"A window unto the world"? "The classical style"?
Thursday, December 11, 2014
Jews on Style
Wednesday, December 10, 2014
Broad and Bright
Requiem for a painter in this evening's NY Times :
In a review for ARTNews , the painter and critic
Fairfield Porter called her work “traditional and radical.”
Her paintings, he wrote, “are broad and bright,
considered without being fussy, thoughtful but never
pedantic.”
Not that there's anything wrong with being pedantic…
Update of Dec. 10, 2014, to a post of Dec. 9 :
The passage from Nicholas of Cusa was added
because it indicates a more reliable source than
Stambaugh, because of its relevance to lines
about the metaphorical significance of light in
"I Origins," and because it contains the number
1111.
Tuesday, December 9, 2014
A Quote for Brit
The title refers to Brit Marling from the previous post.
The quote, below, refers to today's news.
Plan 9…
Or: Bullshit for Brit … continues.
From the new film "I Origins," starring Brit Marling —
Plan 9:
The protagonist of "I Origins" is led to the above billboard
by apparently chance encounters with 11 's — such as the
1111 on the following page —
Update of Dec. 10, 2014: The "bullshit" in the subtitle above refers
to the remarks of Joan Stambaugh, not those of Nicholas of Cusa.
The passage from Nicholas was added because it indicates a more
reliable source than Stambaugh, because it is relevant to lines
about the metaphorical significance of light in "I Origins," and
because it contains the number 1111.
Monday, December 8, 2014
Photo Opportunity
(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."
Language Game
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 —
Sunday, December 7, 2014
Game Box
In memory of a game inventor who reportedly died on
Dec. 6, the feast of St. Nicholas, a link: Game Box.
Update of 12 AM Dec. 8 — See also "How to watch The Game
Awards 2014," from December 5, the date of the Game Awards
and also the date of the Log24 post Language Game.
The Kernel Conundrum
Saturday, December 6, 2014
Six-Point Theology
On the feast of Saint Nicholas
See also the six posts on this year's feast of Saint Andrew
and the following from the University of St. Andrews —
Friday, December 5, 2014
Wittgenstein’s Picture
From Zettel (repunctuated for clarity):
249. « Nichts leichter, als sich einen 4-dimensionalen Würfel
vorstellen! Er schaut so aus… »
"Nothing easier than to imagine a 4-dimensional cube!
It looks like this…
[Here the editor supplied a picture of a 4-dimensional cube
that was omitted by Wittgenstein in the original.]
« Aber das meine ich nicht, ich meine etwas wie…
"But I don't mean that, I mean something like…
…nur mit 4 Ausdehnungen! »
but with four dimensions!
« Aber das ist nicht, was ich dir gezeigt habe,
eben etwas wie…
"But isn't what I showed you like…
…nur mit 4 Ausdehnungen? »
…only with four dimensions?"
« Nein; das meine ich nicht! »
"No, I don't mean that!"
« Was aber meine ich? Was ist mein Bild?
Nun der 4-dimensionale Würfel, wie du ihn gezeichnet hast,
ist es nicht ! Ich habe jetzt als Bild nur die Worte und
die Ablehnung alles dessen, was du mir zeigen kanst. »
"But what do I mean? What is my picture?
Well, it is not the four-dimensional cube
as you drew it. I have now for a picture only
the words and my rejection of anything
you can show me."
"Here's your damn Bild , Ludwig —"
Context: The Galois Tesseract.
Share THIS.
See also …
Papal mace points to education's true purpose, Scottish bishop says
as well as Welcome to Scotland.
Thursday, December 4, 2014
The Pony Argument
The title was suggested by this morning's post "Follow This."
From a previous incarnation of my home website, m759.com —
The second of the site's three pages mentions authors
Alfred Bester and Zenna Henderson :
"Bester and Henderson are particularly good at
fictional accounts of telepathy. The noted Harvard
philosopher W. V. Quine doubts such a thing exists,
but I prefer the 'There must be a pony' argument."
Related material: The date Nov. 27, 2014, in a web search today …
… in The Washington Post …
… and in this journal …
Followup for Josefine
The title refers to the previous post, "Follow This."
Dialogue from "Night at the Museum 3"—
"He's not in charge, we're just following him."
"That's what being in charge means ."
See also Smoke and Mirrors and Angels & Demons.
From Lie Groups for Holy Week :
Stellan Skarsgaard as the head of Vatican Security —
Follow This
The "Phony Pony" images below by Josefine Lyche
may or may not have been created in response to the link
on "magic" in the previous post to Katy Perry's "Dark Horse" video.
Wednesday, December 3, 2014
Pyramid Dance
Oslo artist Josefine Lyche has a new Instagram post,
this time on pyramids (the monumental kind).
My response —
Wikipedia's definition of a tetrahedron as a
"triangle-based pyramid" …
… and remarks from a Log24 post of August 14, 2013 :
Norway dance (as interpreted by an American)
I prefer a different, Norwegian, interpretation of "the dance of four."
Related material: |
See also some of Burkard Polster's triangle-based pyramids
and a 1983 triangle-based pyramid in a paper that Polster cites —
(Click image below to enlarge.)
Some other illustrations that are particularly relevant
for Lyche, an enthusiast of magic :
From On Art and Magic (May 5, 2011) —
|
(Updated at about 7 PM ET on Dec. 3.)
