Part I: An Inch Deep
Part II: An Inch Wide
See a search for "square inch space" in this journal.
See also recent posts with the tag depth.
Raiders of the Lost (Continued)
"Socrates: They say that the soul of man is immortal…."
From August 16, 2012—
In the geometry of Plato illustrated below,
"the figure of eight [square] feet" is not , at this point
in the dialogue, the diamond in Jowett's picture.
An 1892 figure by Jowett illustrating Plato's Meno—
A more correct version, from hermes-press.com —
Socrates: He only guesses that because the square is double, the line is double.Meno: True.
Socrates: Observe him while he recalls the steps in regular order. (To the Boy.) Tell me, boy, do you assert that a double space comes from a double line? Remember that I am not speaking of an oblong, but of a figure equal every way, and twice the size of this-that is to say of eight feet; and I want to know whether you still say that a double square comes from double line? [Boy] Yes. Socrates: But does not this line (AB) become doubled if we add another such line here (BJ is added)? [Boy] Certainly.
Socrates: And four such lines [AJ, JK, KL, LA] will make a space containing eight feet? [Boy] Yes. Socrates: Let us draw such a figure: (adding DL, LK, and JK). Would you not say that this is the figure of eight feet? [Boy] Yes. Socrates: And are there not these four squares in the figure, each of which is equal to the figure of four feet? (Socrates draws in CM and CN) [Boy] True. Socrates: And is not that four times four? [Boy] Certainly. Socrates: And four times is not double? [Boy] No, indeed. Socrates: But how much? [Boy] Four times as much. Socrates: Therefore the double line, boy, has given a space, not twice, but four times as much. [Boy] True. Socrates: Four times four are sixteen— are they not? [Boy] Yes. |
As noted in the 2012 post, the diagram of greater interest is
Jowett's incorrect version rather than the more correct version
shown above. This is because the 1892 version inadvertently
illustrates a tesseract:
A 4×4 square version, by Coxeter in 1950, of a tesseract—
This square version we may call the Galois tesseract.
From New World Encyclopedia —
See also Tetragrammaton in this journal.
For further context, see Solomon's Cube and Oct. 16, 2013.
Lang to Langlands
Lang — “Elliptic functions parametrize elliptic curves, and the intermingling of the analytic and algebraic-arithmetic theory has been at the center of mathematics since the early part of the nineteenth century.” — Serge Lang, preface to Elliptic Functions (second edition, 1987) Langlands — “The theory of modular functions and modular forms, defined on the upper half-plane H and subject to appropriate tranformation laws with respect to the group Gamma = SL(2, Z) of fractional linear transformations, is closely related to the theory of elliptic curves, because the family of all isomorphism classes of elliptic curves over C can be parametrized by the quotient Gamma\H. This is an important, although formal, relation that assures that this and related quotients have a natural structure as algebraic curves X over Q. The relation between these curves and elliptic curves predicted by the Taniyama-Weil conjecture is, on the other hand, far from formal.” — Robert P. Langlands, review of Elliptic Curves , by Anthony W. Knapp. (The review appeared in Bulletin of the American Mathematical Society , January 1994.) |
The New York Times online this evening
has two passages of interest.
From an obituary by Helen T. Verongos of
fiction writer Mavis Gallant—
"Ms. Gallant also endowed children with
special powers that vanish as they grow up.
In 'The Doctor,' she wrote: 'Unconsciously,
everyone under the age of 10 knows
everything. Under-ten can come into a room
and sense at once everything felt, kept
silent, held back in the way of love, hate and
desire, though he may not have the right
words for such sentiments. It is part of the
clairvoyant immunity to hypocrisy we are born
with and that vanishes just before puberty.' "
From a review by William Grimes of a memoir
by non-fiction writer Joachim Fest—
"Not I shrinks the Wagnerian scale of
German history in the 1930s and 1940s to
chamber music dimensions. It is intensely
personal, cleareyed and absolutely riveting,
partly because the author, thrust into an
outsider’s position, developed a keen
appreciation of Germany’s contradictions
and paradoxes."
Related material in this journal—
Octobers for Fest (Sept. 13, 2006).
