See…
"Numbers themselves are fictions, abstractions humans invented
to gain more control over the world." — Keith Devlin
Related material:
“For me it is a sign that we have fundamentally different
conceptions of the work of the intelligence services.”
— Germany’s Chancellor Angela Merkel in
theguardian.com, Saturday, 12 July 2014, 14.32 EDT
Another sort of service, thanks to Dan Brown and Tom Hanks:
Friday, July 11, 2014 |
At the end of today’s previous post, Sequel,
there is a tribute to jazz great Charlie Haden,
who died yesterday.
A darker requiem, for another musical figure
who also died yesterday:
Related material: Prequels to this post—
Willkommen (June 27) and yesterday’s Back to 1955.
A sequel to the 1974 film
Thunderbolt and Lightfoot :
Contingent and Fluky
Some variations on a thunderbolt theme:
These variations also exemplify the larger
Verbum theme:
A search today for Verbum in this journal yielded
a Georgetown University Chomskyite, Professor
David W. Lightfoot.
"Dr. Lightfoot writes mainly on syntactic theory,
language acquisition and historical change, which
he views as intimately related. He argues that
internal language change is contingent and fluky,
takes place in a sequence of bursts, and is best
viewed as the cumulative effect of changes in
individual grammars, where a grammar is a
'language organ' represented in a person's
mind/brain and embodying his/her language
faculty."
Some syntactic work by another contingent and fluky author
is related to the visual patterns illustrated above.
See Tecumseh Fitch in this journal.
For other material related to the large Verbum cube,
see posts for the 18th birthday of Harry Potter.
That birthday was also the upload date for the following:
See esp. the comments section.
Nick Fury takes the Tesseract…
… which travels back to 1955
(see The Call Girls, Nov. 3, 2013)…
Above: A 1955 cover design by Robert Flynn.
Images from December 1955…
… and a fictional image imagined in an earlier year:
“Paradigm Talent Agency are supporting with casting.
Emperor is described as a look at a debauched world
of wealth, sex, manipulation and treason.”
— The Hollywood Reporter : “Cannes: Adrien Brody
to play Charles V in Lee Tamahori‘s ‘Emperor,'”
2:54 AM PST May 19, 2014, by Scott Roxborough
Related material from Santa Cruz, California:
“On or about or between 11/22/2013 and 11/24/2013….”
Related material from this journal:
“Fiction,” a post of St. Cecilia’s Day, 11/22/2013.
See, too, yesterday’s noon post “Nowhere” and
the April 27-28, 2013, posts tagged Around the Clock.
The Decline and Fall of Augustus Gibbons?
From this morning’s post:
“Beyond Noplace, far into wide Nowhere” — John Hollander
Vide Le Guin Geometry.
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"
A search for "Dark Fields of the Republic,"
an F. Scott Fitzgerald phrase mentioned in
the previous post, yields a book by that title.
"When does a life bend toward freedom?
grasp its direction?"
— Adrienne Rich on page 275 of
Later Poems Selected and New: 1971-2012
The book's author, Adrienne Rich, died at 82 on
March 27, 2012. See that date in this journal.
See also the following:
|
The Diamond Cutters by Adrienne Rich (1955)
However legendary,
Now, you intelligence
Be serious, because
Be hard of heart, because
Be proud, when you have set |
Roger Cooke in The History of Mathematics: A Brief Course
(2nd ed., Wiley-Interscience, 2005)—
“Like all numbers, the number four is bound to occur
in many contexts.”
— Ch. 1: “The Origin and Prehistory of Mathematics,”
Part 3, “Symbols,” footnote 1, page 11.
As is the number 382:
Click the above image for some related material.
Commentary:
“Once the students are taken in by the story, it will be
the instructor’s job to elaborate on the historical
calculations and proofs.”
— Gary S. Stoudt, Professor of Mathematics,
Indiana U. of Pennsylvania, review of Cooke’s book
at the Mathematical Association of America
Roger Cooke in the Notices of the American
Mathematical Society , April 2010 —
"Life on the Mathematical Frontier:
Legendary Figures and Their Adventures"
"In most cases involving the modern era, there
are enough documents to produce a clear picture
of mathematical developments, and conjectures
for which there is no eyewitness or documentary
evidence are not needed. Even so, legends do
arise. (Who has not heard the 'explanation' of
the absence of a Nobel Prize in mathematics?)
The situation is different regarding ancient math-
ematics, however, especially in the period before
Plato’s students began to study geometry. Much
of the prehistory involves allegations about the
mysterious Pythagoreans, and sorting out what is
reliable from what is not is a tricky task.
In this article, I will begin with some modern
anecdotes that have become either legend or
folklore, then work backward in time to take a
more detailed look at Greek mathematics, especially
the Pythagoreans, Plato, and Euclid. I hope at the
very least that the reader finds my examples
amusing, that being one of my goals. If readers
also take away some new insight or mathematical
aphorisms, expressing a sense of the worthiness of
our calling, that would be even better."