Tuesday, December 2, 2014
Models
Continued from November 30, 2014
"Number right → Everything right." — Burkard Polster.
See also the six posts of November 30, St. Andrew's Day.
Related material —
Peter J. Cameron today discussing Julia Kristeva on poetry …
"This seems to be saying that the Kolmogorov
complexity of poetry is very low: the entire poem
can be generated from a small amount of information."
… and this journal on St. Andrew's day :
From "A Piece of the Storm,"
by the late poet Mark Strand —
A snowflake, a blizzard of one….
Ender’s Game
Reese Witherspoon in "Wild" (Click to enlarge.)
Witherspoon and Wiggins Streets, Princeton, NJ:
Colorful Tale
"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.
Monday, December 1, 2014
Good Question
"A friend asked why I am saying kaddish.
A good question."
— Kaddish , by Leon Wieseltier, Chapter One
Scarlett Johansson
and Natalie Portman
See Scarlett in Lucy …
Barry Rudd at the end of John Hersey's
1960 novel The Child Buyer :
"Fascinating to be a specimen,
truly fascinating. Do you suppose
I really can develop an I.Q. of
over a thousand?"
… and Natalie in Black Swan .
Midrash :
-
"12:30 pm we leave for the historic
Princeton Cemetery on Witherspoon and
Paul Robson Streets to assemble for
a service and burial at 2:00 pm."
Change Arises
Flashback to St. Andrew's Day, 2013 —
Saturday, November 30, 2013
|
If the object is a cube, change arises from the fact
that the object has six faces…
and is the unit cell for the six -dimensional
hyperspace H over the two-element field —
A different representation of the unit cell of
the hyperspace H (and of the I Ching ) —
Sunday, November 30, 2014
Agents of a Great Despair
Or: Concepts of Space
1976 according to Cullinane:
1976 according to Plotnick:
“Irony and ridicule are entertaining and effective, and . . .
at the same time they are the agents of a great despair
and stasis in U.S. culture.” — David Foster Wallace,
as quoted by Adam Kirsch today at Salon
Electric Dreams
Continued from Black Friday …
"Tell me no secrets, tell me some lies."
— Don't It Make My Brown Eyes Blue
View from the Bottom
Reality's Mirror: Exploring the Mathematics of Symmetry —
"Here is a book that explains in laymen language
what symmetry is all about, from the lowliest snowflake
and flounder to the lofty group structures whose
astonishing applications to the Old One are winning
Nobel prizes. Bunch's book is a marvel of clear, witty
science writing, as delightful to read as it is informative
and up-to-date. The author is to be congratulated on
a job well done." — Martin Gardner
"But, sweet Satan, I beg of you, a less blazing eye!"
— Rimbaud, A Season in Hell
"… the lowliest snowflake and flounder…."
— Martin Gardner
Back to the Real
Continued from June 17, 2009 —
"I sit now in a little room off the bar
at four-thirty in the morning drinking
ochas and then mescal and writing this
on some Bella Vista notepaper I filched
the other night…."
— Malcolm Lowry, Under the Volcano
See too a search for Snowflake in this journal.
This word may serve as Mark Strand's "Rosebud."
Investments
From "A Piece of the Storm," by the late poet Mark Strand —
A snowflake, a blizzard of one….
From notes to Malcolm Lowry's "La Mordida" —
he had invested, in the Valley of the Shadow of Death….
See also Weyl's Symmetry in this journal.
Two Physical Models of the Fano Plane
The seven symmetry axes of the regular tetrahedron
are of two types: vertex-to-face and edge-to-edge.
Take these axes as the "points" of a Fano plane.
Each of the tetrahedron's six reflection planes contains
two vertex-to-face axes and one edge-to-edge axis.
Take these six planes as six of the "lines" of a Fano
plane. Then the seventh line is the set of three
edge-to-edge axes.
(The Fano tetrahedron is not original with me.
See Polster's 1998 A Geometrical Picture Book , pp. 16-17.)
There are three reflection planes parallel to faces
of the cube. Take the seven nonempty subsets of
the set of these three planes as the "points" of a
Fano plane. Define the Fano "lines" as those triples
of these seven subsets in which each member of
the triple is the symmetric-difference sum of the
other two members.
(This is the eightfold cube discussed at finitegeometry.org.)
Saturday, November 29, 2014
Something Missing?
The title refers to this morning's previous post.
The above links from today's aldaily.com : Cubism, Bernstein, Hell.
Mountain, Fountain
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.
Friday, November 28, 2014
The Soul of Stanford
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)—
Religion for Academics
From PhDTree.org —
“Paradox lust”: the fortunate fall
according to Joyce in finnegans wake
Journal Article Neohelicon 38(1) 161-175 (2011)
No abstract.
DOI: 10.1007/s11059-011-0092-y
Download: Full Text PDF
Former-Day Saint
Continued from Friday the 13th of June, 2014 :
"It's going to be accomplished in steps,
this establishment of the Talented
in the scheme of things."
— To Ride Pegasus ,
by Anne McCaffrey (Radcliffe '47)
Related material:
Click Zenna Henderson's dates for
an informative essay from April 5, 2009.
See also posts on, or about, that date in this journal.
For Black Friday
Kristen Wiig, Girl Reporter…
.. in The Skeleton Twins—
"I've got news for you."
Co-starring Bill Hader as Her —
Words and Pictures
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."