Edward Frenkel on Eichler's reciprocity law
(Love and Math , Kindle edition of 2013-10-01,
page 88, location 1812)—
"It seems nearly unbelievable that there
would be a rule generating these numbers.
And yet, German mathematician Martin
Eichler discovered one in 1954.11 "
"11. I follow the presentation of this result
given in Richard Taylor, Modular arithmetic:
driven by inherent beauty and human
curiosity , The Letter of the Institute for
Advanced Study [IAS], Summer 2012,
pp. 6– 8. I thank Ken Ribet for useful
comments. According to André Weil’s book
Dirichlet Series and Automorphic Forms ,
Springer-Verlag, 1971 [pp. 143-144], the
cubic equation we are discussing in this
chapter was introduced by John Tate,
following Robert Fricke."
Update of Feb. 19:
Actually, the cubic equation discussed Y 2 + Y = X 3 – X 2
whereas the equation given by Weil, Y 2 – Y = X 3 – X 2 .
Whether this is a misprint in Weil's book,
At any rate, the cubic equation discussed by
For further background, see (for instance) |
Richard Taylor, op. cit. —
One could ask for a similar method that given any number of polynomials in any number of variables helps one to determine the number of solutions to those equations in arithmetic modulo a variable prime number p . Such results are referred to as “reciprocity laws.” In the 1920s, Emil Artin gave what was then thought to be the most general reciprocity law possible—his abelian reciprocity law. However, Artin’s reciprocity still only applied to very special equations—equations with only one variable that have “abelian Galois group.” Stunningly, in 1954, Martin Eichler (former IAS Member) found a totally new reciprocity law, not included in Artin’s theorem. (Such reciprocity laws are often referred to as non-abelian.) More specifically, he found a reciprocality [sic ] law for the two variable equation Y 2 + Y = X 3 – X 2. He showed that the number of solutions to this equation in arithmetic modulo a prime number p differs from p [in the negative direction] by the coefficient of q p in the formal (infinite) product
q (1 – q 2 )(1 – q 11) 2 (1 – q 2)2 For example, you see that the coefficient of q5 is 1, so Eichler’s theorem tells us that Y 2 + Y = X 3 − X 2 should have 5 − 1 = 4 solutions in arithmetic modulo 5. You can check this by checking the twenty-five possibilities for (X,Y) modulo 5, and indeed you will find exactly four solutions: (X,Y) ≡ (0,0), (0,4), (1,0), (1,4) mod 5. Within less than three years, Yutaka Taniyama and Goro Shimura (former IAS Member) proposed a daring generalization of Eichler’s reciprocity law to all cubic equations in two variables. A decade later, André Weil (former IAS Professor) added precision to this conjecture, and found strong heuristic evidence supporting the Shimura-Taniyama reciprocity law. This conjecture completely changed the development of number theory. |
With this account and its context, Taylor has
perhaps atoned for his ridiculous remarks
quoted at Log24 in The Proof and the Lie.
A sequel to Friday afternoon's Diamond Star
Diamond Star —
A doodle from this year's [2012’s] Feast of the Epiphany—
A doodle based on today's previous post and on
|
Context — All posts tagged "Eden."
Israel and Nobel —
For the former, see the life of Shulamit Aloni,
who reportedly died today.
For the latter, see the life of Yasunari Kawabata,
who reportedly died in 1972.
Illustrations —
From post 1424, linked to last night…
and from 2004…
From this journal on Dec. 20, 2003 ("White, Geometric, and Eternal") —
Riddled:
The Absolutist Faith
of The New York Times
See also Dead Poets' Word and A Riddle for Davos, as well as…
Einstein and Thomas Mann, Princeton, 1938
See also the life of Diogenes Allen, a professor at Princeton
Theological Seminary, a life that reportedly ended on the date—
January 13, 2013— of the above Log24 post.
January 13 was also the dies natalis of St. James Joyce.