Aphorism: "Triangles are square."
(American Mathematical Monthly , June-July 1984)
Insight: The Square-Triangle Theorem.
An essay linked to here on the date of Kuhn’s
death discussed the film “Good Will Hunting”:
“You can be sure that when an experienced movie director
like Gus Van Sant selects an establishing shot for the lead
character, he does so with considerable care, on the advice
of an expert.”
Establishing shots —
1. From a post of January 29, 2014:
2. From a post of April 12, 2011:
Parting shot —
From another post of January 29, 2014:
Note Watson‘s title advice.
The date of a Vanity Fair post on Hugh Jackman—
Sunday, June 8, 2014— suggests a review of the following
quotation from this journal on that date —
Zen ideal —
The title is from this morning's previous post.
From a theater review in that post—
… "all flying edges and angles, a perpetually moving and hungry soul"
… "a formidably centered presence, the still counterpoint"
A more abstract perspective:
See also Desargues via Galois (August 6, 2013).
And now for the musical!
From Ben Brantley’s July Fourth review of a British play —
|
“These two redefine the laws not just of chemistry but also of physics, with each coming across as both immovable object and irresistible force…. I was always aware of how ineffably, achingly attracted each was to the other, and of the diametrically opposed ways in which that attraction became flesh…. … His Tom is all flying edges and angles, a perpetually moving and hungry soul who never pauses in the pursuit of his appetites…. … this Kyra is a formidably centered presence, the still counterpoint to Tom’s charming, full-court-press animation…. … The friction and the possibilities of fusion between Kyra and Tom— who must be together and cannot be together— make ‘Skylight’ one of the most intelligently sentimental love stories of our time.” |
“The friction and the possibilities of fusion” —
“Rubbin’ sticks and stones together
makes the sparks ignite…
Skyrockets in flight!”
Separatrix and Mulligan
An image from this journal on September 16, 2013:
Mulligan:
“A mulligan, in a game, happens when a player gets a second chance
to perform a certain move or action.” — Wikipedia
New York Times obituary for Richard Mellon Scaife:
“He had the caricatured look of a jovial billionaire promoting ‘family values’
in America: a real-life Citizen Kane with red cheeks, white hair, blue eyes and
a wide smile for the cameras. Friends called him intuitive but not intellectual.
He told Vanity Fair his favorite TV show was ‘The Simpsons,’ and his favorite
book was John O’Hara’s Appointment in Samarra , about a rich young
Pennsylvanian bent on self-destruction.” — Robert D. McFadden
Click image below for some nuclear family values in memory of Scaife:
See also the previous post,
Core Curriculum.
This post was suggested by reviews of the David Hare play “Skylight” at
The New York Times , at WorldSocialism.org, and at ChicagoCritic.com.
Vide Atoms in the Family , by Laura Fermi, a book I read in high school.
“Oh, pretty baby…” — Frankie Valli at A Capitol Fourth last night.
Related material — Mira Sorvino in The Great Gatsby .
“Jersey girls are tough.” — Garfield.
“A physicist who played a central role in developing
the theory of supersymmetry – often known as SUSY –
has died.”
— Times Higher Education , July 3, 2014
In honor of the above physicist, Bruno Zumino,
here are two sets of Log24 posts:
Structure, May 2-4, 2013 (the dates of a physicists’ celebration
for Zumino’s 90th birthday)
Hallmark, June 21, 2014 (the date of Zumino’s death)
(Continued from yesterday’s noon post, from “Block That Metaphor,”
and from “Mystery Box III: Inside, Outside“)
“In one corner are the advocates of the Common Core,
led by the Bill and Melinda Gates Foundation, which
helped develop the standards and has defended them
against efforts by some states to roll them back. In the
challengers’ corner, a lineup of foundations and
philanthropists…. Other funders in the opponents’ corner
read like a ‘who’s who’ of well-heeled conservative
philanthropists, including Pittsburgh media magnate
Richard Mellon Scaife….”
— “Meet the Funders Fighting the Common Core,”
from Inside Philanthropy , Feb. 10, 2014
Scaife reportedly died this morning.
The Los Alamos Vision
“Gates said his foundation is an advocate for the Common Core State Standards
that are part of the national curriculum and focus on mathematics and language
arts. He said learning ‘needs to be on the edge’ where it is challenging but not
too challenging, and that students receive the basics through Common Core.
‘It’s great to teach other things, but you need that foundation,’ he said.”
— T. S. Last in the Albuquerque Journal , 12:05 AM Tuesday, July 1, 2014
See also the previous post (Core Mathematics: Arrays) and, elsewhere
in this journal,
“Eight is a Gate.” — Mnemonic rhyme:
Mathematics vulgarizer Keith Devlin on July 1
posted an essay on Common Core math education.
His essay was based on a New York Times story from June 29,
“Math Under Common Core Has Even Parents Stumbling.”