Off the Map
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! |
Thursday, November 27, 2014
In the Details
For the late novelist P. D. James, author of, among other things,
The Children of Men .
Michael Caine in the film of that book —
Detail —
Raven's Progressive Matrices example —
A quote for tellers of tales —
“There have long been rumors of a mythical Ninth Element
that grants ultimate power to the Wizard who masters it.
The Order of Magick says there is no such thing. But….”
— Website of Magicka: The Ninth Element Novel
Art Photography
The New York Times this morning:
Lucien Clergue, Master and Promoter
of Art Photography, Dies at 80.
Clergue reportedly died on November 15.
From Log24 on that date— Un-Art Photography :
From the American Mathematical Society,
another death, also on November 15:
(Click image for further details.)
Midrash by Eliot:
(Click the Eliot quotations to enlarge them.)
Wednesday, November 26, 2014
Mathematics and Narrative
Mathematics: Galois-Plane Models.
Narrative: "The Dreaming Jewels."
A Tetrahedral Fano-Plane Model
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.
Class Act
Update of Nov. 30, 2014 —
For further information on the geometry in
the remarks by Eberhart below, see
pp. 16-17 of A Geometrical Picture Book ,
by Burkard Polster (Springer, 1998). Polster
cites a different article by Lemay.
A search for background to the exercise in the previous post
yields a passage from the late Stephen Eberhart:
The first three primes p = 2, 3, and 5 therefore yield finite projective planes with 7, 13, and 31 points and lines, respectively. But these are just the numbers of symmetry axes of the five regular solids, as described in Plato's Timaeus : The tetrahedron has 4 pairs of face planes and corner points + 3 pairs of opposite edges, totalling 7 axes; the cube has 3 pairs of faces + 6 pairs of edges + 4 pairs of corners, totalling 13 axes (the octahedron simply interchanges the roles of faces and corners); and the pentagon dodecahedron has 6 pairs of faces + 15 pairs of edges + 10 pairs of corners, totalling 31 axes (the icosahedron again interchanging roles of faces and corners). This is such a suggestive result, one would expect to find it dealt with in most texts on related subjects; instead, while "well known to those who well know such things" (as Richard Guy likes to quip), it is scarcely to be found in the formal literature [9]. The reason for the common numbers, it turns out, is that the groups of symmetry motions of the regular solids are subgroups of the groups of collineations of the respective finite planes, a face axis being different from an edge axis of a regular solid but all points of a projective plane being alike, so the latter has more symmetries than the former. [9] I am aware only of a series of in-house publications by Fernand Lemay of the Laboratoire de Didactique, Faculté des Sciences de I 'Éducation, Univ. Laval, Québec, in particular those collectively titled Genèse de la géométrie I-X.
— Stephen Eberhart, Dept. of Mathematics, |
Eberhart died of bone cancer in 2003. A memorial by his
high school class includes an Aug. 7, 2003, transcribed
letter from Eberhart to a classmate that ends…
… I earned MA’s in math (UW, Seattle) and history (UM, Missoula) where a math/history PhD program had been announced but canceled. So 1984 to 2002 I taught math (esp. non-Euclidean geometry) at C.S.U. Northridge. It’s been a rich life. I’m grateful. Steve |
See also another informative BRIDGES paper by Eberhart
on mathematics and the seven traditional liberal arts.
Tuesday, November 25, 2014
Euclidean-Galois Interplay
For previous remarks on this topic, as it relates to
symmetry axes of the cube, see previous posts tagged Interplay.
The above posts discuss, among other things, the Galois
projective plane of order 3, with 13 points and 13 lines.
These Galois points and lines may be modeled in Euclidean geometry
by the 13 symmetry axes and the 13 rotation planes
of the Euclidean cube. They may also be modeled in Galois geometry
by subsets of the 3x3x3 Galois cube (vector 3-space over GF(3)).
The 3×3×3 Galois Cube
Exercise: Is there any such analogy between the 31 points of the
order-5 Galois projective plane and the 31 symmetry axes of the
Euclidean dodecahedron and icosahedron? Also, how may the
31 projective points be naturally pictured as lines within the
5x5x5 Galois cube (vector 3-space over GF(5))?
Update of Nov. 30, 2014 —
For background to the above exercise, see
pp. 16-17 of A Geometrical Picture Book ,
by Burkard Polster (Springer, 1998), esp.
the citation to a 1983 article by Lemay.
Monday, November 24, 2014
“What Reality?”
"We tried to create new realities overnight,
careful sets of words that resemble advertising slogans
in memorability and repeatability."
… Our Most Important Product …
"Omega is as real as we need it to be."
— Burt Lancaster in Sam Peckinpah's last film
Homemade Aesthetics
Continued from Tuesday, November 18, 2014
International poster for the 2010 film "Black Swan"—
"Death is a black swan." — Graciela Chichilnisky
Metaphysician in the Dark
Continued from Friday, November 21:
Sunday, November 23, 2014
Remarks on Reality
Wallace Stevens in "An Ordinary Evening in New Haven"
(1950) on "The Ruler of Reality" —
"Again, 'He has thought it out, he thinks it out,
As he has been and is and, with the Queen
Of Fact, lies at his ease beside the sea.'"
One such scene, from 1953 —
Another perspective, from "The Osterman Weekend" (1983) —
Style
Corrections to the NY Times obituary of Alexander Grothendieck
are shown below. For the original Sunday, Nov. 16, NY Times
print obituary (with its online date, Nov. 14), see a copy taken
from a weblog.