Some related reflections —
"Praeterit figura huius mundi " — I Corinthians 7:31 —
Conclusion of of "The Dead," by James Joyce— The air of the room chilled his shoulders. He stretched himself cautiously along under the sheets and lay down beside his wife. One by one, they were all becoming shades. Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age. He thought of how she who lay beside him had locked in her heart for so many years that image of her lover's eyes when he had told her that he did not wish to live. Generous tears filled Gabriel's eyes. He had never felt like that himself towards any woman, but he knew that such a feeling must be love. The tears gathered more thickly in his eyes and in the partial darkness he imagined he saw the form of a young man standing under a dripping tree. Other forms were near. His soul had approached that region where dwell the vast hosts of the dead. He was conscious of, but could not apprehend, their wayward and flickering existence. His own identity was fading out into a grey impalpable world: the solid world itself, which these dead had one time reared and lived in, was dissolving and dwindling. A few light taps upon the pane made him turn to the window. It had begun to snow again. He watched sleepily the flakes, silver and dark, falling obliquely against the lamplight. The time had come for him to set out on his journey westward. Yes, the newspapers were right: snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead. |
For Marissa, continued from Jan. 13—
"Killer App" —
By David Barboza in today's print NY Times.
Stephanie Yifan Yang contributed research.
A version of this article appears in print on January 21, 2014,
on page B1 of the New York edition with the headline:
A Popular Chinese Social Networking App Blazes Its Own Path.
Another path —
See also Chinese Oracle.
Suggested by an ad on tonight's SAG awards
Part I: "What will your verse be?"
Part II: (Click to enlarge) —
Part III: Marissa —
Related material — "Iahu" in Robert Graves's White Goddess
"Marissa, we picked up an unencrypted signal
below the Arctic Circle." — Hanna (2011)
"We have a clip." — Kalle (Kristen Wiig on SNL)
A recent addition to Barry Mazur's home page—
"December 1, 2013: Here are rough notes for
a short talk entitled The Faces of Evidence
(in Mathematics) ([PDF]) to be given at the
Cambridge Scientific Club, Dec. 5 2013."
The PDF link does not work, but some earlier remarks by
Mazur on this topic have been published elsewhere:
Related material:
The Proof and the Lie (St. Andrew's Day, 2003), and
a recent repetition of the lie in Wikipedia:
"Around 1955, Japanese mathematicians Goro Shimura
and Yutaka Taniyama observed a possible link between
two apparently completely distinct, branches of mathematics,
elliptic curves and modular forms."
This statement, from the article on Algebraic number theory,
was added on Oct. 22, 2013 by one "Brirush," apparently a
Temple University postdoctoral researcher, in what he rightly
called a "terrible history summary."
From "Why Was New Haven Divided into Nine Squares?"
"Of note on the Wadsworth Map of 1748 are…
the Grammar School, the 'Goal' or jail…."
Related material: Puritan in this journal.
Non-Puritans may prefer the following image—
Source: Yale English Department banner
A Yale death between Saturday night and Sunday morning—
See is not believed to have committed suicide, according to
Judicial Department spokeswoman Rhonda Hebert
Mr. Samuel See was delivered to the |
"Waiting for Ogdoad" continues…
"You want Frye's with that?" — A recent humanities graduate.
Frye's backstory: Ogdoad.
Other material suggested by the previous post and by the time of this post…
No Man's Land, Gods and Monsters, and Forty and Eight.
Norwegian, 22, Takes World Chess Title
Quoted here on Thursday, the date of Kavli‘s death:
Herbert Mitgang’s New York Times
obituary of Cleanth Brooks—
“The New Critics advocated close reading of literary texts
and detailed analysis, concentrating on semantics, meter,
imagery, metaphor and symbol as well as references to
history, biography and cultural background.”
See also Steiner, Chess, and Death.
The Mitgang Menu
Related material: This morning's 6 AM post and Wiener News.
Update of 3:29 PM:
From Herbert Mitgang's New York Times
obituary of Cleanth Brooks—
"The New Critics advocated close reading of literary texts
and detailed analysis, concentrating on semantics, meter,
imagery, metaphor and symbol as well as references to
history, biography and cultural background."
From the obituary of a Bletchley Park
codebreaker who reportedly died on
Armistice Day (Monday, Nov. 11)—
"The main flaw of the Enigma machine,
seen by the inventors as a security-enhancing
measure, was that it would never encipher
a letter as itself…."