An image from that story:
The Times gave no source, other than the photographer’s name,
for the above image. Devlin said,
“… the image of a Common Core math worksheet
the Times chose to illustrate its story showed
a very sensible, and deep use of dot diagrams,
to understand structure in arithmetic.”
Devlin seems ignorant of the fact that there is
no such thing as a “Common Core math worksheet.”
The Core is a set of standards without worksheets
(one of its failings).
Neither the Times nor whoever filled out the worksheet
nor Devlin seemed to grasp that the image the Times used
shows some multiplication word problems that are more
advanced than the topic that Devlin called the
“deep use of dot diagrams to understand structure in arithmetic.”
This Core topic is as follows:
For some worksheets that are (purportedly) relevant, see,
for instance…
http://search.theeducationcenter.com/search/
_Common_Core_Label-2.OA.C.4–keywords-math_worksheets,
in particular the worksheet
http://www.theeducationcenter.com/editorial_content/multipli-city:
Some other exercises said to be related to standard 2.OA.C.4:
| http://www.ixl.com/standards/ common-core/math/grade-2
|
The Common Core of course fails to provide materials for parents
that are easily findable on the Web and that give relevant background
for the above second-grade topic. It leaves this crucial task up to
individual states and school districts, as well as to private enterprise.
This, and not the parents’ ignorance described in Devlin’s snide remarks,
accounts for the frustration that the Times story describes.
A columnist for the Mathematical Association of America,
Keith Devlin, yesterday posted an essay on Common Core
math education. A response:
Screenshot from a June 14, 2014, New York Times video.
See also the “Cartoon Heroes” video by Aqua, and Aqua in the three previous posts.
Version 1:
(See the June 30 posts Toward Evening,
Joke, and High Concept.)
Version 2:
Version 3:
For the title, see a post of Nov. 4, 2007.
Related material:
Hexagram 29, Water, and a pattern resembling
the symbol for Aquarius:
.
For some backstory about the former,
see the June 21 post Hallmark.
For some backstory about the latter,
see today’s post Toward Evening.
Tom Wolfe has supplied some scaffolding*
to support the concept.
“There’s a Michelangelo joke to be made.”
— Remark in the recent film “The Monuments Men”
Vide Michelangelo in this journal.
(Friday’s Latin Club posts, continued)
The poet Allen Grossman reportedly died in
the morning on Friday, June 27, 2014.
Fish Story
See also Panofsky’s Perspective as Symbolic Form in an online PDF.
New York Times lead obit at 11:06 PM ET June 28:
Compare and contrast:
The above video promoting a book, The OMG Chronicles , was
uploaded by a marketer on March 1, 2011. For a different perspective,
see this journal on that date.
“We specialize in bachelorette parties.”
“What’s on the program?”
— Seymour Glass to Sybil in “A Perfect Day for Bananafish”
Related material from yesterday afternoon…
… and from this morning:
(Continued from 10:09 AM today)
The quotation below is from a webpage on media magnate
Walter Annenberg.
Annenberg Hall at Harvard, originally constructed to honor
the Civil War dead, was renamed in 1996 for his son Roger,
Harvard Class of ’62.
www.broadcastpioneers.com/
walterannenberg.html —
“It was said that Roger was ‘moody and sullen’
spending large parts of his time reading poetry
and playing classical music piano. It had been
reported that Roger attempted suicide at the
age of eleven by slitting his wrists. He recovered
and was graduated Magna Cum Laude from
Episcopal Academy in our area. For awhile,
Roger attended Harvard, but he was removed
from the school’s rolls after Roger stopped doing
his school work and spent almost all his time
reading poetry in his room. He then was sent to
an exclusive and expensive treatment center
in Bucks County, Pennsylvania. At that facility,
Roger became more remote. It was said that he
often didn’t recognize or acknowledge his father.
On August 7, 1962, Roger Annenberg died from
an overdose of sleeping pills.”
A more appropriate Annenberg memorial, an article
in The Atlantic magazine on June 25, notes that…
“Among those who ended up losing their battles
with mental illness through suicide are
Virginia Woolf, Ernest Hemingway, Vincent van Gogh,
John Berryman, Hart Crane, Mark Rothko, Diane Arbus,
Anne Sexton, and Arshile Gorky.”
The authors of the following offer an introduction to symmetry
in quilt blocks. They assume, perhaps rightly, that their audience
is intellectually impaired:
“A quilt block is made of 16 smaller squares.
Each small square consists of two triangles.”
Study this example of definition.
(It applies quite precisely to the sorts of square patterns
discussed in the 1976 monograph Diamond Theory , but
has little relevance for quilt blocks in general.)
Some background for those who are not intellectually impaired:
Robinson’s book Definition , in this journal and at Amazon.
"History is a deep and complicated puzzle—
especially when it involves more dimensions than time."