For another poetic remark in memory of Grothendieck,
see a Log24 post from November 13, the day of his death.
Saturday, November 22, 2014
About Nothing
See the easy grace link in this morning's previous post.
See also Michael Dubruiel and Log24 posts of Feb. 3
and Feb. 9, 2009.
The November 22 Candidate
Welcome to the Garden Club, Pilgrim
"A journalist with a literary bent, Mr. Eder wrote with an easy grace
and a practiced eye for detail. In 1974, he assessed a cultural
malaise in England during an economic downturn.
'In the West Country town of Hereford,' he began, 'the president
of a women’s club told a year-end meeting that the January bingo
game would be canceled to save electricity. Then she proposed a
New Year’s resolution. "Let us all work to get England back on her
dear old feet," she said and bumped down pinkly into her chair,
overwhelmed by applause.'" — Bruce Weber, NY Times
See also Bingo in this journal.
Friday, November 21, 2014
More
“When Three Into One Equals More” — New York Times headline
See also Trinity in this journal. From that search:
… The actor is
A metaphysician in the dark….
— Wallace Stevens,
“Of Modern Poetry“
Thursday, November 20, 2014
The Unit
The Manchurian Candidate
Continued from Tuesday, Nov. 18
The above conclusion of a NY Times obituary
about a Monday death may also serve as the
missing conclusion of Monday's "A Search for
Missing Pieces" —
Related material starring Einstein and
Thomas Mann: "A Riddle for Davos."
Wednesday, November 19, 2014
The Eye/Mind Conflict
Harold Rosenberg, "Art and Words,"
The New Yorker , March 29, 1969. From page 110:
"An advanced painting of this century inevitably gives rise
in the spectator to a conflict between his eye and his mind;
as Thomas Hess has pointed out, the fable of the emperor's
new clothes is echoed at the birth of every modemist art
movement. If work in a new mode is to be accepted, the
eye/mind conflict must be resolved in favor of the mind;
that is, of the language absorbed into the work. Of itself,
the eye is incapable of breaking into the intellectual system
that today distinguishes between objects that are art and
those that are not. Given its primitive function of
discriminating among things in shopping centers and on
highways, the eye will recognize a Noland as a fabric
design, a Judd as a stack of metal bins— until the eye's
outrageous philistinism has been subdued by the drone of
formulas concerning breakthroughs in color, space, and
even optical perception (this, too, unseen by the eye, of
course). It is scarcely an exaggeration to say that paintings
are today apprehended with the ears. Miss Barbara Rose,
once a promoter of striped canvases and aluminum boxes,
confesses that words are essential to the art she favored
when she writes, 'Although the logic of minimal art gained
critical respect, if not admiration, its reductiveness allowed
for a relatively limited art experience.' Recent art criticism
has reversed earlier procedures: instead of deriving principles
from what it sees, it teaches the eye to 'see' principles; the
writings of one of America's influential critics often pivot on
the drama of how he failed to respond to a painting or
sculpture the first few times he saw it but, returning to the
work, penetrated the concept that made it significant and
was then able to appreciate it. To qualify as a member of the
art public, an individual must be tuned to the appropriate
verbal reverberations of objects in art galleries, and his
receptive mechanism must be constantly adjusted to oscillate
to new vocabularies."
New vocabulary illustrated:
Graphic Design and a Symplectic Polarity —
Background: The diamond theorem
and a zero system .
Tuesday, November 18, 2014
For the Green Mountain Girls
Tom Wolfe 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.”
“Parable of American Painting,” 1954 — From The Tradition of the New , by Harold Rosenberg
“In this essay Rosenberg set out to explain what he believed to be definitively American about Abstract Expressionism. He did so by drawing on the American Revolutionary War for his metaphors, likening the new Americans to the coonskin trappers whose knowledge of their terrain enabled them to pick off the British soldiers (Redcoats), who followed the dictates of their military training. The professionally- trained soldiers were defeated because, as Rosenberg states, ‘They were such extreme European professionals … they did not even see the American trees.’ ‘Redcoatism’ was, Rosenberg argued, a symptom of the old European world’s stubborn rejection of the new. It did at one time also ‘[dominate] the history of American art,’ he wrote, but with the advent of Abstract Expressionism, times had changed. And just as the Coonskins were victorious because they stood apart from the professional military, so the new American art was triumphant because, as Rosenberg saw it, it marked a profound break with the traditions of European art.” |
Lectures at Bennington, 1971 |
For example:
Art adapted today from the Google search screen. Discuss.
The Abacus Conundrum…
Prequel from 1961 (click image for context):
Detail that may be interpreted as the Chinese
3×3 "Holy Field" and a Chinese temple bell—
"Ting-a-ling." — Kurt Vonnegut.
Our Most Important Product
Hexagram 35:
Progress
"Then came a 'Robot Psychologist,' known as a Psychological Matrix Rotator,
developed for the Department of Defense. It is still used to literally 'see' that
the right man gets the right Army job."
— Ronald Reagan, 1961 GE Sales Meeting
"Always with a little humor." — Yen Lo
In memory of Dr. Irving Peress,
who reportedly died on Thursday,
November 13, 2014.
Monday, November 17, 2014
A Search for Missing Pieces
A detail from the image search below —
A Google image search today for
“portal del aguila de oro” “bella vista” —
Click for a larger (4.2 MB) version.