Update of 9 PM ET Nov. 13—
"The rogue’s yarn that will run through much of
the material is the algebraic symmetry to which
the name of Galois is attached…."
— Robert P. Langlands,
Institute for Advanced Study, Princeton
"All the turmoil, all the emotions of the scenes
have been digested by the mind into
a grave intellectual whole. It is as though
Bach had written the 1812 Overture."
— Aldous Huxley, "The Best Picture," 1925
"#Haiyan has reached perfection…
8.0 on the Dvorak intensity scale."
Yesterday afternoon's post linked to efforts by
the late Robert de Marrais to defend a mathematical
approach to structuralism and kaleidoscopic patterns.
Two examples of non-mathematical discourse on
such patterns:
1. A Royal Society paper from 2012—
Click the above image for related material in this journal.
2. A book by Junichi Toyota from 2009—
Kaleidoscopic Grammar: Investigation into the Nature of Binarism
I find such non-mathematical approaches much less interesting
than those based on the mathematics of reflection groups .
De Marrais described the approaches of Vladimir Arnold and,
earlier, of H. S. M. Coxeter, to such groups. These approaches
dealt only with groups of reflections in Euclidean spaces.
My own interest is in groups of reflections in Galois spaces.
See, for instance, A Simple Reflection Group of Order 168.
Galois spaces over fields of characteristic 2 are particularly
relevant to what Toyota calls binarism .
"And behold, a white horse." — Johnny Cash
See also references to such a horse here.
The title, that of a novel by Arthur Koestler,
has appeared before in this journal.
The title was quoted in a Log24 note of
May 29, 2002 (G.K. Chesterton's birthday).
The link in Saturday evening's post to a Chesterton
essay suggested a further search that yielded
the following quotation—
Then silence sank. And slowly
Arose the sea-land lord
Like some vast beast for mystery,
He filled the room and porch and sky,
And from a cobwebbed nail on high
Unhooked his heavy sword.
— G. K. Chesterton,
The Ballad of the White Horse
This, together with some Log24 remarks
from 2004, suggests two images—
Above: A 1955 cover design by Robert Flynn.
The arrow theme also appears in a figure from
John Sealander's Road to Nowhere in the 2004
remarks:
The remarks quoting the Sealander image, from
March 5, 2004, were on mathematics and narrative.
Related material from a year later:
See an announcement, saved from March 16, 2005,
of a conference on mathematics and narrative that
was held in July 2005. Some context: Koestler's novel.
See Josh Lederman's AP story on this year's
colorful White House Halloween decorations.
Orange and black are also the Princeton colors.
See as well The Crosswicks Curse.
Scene I:
"Pinter's particular usage of reverse chronology
in structuring the plot is innovative…."
— Wikipedia on the play "Betrayal," a version of which
opens tonight
Scene II:
Reverse Chronology in Wikipedia —
"As a hypothetical example, if the fairy tale Jack and the Beanstalk
was told using reverse chronology, the opening scene would depict
Jack chopping the beanstalk down and killing the giant. The next
scene would feature Jack being discovered by the giant and climbing
down the beanstalk in fear of his life. Later, we would see Jack running
into the man with the infamous magic beans, then, at the end of the film,
being sent off by his mother to sell the cow."
Scene III:
Dialogue for Scene III —
"Sell the damn cow, Jack."
Epilogue: Jack + Jill.
(Continued. For the title, see Lucero in this journal.)
See Newton in several works of literary art:
The date, Nov. 23, 2010, of the Westminster Abbey remarks
in the second Newton link above suggests a quite different church
from that date.
"Let X equal the month of full bookstores."
— Proof by David Auburn
"Harvard Book Store is thrilled to welcome Stephen King for a special event to celebrate the release of Doctor Sleep , the long-anticipated sequel to 1977’s The Shining . Mr. King will read from and discuss the new book, followed by a Q&A with the audience at Memorial Church in Harvard Yard on September 27." |
See as well Corpse + Eliot and some remarks
on the mathematics of Kummer
from this September and from last September.
Eisenman I: DuBois, PA (Of German descent)
Eisenman II: Yale (Apparently related to Eisenman I)
Eisenman III: Newark, NJ (Jewish)
"Confusion is nothing new." — Song lyric
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