— Introduction to a novella in Analog Science Fiction
"Annenberg Hall" at Harvard was originally part of a memorial for
Civil War dead. Formerly "Alumni Hall," it was renamed in 1996.
In memory of an actor “who as a boy was one of the few Jewish children
in his mostly Italian-American neighborhood in Brooklyn” —
See the link nocciolo from The Book of Abraham (Oct. 7, 2013).
Introduction to a review of two books in
The American Interest , June 17, 2014:
“A believer and an atheist seek out their antitheses.
Do they meet somewhere in the middle,
or pass in the murk of half-baked pseudo-syntheses?”
“Waiting for the harvest, and the time of reaping,
We shall come rejoicing, passing in the murk.”
Related material:
This morning’s passage by Friedrich Gundolf.
For some backstory, see Gundolf in
Secret Germany: Stefan George and His Circle ,
by Robert E. Norton, Cornell University Press, 2002.
… und Nachtformen des Urgrundes
From George , by Friedrich Gundolf (Berlin, Bondi, 1920):
Wenn das Schlußgedicht des Teppichs "Der Schleier"
das ganze gestaltige "Leben" des Dichters als
einen Traum-nu des Geistes zeigt so ist damit
der Geistestag vollbracht und der Geist selbst
der dies vermag ist am Ende seiner Herrschaft
er steht vor dem Urgrund der ihn bewegt:
er erkennt sich selbst wenn nicht als Stoff
so doch als Kraft zu träumen. Die kosmische Nacht
in die er blickt ist zugleich Widerspiel des Gestaltenreiches
das er als Geist der Erde verwirk licht
und Widerspiel des Gesetzes das er als Geist des Lebens
verewigt kurz sie ist Traum und Tod "Traum"
nicht als die Fülle der Gesichte sondern als "Maja"
die Scheinung des Wesens vermöge
deren der Urgrund sich der Bindung im Raum immer wieder entzieht
wie er im Tod der Bindung durch die Zeit entgeht.
Traum ist die Aufhebung des Raum-Ichs,
Tod die Aufhebung des Zeit-Ichs— beides sind
Nachtformen des Urgrundes
die raumschaffende und -vernichtende Bewegung und
das zeitschaffende und -vernichtende Sein.
The original:
Related material: Die Scheinung in this journal.
Or: Mathematics and Narrative, Continued
In memory of a Stanford Arabist who reportedly died yesterday:
Another dream palace, from science fiction:
From Catherine Asaro’s The Spacetime Pool :
|
She couldn’t believe him. That he sounded sane made none of this more plausible. “And you have no idea how this gate works?” she challenged. His gaze flashed. “Of course I do. It’s a branch. From here to your mountains.” “A tree, you mean?” “No. A branch cut to another page. Your universe is one sheet, mine is another.” She gaped at him. “Do you mean a Riemann sheet? A branch cut from one Riemann sheet to another?” “That’s right.” He hesitated. “You know these words?” She laughed unsteadily. “It’s nonsense. Not the sheets, I mean, but they’re just mathematical constructs! They don’t actually exist. You can’t physically go through a branch cut any more than you could step into a square root sign.” He was watching her with an expression that mirrored how she had felt when he told her about his prophecy. “I have no idea what you’re talking about.” “Complex variable analysis.” She felt as if she were in a play where she only knew part of the script. “A branch cut is like a slit in a sheet of paper. It opens onto another sheet. I suppose you could say the sheets are alternate universes. But they aren’t real.” “They seem quite real,” he said. |
Related material: From Sunday, the day of the Stanford Arabist’s death,
a quotation from a 2013 book on “the rise of complex function theory.”
Some bizarre remarks on “purity” in the previous post
suggest a review of some pure mathematics.
A suitable hallmark for
the previous post, Logical Death:
Hexagram 29: "K'an represents…
the principle of light inclosed in the dark."
— The Richard Wilhelm I Ching
A related page from Stanford:
The May 29 death of a Stanford logician, combined
with this morning’s previous post, suggests a review
of the May 29 post Lost in Translation.
Context— Posts tagged “Bregnans.”
“… near-death experiences have all the
hallmarks of mystical experience…”
— “Bolt from the Blue,” by Oliver Sacks
(See “Annals of Consciousness,” June 20, 2014)
The late Charles Barsotti once “worked for Kansas City-based
Hallmark Cards,” according to an obituary.
See also Mad Day.
Some related deconstructive criticism:
A search for the late Charles Barsotti’s art
in this journal leads to the following passage:
For related material from Bloomsday 2014,
the date of Barsotti’s death, see posts tagged
“consciousness growth.”
Update of 2 AM June 21, 2014:
“… near-death experiences have all the
hallmarks of mystical experience…”
— “Bolt from the Blue,” by Oliver Sacks
Barsotti once “worked for Kansas City-based
Hallmark Cards,” according to an obituary.
Tonight I finally got around to seeing "Return of the King,"
the end of Peter Jackson's Lord of the Rings trilogy, and
listened to Annie Lennox sing "Into the West"* over the
closing credits.