See also yesterday’s post.
Sunday, November 16, 2014
Along the Way
“Bit by bit, putting it together.
Piece by piece, working out the vision night and day.
All it takes is time and perseverance
With a little luck along the way.”
— Stephen Sondheim
Saturday, November 15, 2014
A Dark Detective Story
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.
Google Translate version:
To the joy at its height, I would add that the so-called Saavedra
seems to have disappeared from circulation without leaving any trace….
Suddenly, the story looks like a dark detective story.
Or horror film —
Enigma Variations
Grothendieck reportedly died on Thursday, November 13, 2014.
From this journal a year earlier:
After clicking on the link “a grave intellectual whole” from the Nov. 13, 2013, post
see also Benedict Cumberbatch’s less serious approach to Bletchley Park:
“I want to see this film; this film’s been up my ass for the last five years.”
Friday, November 14, 2014
Another Opening, Another Show
“What happens when you mix the brilliant wit of Noel Coward
with the intricate plotting of Agatha Christie? Set during a
weekend in an English country manor in 1932, Death by Design
is a delightful and mysterious ‘mash-up’ of two of the greatest
English writers of all time. Edward Bennett, a playwright, and
his wife Sorel Bennett, an actress, flee London and head to
Cookham after a disastrous opening night. But various guests
arrive unexpectedly….”
— Samuel French (theatrical publisher) on a play that
opened in Houston on September 9, 2011.
Related material:
- This journal on May 28, 2014,
- on October 7, 2014,
- on November 13, 2014,
- and on the above opening night, September 9, 2011.
Some Symplectic History
A paper from 1976 on symplectic torsors and finite geometry:
FINITE GEOMETRIES IN THE THEORY OF THETA CHARACTERISTICS
Autor(en): Rivano, Neantro Saavedra
Objekttyp: Article
Zeitschrift: L’Enseignement Mathématique
Band (Jahr): 22 (1976)
Heft 1-2: L’ENSEIGNEMENT MATHÉMATIQUE
PDF erstellt am: 14.11.2014
Persistenter Link: http://dx.doi.org/10.5169/seals-48185
(Received by the journal on February 20, 1976.)
Saavedra-Rivano was a student of Grothendieck, who reportedly died yesterday.
Thursday, November 13, 2014
Mort de Grothendieck
“Alexandre Grothendieck est mort jeudi matin
à l’hôpital de Saint-Girons (Ariège), à l’âge de 86 ans.”
Update of 6: 16 PM ET: A memorial of sorts, from May 27 this year:
Progressive Matrix
Yesterday's post and recent Hollywood news suggest
a meditation on a Progressive Matrix —
Click to enlarge.
"My card."
Structurally related images —
A sample Raven's Progressive Matrices test item
(such items share the 3×3 structure of the hash symbol above):
Structural background —
Wednesday, November 12, 2014
Harrowing Cuteness
The title is a phrase from yesterday's post.
An example of harrowing cuteness:
Charlize Theron in "Young Adult" (2011) —
Related material for older adults: Ravenna and Nietzsche.
Tuesday, November 11, 2014
Monday, November 10, 2014
Narrative Line
"We live entirely, especially if we are writers, by the imposition
of a narrative line upon disparate images…." — Joan Didion
Narrative Line:
Disparate images:
Exercise:
Can the above narrative line be imposed in any sensible way
upon the above disparate images?
Sunday, November 9, 2014
Sermon
The Ideas
“We tell ourselves stories in order to live…. We interpret what we see, select the most workable of multiple choices. We live entirely, especially if we are writers, by the imposition of a narrative line upon disparate images, by the ‘ideas’ with which we have learned to freeze the shifting phantasmagoria which is our actual experience.” — Joan Didion |
See Didion and the I Ching and posts tagged Plato in China .
Twaddle
“There exists a considerable literature
devoted to the Lo shu , much of it infected
with the kind of crypto-mystic twaddle
met with in Feng Shui.”
— Lee C. F. Sallows, Geometric Magic Squares ,
Dover Publications, 2013, page 121
Cf. Raiders of the Lost Theorem, Oct. 13, 2014.
See also tonight’s previous post and
“Feng Shui” in this journal.
Saturday, November 8, 2014
At 11:59*
“Fantasy and the Buffered Self.”
*For the title, see Enormous Changes.
Friday, November 7, 2014
The Missing ART
Back together, but missing an article.
“An article (abbreviated ART) is a word (or prefix or suffix)
that is used with a noun to indicate the type of reference
being made by the noun.” — Wikipedia
Perhaps Tommy Lee Jones has it.
The Crosswicks Curse…
There is such a thing as an MBTI Tesseract.
See a thread at http://www.typologycentral.com/forums/
from August 17 and 18, 2010.
See also this journal on those dates: The Kermode Game.
Thursday, November 6, 2014
Working Backward
“This setting of the Ave Verum Corpus text was composed
to celebrate the feast of Corpus Christi .” — Wikipedia
“Ave Verum Corpus .”— Madison in the BBC America TV series
“Intruders,” Season 1, Episode 3: “Time Has Come Today.”
See also the Eucharistic meditation of Feb. 13, 2006, linked to in yesterday’s post
on Guy Fawkes Day. (That British holiday originally commemorated the Catholic
Gunpowder Plot of 1605.)
Wednesday, November 5, 2014
Dark Fields…
From the first of previous Log24 posts tagged “Dark Fields”—
“A link in memory of Donald G. Higman,
dead on Feb. 13, 2006,
the day after Lincoln’s birthday:
On the Graphs of Hoffman-Singleton and Higman-Sims.
His truth is marching on.”
See also Foundation Square (October 25, 2014).
Monday, November 3, 2014
Plan 9 Continues…
A link to “Nine Tailors” in this journal may serve as
a memorial to the late David M. Abshire, who
reportedly died at 88 on Halloween.
See also tonight’s previous post and a remark by
Mira Sorvino in her version of The Great Gatsby .
Wisconsin Death Trip*
Courtesy of Mira Sorvino.
Enter Madison :
From “Intruders,” BBC America, Season 1, Episode 2, at 1:07 of 43:31.
“You sure know how to show a girl a good time.“
* The title is a reference to a Wisconsin-related Halloween post.
Gods and Giants
A weblog reports Chris Rock's remarks
on Saturday Night Live this past weekend:
"It’s America, we commercialize everything.
Look at what we did to Christmas.
Christmas. Christmas is Jesus’ birthday.
It’s Jesus’ birthday. Now, I don’t know Jesus
but from what I’ve read, Jesus is the least
materialistic person to ever roam the earth.
No bling on Jesus.
Jesus kept a low profile and we turned his
birthday into the most materialistic day of the
year. Matter of fact, we have the Jesus birthday
season. It’s a whole season of materialism.
Then, at the end of the Jesus birthday season
we have the nerve to have an economist come
on TV and tell you how horrible the Jesus birthday
season was this year. Oh, we had a horrible Jesus’
birthday this year. Hopefully, business will pick up
by his Crucifixion.”
Related music and image:
"Show us the way to the next little girl …"
Natalie Wood in "Miracle on 34th Street" (1947)
Related non-materialistic meditations:
The Rhetoric of Abstract Concepts and Gods and Giants.
The Rhetoric of Abstract Concepts
From a post of June 3, 2013:
New Yorker editor David Remnick at Princeton today
(from a copy of his prepared remarks):
“Finally, speaking of fabric design….”
I prefer Tom and Harold:
Tom Wolfe in The Painted Word —
“I am willing (now that so much has been revealed!)
to predict that in the year 2000, when the Metropolitan
or the Museum of Modern Art puts on the great
retrospective exhibition of American Art 1945-75,
the three artists who will be featured, the three seminal
figures of the era, will be not Pollock, de Kooning, and
Johns-but Greenberg, Rosenberg, and Steinberg.
Up on the walls will be huge copy blocks, eight and a half
by eleven feet each, presenting the protean passages of
the period … a little ‘fuliginous flatness’ here … a little
‘action painting’ there … and some of that ‘all great art
is about art’ just beyond. Beside them will be small
reproductions of the work of leading illustrators of
the Word from that period….”
Harold Rosenberg in The New Yorker (click to enlarge)—
From Gotay and Isenberg, “The Symplectization of Science,”
Gazette des Mathématiciens 54, 59-79 (1992):
“… what is the origin of the unusual name ‘symplectic’? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure ‘line complex group’ the ‘symplectic group.’
… the adjective ‘symplectic’ means ‘plaited together’ or ‘woven.’
This is wonderfully apt….”
— Steven H. Cullinane,
diamond theorem illustration
Sunday, November 2, 2014
A Singular Place
"Macy’s Herald Square occupies a singular place
in American retailing." — NY Times today, in print
on page BU1 of the New York edition with the headline:
A Singular Time:
See Remember Me to Herald Square, at noon on
August 21, 2014, and related earlier Log24 posts.
Also on Aug. 21, 2014: from a blog post, 'Tiles,' by
Theo Wright, a British textile designer —
The 24 tile patterns displayed by Wright may be viewed
in their proper mathematical context at …
Saturday, November 1, 2014
Not Saints
“We are not saints.” — Alcoholics Anonymous , Chapter 5
The New York Times on AA’s co-founder Bill Wilson in 1934:
Click for the rest of the story.
Friday, October 31, 2014
For the Late Hans Schneider
See a University of Wisconsin obituary for Schneider,
a leading expert on linear algebra who reportedly died
at 87 on Tuesday, October 28, 2014.
Some background on linear algebra and “magic” squares:
tonight’s 3 AM (ET) post and a search in this
journal for Knight, Death, and the Devil.
Click image to enlarge.
Structure
Introducing a group of 322,560 affine transformations of Dürer’s ‘Magic’ Square
The four vector-space substructures of digits in 1st, 2nd, 3rd, 4th place,
together with the diamond theorem, indicate that Dürer’s square “minus one”
can be transformed by permutations of rows, columns, and quadrants to a
square with (decimal) digits in the usual numerical order, increasing from
top left to bottom right. Such permutations form a group of order 322,560.
(Continued from Vector Addition in a Finite Field, Twelfth Night, 2013.)
Thursday, October 30, 2014
Mimicry
This journal Tuesday, Oct. 28, 2014, at 5 PM ET:
"What is a tai chi master, and what is it that he unfolds?"
From an earlier post, Hamlet's father's ghost
on "the fretful porpentine":
Hamlet , Act 1, Scene 5 —
Ghost:
“I could a tale unfold whose lightest word
Would harrow up thy soul, freeze thy young blood,
Make thy two eyes, like stars, start from their spheres,
Thy knotted and combinèd locks to part
And each particular hair to stand on end,
Like quills upon the fretful porpentine:
But this eternal blazon must not be
To ears of flesh and blood."