Searching for some background on the song, I found it
was said to have been first publicly performed at the funeral
of a young New Zealand filmmaker, Cameron Duncan.
Duncan reportedly died in Houston, Texas,
on November 12, 2003. See posts from that day and
the day before now tagged 'For Cameron Duncan."
* There is a 1992 film with the same title about Irish Travellers.
The title refers to…
Online Etymology Dictionary on the title of the first Holden Caulfield
story, “I’m Crazy,” in Collier’s , December 22, 1945 —
Meaning “full of cracks or flaws” is from 1580s;
that of “of unsound mind, or behaving as so” is from 1610s.
Jazz slang sense “cool, exciting” attested by 1927….
Phrase crazy like a fox recorded from 1935.
This journal on the morning of January 27, 2010,
the day of J. D. Salinger’s death, had a post on
Nietzsche and Heraclitus titled “To Apollo.”
Related material:
“… the wind was noisy the way it is in spooky movies
on the night the old slob with the will gets murdered.”
— From the opening sentence of the first Holden Caulfield
story, published in the Collier’s of December 22, 1945
See also Peter Matthiessen on Zen, Salinger and Vedanta,
and Heraclitus in this journal. Some background—
A quotation from Nietzsche…
(Sämtliche Werke, Kritische Studienausgabe in 15 Bänden (KSA).
Herausgegeben von Giorgio Colli und Mazzino Montinari.
Berlin: De Gruyter, 1980):
“Nietzsche wrote:
‘Seeing the world as a divine game and beyond good and evil:
in this both the Vedanta and Heraclitus are my predecessors.'”
— KSA vol. 11, page 26, as quoted by André van der Braak
in a chapter from his 2011 book Nietzsche and Zen
(Darin, dass die Welt ein göttliches Spiel sei
und jenseits von Gut und Böse —
habe ich die Vedanta-Philosophie
und Heraklit zum Vorgänger.)
The previous two posts were on adman Julian Koenig,
who reportedly died on Thursday, June 12, 2014.
He was married twice, first to Aquila Connolly,
and later to Maria Eckhart. He has four children:
Pim, an artist; John, a businessman and
horseracing enthusiast; Antonia, a law student;
and Sarah, a producer for the public radio show
This American Life.
The Hotchkiss School on Peter Matthiessen ’45:
Mr. Matthiessen is survived by his wife, Maria Eckhart;
… two stepdaughters, Antonia and Sarah Koenig ….
See also Log24 posts referring to “Matthiessen.”
(These include references to one F. O. Matthiessen, who according
to the Guardian in 2002 was a cousin of Peter Matthiessen’s father.)
In memory of ad writer Julian Koenig, who apparently
coined the phrase “Earth Day” for April 22 (his birthday):
| Tuesday, April 22, 2014
Filed under: Uncategorized — m759 @ 10:00 PM
|
See also all instances of the phrase “colorful tale” in this journal.
Anyone tackling the Raumproblem described here
on Feb. 21, 2014 should know the history of coordinatizations
of the 4×6 Miracle Octad Generator (MOG) array by R. T. Curtis
and J. H. Conway. Some documentation:
The above two images seem to contradict a statement by R. T. Curtis
in a 1989 paper. Curtis seemed in that paper to be saying, falsely, that
his original 1973 and 1976 MOG coordinates were those in array M below—
This seemingly false statement involved John H. Conway's supposedly
definitive and natural canonical coordinatization of the 4×6 MOG
array by the symbols for the 24 points of the projective line over GF(23)—
{∞, 0, 1, 2, 3… , 21, 22}:
An explanation of the apparent falsity in Curtis's 1989 paper:
By "two versions of the MOG" Curtis seems to have meant merely that the
octads , and not the projective-line coordinates , in his earlier papers were
mirror images of the octads that resulted later from the Conway coordinates,
as in the images below.
See the January 6, 2014, post For the Padres
as well as Consciousness Growth.
“Even paranoids have real enemies.”
— Attributed to Delmore Schwartz
“There is a difference as to whether you are describing paranoia
or whether you in fact are paranoid yourself.”
— The late Frank Schirrmacher, dw.de , July 2, 2013.
Schirrmacher reportedly died on Thursday, June 12, 2014.
See that date in this journal.
Paranoia is, of course, a fertile field for politicians and filmmakers:
Related material in this journal:
I, Frankenstein (May 15, 2014) and, for the Eckhart film “Erased,”
Hour of the Wolf (Nov. 9, 2006).
“The growth of consciousness is everything…
the seed of awareness sending its roots
across space and time. But it can grow in so many ways,
spinning its web from mind to mind like the spider
or burrowing into the unconscious darkness like the snake.
The biggest wars are the wars of thought.”
— Fritz Leiber, “The Oldest Soldier” (1960)
Update of 10 PM Saturday, June 14, 2014:
The first link above now leads to Log24 posts tagged
“Consciousness Growth.” This tag is used only to select
specific posts in this journal. It should not be seen as
related to any material of the sort one can find in
a Web search for “growth of consciousness.”
"The wind of change is blowing throughout the continent.
Whether we like it or not, this growth of national consciousness
is a political fact."— Prime Minister Harold Macmillan,
South Africa, 1960
"Lord knows when the cold wind blows
it'll turn your head around." — James Taylor
From a Log24 post of August 27, 2011:
For related remarks on "national consciousness," see Frantz Fanon.
The Walk
From last night’s viewing, an image of Africa in 1947 at the end
of the alternate version of Exorcist: The Beginning ,
also starring Stellan Skarsgård—
The Talk
From this morning’s reading, Macmillan’s 1960 “wind of change” speech—
From Wikipedia:
Wilf might prefer to be remembered not,
as in Thursday’s post, on the latter day above,
but rather on the former.
Happy birthday, Stellan Skarsgård.
Skarsgård in Exorcist: The Beginning .
Wikipedia article on mathematician Herbert Wilf:
“One of Wilf’s former students is Richard Garfield,
the creator of the collectible card game
Magic: The Gathering .”
For more about Garfield, see yesterday’s post House of Cards.
Related material: This journal on the date of Wilf’s death—
See also 2/02, 2014.
“What was this Frankenstein he was creating?”
— David Kushner, Jonny Magic and the Card Shark Kids
Happy birthday, Gene Wilder.
“Orson Scott Card offers a Christmas gift to his millions of fans
with A War of Gifts …. The War over Santa Claus will force
everyone to make a choice.” — Publisher’s description
” ‘Peace on Earth, good will toward brats,’ said Peter. ”
— Orson Scott Card, “Ender’s Stocking” in A War of Gifts
"The relevance of a geometric theorem is determined by what the theorem
tells us about space, and not by the eventual difficulty of the proof."
— Gian-Carlo Rota discussing the theorem of Desargues
What space tells us about the theorem :
In the simplest case of a projective space (as opposed to a plane ),
there are 15 points and 35 lines: 15 Göpel lines and 20 Rosenhain lines.*
The theorem of Desargues in this simplest case is essentially a symmetry
within the set of 20 Rosenhain lines. The symmetry, a reflection
about the main diagonal in the square model of this space, interchanges
10 horizontally oriented (row-based) lines with 10 corresponding
vertically oriented (column-based) lines.
Vide Classical Geometry in Light of Galois Geometry.
* Update of June 9: For a more traditional nomenclature, see (for instance)
R. Shaw, 1995. The "simplest case" link above was added to point out that
the two types of lines named are derived from a natural symplectic polarity
in the space. The square model of the space, apparently first described in
notes written in October and December, 1978, makes this polarity clearly visible:
Thanks to the Museum of Modern Art for pointing out
a new emphasis on design in U.S. Army Field Manual 5-0.
MoMA supplies a link to an article from May 3, 2010:
Design Thinking Comes to the U.S. Army.
An excerpt from the manual:
An approach to this text by Harvard's legendary "unreliable reader"—
"The risks multiply, especially when a problem involves 26 March 2010…."
The previous post told how user58512 at math.stackexchange.com
sought in 2013 a geometric representation of Q8 , the quaternion group.
He ended up displaying an illustration that very possibly was drawn,
without any acknowledgement of its source, from my own work.
On the date that user58512 published that illustration, he further
pursued his March 1, 2013, goal of a “twisty” quaternion model.
On March 12, 2013, he suggested that the quaternion group might be
the symmetry group of the following twisty-cube coloring:
Illustration by Jim Belk
Here is part of a reply by Jim Belk from Nov. 11, 2013, elaborating on
that suggestion:
Belk argues that the colored cube is preserved under the group
of actions he describes. It is, however, also preserved under a
larger group. (Consider, say, rotation of the entire cube by 180
degrees about the center of any one of its checkered faces.) The
group Belk describes seems therefore to be a symmetry group,
not the symmetry group, of the colored cube.
I do not know if any combination puzzle has a coloring with
precisely the quaternion group as its symmetry group.
(Updated at 12:15 AM June 6 to point out the larger symmetry group
and delete a comment about an arXiv paper on quaternion group models.)
The title refers to a Scientific American weblog item
discussed here on May 31, 2014:
Some closely related material appeared here on
Dec. 30, 2011:
A version of the above quaternion actions appeared
at math.stackexchange.com on March 12, 2013:
"Is there a geometric realization of Quaternion group?" —
The above illustration, though neatly drawn, appeared under the
cloak of anonymity. No source was given for the illustrated group actions.
Possibly they stem from my Log24 posts or notes such as the Jan. 4, 2012,
note on quaternion actions at finitegeometry.org/sc (hence ultimately
from my note "GL(2,3) actions on a cube" of April 5, 1985).