Galway Kinnell:
"I roll
this way and that in the great bed, under
the quilt
that mimics this country of broken farms and woods"
— "The Porcupine"
For quilt-block designs that do not mimic farms or woods,
see the cover of Diamond Theory . See also the quotations
from Wallace Stevens linked to in the last line of yesterday's
post in memory of Kinnell.
"… a bee for the remembering of happiness" — Wallace Stevens
Wednesday, October 29, 2014
Dead Poet
For poet Galway Kinnell, Princeton ’48:
Kinnell was named "Tiger of the Week" in a
Princeton Alumni Weekly post of August 27, 2014.
See his obituary in today's New York Times
as well as posts here on August 27, 2014.
Tuesday, October 28, 2014
Raiders of the Lost Symbol
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”
Go Figure
For Karl Pribram and Katherine Neville,
a sequel to this morning's Figural Processing —
See also Christmas 2013.
Figural Processing
Monday, October 27, 2014
Revolutions in Geometry
A post in honor of Évariste Galois (25 October 1811 – 31 May 1832)
From a book by Richard J. Trudeau titled The Non-Euclidean Revolution —
See also “non-Euclidean” in this journal.
One might argue that Galois geometry, a field ignored by Trudeau,
is also “non-Euclidean,” and (for those who like rhetoric) revolutionary.
Sunday, October 26, 2014
Centennial
The "Chern" of today's previous post is mathematician
Shiing-Shen Chern (b. Oct. 26, 1911, d. Dec. 3, 2004).
For an observance of the 2011 centennial of his birth,
see a website in China.
See also this journal on the centennial date —
Erlanger and Galois, a post of Oct. 26, 2011.
Saturday, October 25, 2014
Foundation Square
In the above illustration of the 3-4-5 Pythagorean triangle,
the grids on each side may be regarded as figures of
Euclidean geometry or of Galois geometry.
In Euclidean geometry, these grids illustrate a property of
the inner triangle.
In elementary Galois geometry, ignoring the connection with
the inner triangle, the grids may be regarded instead as
illustrating vector spaces over finite (i.e., Galois) fields.
Previous posts in this journal have dealt with properties of
the 3×3 and 4×4 grids. This suggests a look at properties of
the next larger grid, the 5×5 array, viewed as a picture of the
two-dimensional vector space (or affine plane) over the finite
Galois field GF(5) (also known as ℤ5).
The 5×5 array may be coordinatized in a natural way, as illustrated
in (for instance) Matters Mathematical , by I.N. Herstein and
Irving Kaplansky, 2nd ed., Chelsea Publishing, 1978, p. 171:
See Herstein and Kaplansky for the elementary Galois geometry of
the 5×5 array.
For 5×5 geometry that is not so elementary, see…
-
"The Hoffman-Singleton Graph and its Automorphisms," by
Paul R. Hafner, Journal of Algebraic Combinatorics , 18 (2003), 7–12, and -
the Web pages "Hoffman-Singleton Graph" and "Higman-Sims Graph"
of A. E. Brouwer.
Hafner's abstract:
We describe the Hoffman-Singleton graph geometrically, showing that
it is closely related to the incidence graph of the affine plane over ℤ5.
This allows us to construct all automorphisms of the graph.
The remarks of Brouwer on graphs connect the 5×5-related geometry discussed
by Hafner with the 4×4 geometry related to the Steiner system S(5,8,24).
(See the Miracle Octad Generator of R. T. Curtis and the related coordinatization
by Cullinane of the 4×4 array as a four-dimensional vector space over GF(2).)
Friday, October 24, 2014
New Key
See Langer (Harvard U. Press, Third Edition, Jan. 31, 1957, pp. 3-4-5).
See also Old Key : Pythagoras, harmony, and the 3-4-5 triangle.
Thursday, October 23, 2014
Wednesday, October 22, 2014
The Seventh Stage
Robin Williams and the Stages of Math
i) shock & denial
ii) anger
iii) bargaining
iv) depression
v) acceptance
And then…
vi) checking
vii) Joan Rivers
See also
- today’s previous post, Claves Regni Caelorum ,
- Robin Williams in “The Final Cut,” and
- a book with a related title (illustrated below).
Claves Regni Caelorum
Continued from Day at the Museum, last Sunday, October 19, 2014.
This post was suggested by…
- A piece in the Bookends section of the New York Times
Sunday Book Review (page BR31 last Sunday, Oct. 19):
Daniel Mendelsohn on rereading The Catcher in the Rye . - A detail in Day at the Museum— The New York Times ‘s
appraisal of Joan Rivers: “A Comic Without a Shut-Off Switch.” - A Sept. 7 Log24 post, Sunday School, in memory of Joan Rivers.
From The Catcher in the Rye , a passage just before the
museum passage quoted by Mendelsohn:
“She was having a helluva time tightening her skate.
She didn’t have any gloves on or anything and her hands
were all red and cold. I gave her a hand with it. Boy, I
hadn’t had a skate key in my hand for years. It didn’t feel
funny, though. You could put a skate key in my hand
fifty years from now, in pitch dark, and I’d still know
what it is. She thanked me and all when I had it tightened
for her. She was a very nice, polite little kid. God, I love it
when a kid’s nice and polite when you tighten their skate
for them or something. Most kids are. They really are.