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 title was suggested by a post on The Piano
and by the dimensions of an image in this morning’s
previous post: 404 x 211 pixels, suggesting
4/04, a date significant to author Katherine Neville,
and 2/11, the date of a Log24 post from 2014.
These dates are both related to the post…
Everybody Comes to Rick’s
(original title of Casablanca ).
Whimsical, yes, but see Iris Murdoch
on the contingent in literature and the word
“whimsical” in a post of January 26, 2004
(in a series of posts involving Michael Sprinker).
Jungle music suggested by yesterday’s Black Widow Club post,
by the midnight post that followed, and by a May 24 death:
Or: Corrections
Factually Incorrect:
Ed Koch in the Las Vegas Sun , May 26, 2014:
“In addition to Pearl, Bob’s other cousin, Bill Bailey,
was a song and dance man who was the inspiration
for the hit song ‘Bill Bailey Won’t You Please Come Home.’
In fact, when William Bailey went into show business,
he took the nickname ‘Bob’ to avoid any confusion
with his older, more established cousin Bill.”
(Links added for greater depth.)
Politically Incorrect:
Correction:
… and for Anthony Hopkins and a Black Widow,
as well as for a filmmaker who reportedly died on May 19.
Update of 4:48 PM ET: See also Philip Roth on an ambiguity.
* The title was suggested in part by a series of Isaac Asimov mysteries.
The ninefold square, the eightfold cube, and monkeys.
For posts on the models above, see quaternion
in this journal. For the monkeys, see
"Nothing Is More Fun than a Hypercube of Monkeys,"
Evelyn Lamb's Scientific American weblog, May 19, 2014:
The Scientific American item is about the preprint
"The Quaternion Group as a Symmetry Group,"
by Vi Hart and Henry Segerman (April 26, 2014):
See also Finite Geometry and Physical Space.
A book by this title, Richard A. Brualdi’s Combinatorial Matrix Classes ,
was published by Cambridge University Press in 2006:
For some related remarks, see The Counter (March 13, 2011).
My own work deals with combinatorial properties of matrices
of 0’s and 1’s, but in the context of Galois (i.e., finite) fields,
not the real or complex fields. Despite the generality of
their titles, Combinatorial Matrix Theory and Combinatorial
Matrix Classes do not deal with Galois matrices.
Some mathematical background for yesterday's
remarks "For the Bregnans" and "Lost in Translation"—
"Matching Theory: A Sampler, from Dénes König
to the Present," by Michael D. Plummer, 1991.
See also Matching Theory by Plummer and Lovász.
Translation by Barbara Johnson:
"The minimum number of rows— lines or columns—
that contain all the zeros in a matrix is equal to
the maximum number of zeros
located in any individual line or column ."
In the original:
"situés sur des lignes ou des colonnes distinctes "
Update of 11:30 PM ET May 29, 2014:
Derrida in 1972 was quoting Philippe Sollers, Nombres
(Paris: Éditions du Seuil , 1968). Sollers in turn was
perhaps quoting A. Kaufmann, Méthodes et Modèles
de la Recherche Opérationnelle , Paris, Dunod , 1964,
L'Économie d'Entreprise 10 , vol. 2, page 305:
"Le nombre minimal de rangées
(lignes et/ou colonnes) contenant
tous les zéros d'une matrice, est égal
au nombre maximal de zéros
situés sur des lignes et des colonnes distinctes."
The Shining of May 29…
The original note and references to it here.
* As opposed to the Monicans . See previous post.
“Aeon Flux suffered a decline of 63.97% in box office earnings, going down to No. 6 the following week. On 9 February 2006, it completed its theatrical run, grossing a domestic take of $25,874,337 and a worldwide box office total of $52,304,001. It failed to recoup its $62 million budget.” — Wikipedia
See also posts on the above date, 9 February 2006, and posts on Aeon Flux .
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.
For a place where entertainment is not God* —
This post was suggested by a passage in the Prasna Upanishad :
“That person who is to be known,
he in whom these parts rest,
like spokes in the nave of a wheel,
you know him,
lest death should hurt you.”
See Sept. 9, 2003.
* There are other sorts of places.
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 .
… Continues.
A post by Margaret Soltan this morning:
Links (in blue) from the above post:
Cane and Mondo Cane.
Bagger Vance — “Time for you to see the field.”
From Pictures for Kurosawa (Sept. 6, 2003) —
“As these flowing rivers that go towards the ocean,
when they have reached the ocean, sink into it,
their name and form are broken, and people speak of
the ocean only, exactly thus these sixteen parts
of the spectator that go towards the person (purusha),
when they have reached the person, sink into him,
their name and form are broken, and people speak of
the person only, and he becomes without parts and
immortal. On this there is this verse:
‘That person who is to be known, he in whom these parts
rest, like spokes in the nave of a wheel, you know him,
lest death should hurt you.’ “
— Prasna Upanishad
Related material — Heaven’s Gate images from Xmas 2012:
“This could be heaven or this could be hell.” — Hotel California
Those who prefer mathematics to narrative may consult Root Circle.