I asked her if she’d care to have a hot chocolate or something
with me, but she said no, thank you. She said she had to meet
her friend. Kids always have to meet their friend. That kills me.
Even though it was Sunday and Phoebe wouldn’t be there
with her class or anything, and even though it was so damp
and lousy out, I walked all the way through the park over to
the Museum of Natural History. I knew that was the museum
the kid with the skate key meant.”
Tuesday, October 21, 2014
Eerie Twist
(Continued from Nov. 15, 2011)
Ben Bradlee, legendary Washington Post editor, dies at 93
See also a post of Jan. 20, 2011, and an earlier post on Twelfth Night, 2010.
A star figure and the Galois quaternion.
The square root of the former is the latter.
Art as a Tool
Two news items on art as a tool:
Two Log24 posts related to the 3×3 grid, the underlying structure for China’s
ancient Lo Shu “magic” square:
Finally, leftist art theorist Rosalind Krauss in this journal
on AntiChristmas, 2010:
Which is the tool here, the grid or Krauss?
Tools
(Night at the Museum continues.)
"Strategies for making or acquiring tools
While the creation of new tools marked the route to developing the social sciences,
the question remained: how best to acquire or produce those tools?"
— Jamie Cohen-Cole, “Instituting the Science of Mind: Intellectual Economies
and Disciplinary Exchange at Harvard’s Center for Cognitive Studies,”
British Journal for the History of Science vol. 40, no. 4 (2007): 567-597.
Obituary of a co-founder, in 1960, of the Center for Cognitive Studies at Harvard:
"Disciplinary Exchange" —
In exchange for the free Web tools of HTML and JavaScript,
some free tools for illustrating elementary Galois geometry —
The Kaleidoscope Puzzle, The Diamond 16 Puzzle,
The 2x2x2 Cube, and The 4x4x4 Cube
"Intellectual Economies" —
In exchange for a $10 per month subscription, an excellent
"Quilt Design Tool" —
This illustrates not geometry, but rather creative capitalism.
Related material from the date of the above Harvard death: Art Wars.
Monday, October 20, 2014
The Library
The online Harvard Crimson today:
“ ‘I don’t like how they check your bags
when you leave the library
even though you have to swipe your
student ID to get in.’
But what else would I be carrying in this
Gutenberg Bible-sized backpack? ”
Nicole Kidman at the end of “Hemingway & Gellhorn” (2012)
Sunday, October 19, 2014
Night at the Museum
Or: The Long, Long Trailer
See also a Log24 post from the date of the above tweet: Welcome to the Ape Stuff.
Day at the Museum
Saturday, October 18, 2014
Educational Series
Barron's Educational Series (click to enlarge):
The Tablet of Ahkmenrah:
"With the Tablet of Ahkmenrah and the Cube of Rubik,
my power will know no bounds!"
— Kahmunrah in a novelization of Night at the Museum:
Battle of the Smithsonian , Barron's Educational Series
Another educational series (this journal):
Friday, October 17, 2014
Raiders of the Inarticulate
On Walter Isaacson’s The Innovators :
“Yet as the book’s five hundred–plus pages unwind, Isaacson interrupts himself to present small bromides about what it means to innovate and what we might learn from these innovators, our presumed betters. “Innovation requires articulation,” he tells us, after explaining how the main strength of Grace Hopper, a trailblazing computer scientist for the US Navy, was her ability to speak in the languages of mathematicians, engineers, programmers, and soldiers alike. ‘One useful leadership talent is knowing when to push ahead against doubters and when to heed them,’ he offers later.
The book is peppered with these kinds of passages, which often intrude on the narrative, depriving us of moments of real emotional power.”
— Jacob Silverman in Bookforum , Sept/Oct/Nov 2014
From Isaacson’s book:
Related material:
In memory of T. S. Eliot…
… and in memory of Stanley Chase, producer of Colossus: The Forbin Project
and of Threepenny Opera :
Ninefold square from Colossus
(“There is another system”) —
Fourfold square introducing Brecht
in Dreigroschen Trifft Vierfarben —
Mathematics and Narrative, continued:
Raiders of the Lost Archetype
“… an unexpected development: the discovery of a lost archetype….”
— “The Lost Theorem,” by Lee Sallows, Mathematical Intelligencer, Fall 1997
Related material:
A scene from the 1954 film:
A check of this journal on the above MetaFilter date — Jan. 24, 2012 —
yields a post tagged “in1954.” From another post with that tag:
Backstory: Posts tagged Root Circle.
Thursday, October 16, 2014
Seeking Kleos
Rebecca Newberger Goldstein, quoted in a webpage dated
October 7, 2014 (presumably according to Australian time):
"For the Athenians, kleos mattered more than anything,
according to Goldstein.
'Kleos is fame: it’s the deed that brings fame, it’s the poem
that sings your triumphs, it’s having your life replicated in
other minds, acquiring a kind of moreness, a kind of
secular immortality.' "
Related material:
A check of Goldstein's definition…
… and an image for Broomsday:
From Argument for the Existence of Rebecca (Feb. 6, 2010)
A Forkèd Tongue
This post was suggested by today's previous posts, Broom Bridge Day
and Taking the Fork, as well as by Alyssa is Wonderland.
For the meaning of the title, see Serpent + Derrida and Symbology.