"In August 1884, he wrote to Resa von Schirnhofer:
'Here one can live well, in this strong, bright atmosphere,
here where nature is amazingly mild and solemn
and mysterious all at once— in fact, there is no place
that I like better than Sils-Maria.'"
For more about Resa, see another weblog's post
of April 30, 2013.
A remark on Nietzsche from the epigraph of that weblog:
"His life's work was devoted to finding one's 'style'
within the chaos of existence. The trick, obviously,
is not to lose your mind in the process."
A remark from this weblog on the above date —
Walpurgisnacht 2013 —
Finite projective geometry explains
the surprising symmetry properties
of some simple graphic designs—
found, for instance, in quilts.
The story thus summarized is perhaps not
destined for movie greatness.
As opposed to, say, Chloe Grace Moretz —
For instance:
See Log24 instances of the above Binoche image,
as well as other posts on Binoche + Bleu .
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 “
(Continued from previous post, Clue)
The quoted lyric is not by Elliot Rodger, but rather by
Don Henley in his 1995 album “Actual Miles: Henley’s Greatest Hits.”
See also some related Hollywood notes.
Update of 6:30 PM ET on May 24:
LA Times opinion piece of May 19, 2014 —
“At UC Santa Barbara, the student government
has formally requested that professors provide
trigger warnings on their syllabuses.”
See also an laist introduction to an LA Times transcript
of a frightening Santa Barbara “trigger warning” video .
The introduction is itself a trigger warning —
“… the LA Times has a transcript, although we
warn that the content is truly disturbing.”
Arts & Letters Daily today —
New Books
What makes a novel worth reading:
All sorts of people can do justice to that subject.
Academics, however, haven’t a clue… more»
For related material, see a post for Deresiewicz.
Follow the link there to Lyric Intelligence, and
from that post to Meadow-Down posts.
From a spring 2004 Michigan State University syllabus for the
T-Th course English 487, “The Twentieth Century English Novel”—
Tuesday, March 30: Murdoch
(her essay “ The Sublime and the Beautiful Revisited “)
Thursday, April 1: Murdoch
Related material from this journal—
Posts of Tuesday, March 30, 2004, and of Thursday, April 1, 2004.
For a related reference to the mathematician Michael Harris from
the Free-Floating Signs link in this afternoon’s 4:30 post, see
the posts of Wednesday, March 31, 2004, the day intervening
between the above two class dates.
“You’ve got to pick up every stitch…”
— Donovan, song on closing credits of To Die For
“…’Supersymmetry’ was originally written
specifically for Her ….” — Pitchfork
“Eventually we see snow particles….”
— Her screenplay by Spike Jonze
This journal on January 24, 2006:
Context: See Free-Floating Signs.
Backstory: Digital Member and Uneven Break.
She:
The White Goddess in this journal.
Her:
“Eventually we see snow particles….”
— Screenplay by Spike Jonze
“Chaos is order yet undeciphered.”
— The novel The Double , by José Saramago,
on which the recent film "Enemy" was based
For Louise Bourgeois — a post from the date of Galois's death—
For Toronto — Scene from a film that premiered there on Sept. 8, 2013:
Related material: This journal on that date, Sept. 8, 2013:
"I still haven't found what I'm looking for." — Bono
"In fact Surrealism found what it had been looking for
from the first in the 1920 collages [by Max Ernst],
which introduced an entirely original scheme of
visual structure…."
— Rosalind Krauss quoting André Breton*
in "The Master's Bedroom"
* "Artistic Genesis and Perspective of Surrealism"
(1941), in Surrealism and Painting (New York,
Harper & Row, 1972, p. 64).
See also Damnation Morning in this journal.
The page of Whitehead linked to this morning
suggests a review of Polster's tetrahedral model
of the finite projective 3-space PG(3,2) over the
two-element Galois field GF(2).
|
The above passage from Whitehead's 1906 book suggests
that the tetrahedral model may be older than Polster thinks.
Shown at right below is a correspondence between Whitehead's
version of the tetrahedral model and my own square model,
based on the 4×4 array I call the Galois tesseract (at left below).
(Click to enlarge.)
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.
From a recreational-mathematics weblog yesterday:
"This appears to be the arts section of the post,
so I’ll leave Martin Probert’s page on
The Survival, Origin and Mathematics of String Figures
here. I’ll be back to pick it up at the end. Maybe it’d like
to play with Steven H. Cullinane’s pages on the
Finite Geometry of the Square and Cube."
I doubt they would play well together.
Perhaps the offensive linking of the purely recreational topic
of string figures to my own work was suggested by the
string figures' resemblance to figures of projective geometry.
A pairing I prefer: Desargues and Galois —
For further details, see posts on Desargues and Galois.
File: This journal on November 14, 2009.
Photo:
Click photo for some backstory.
Willis reportedly died on Sunday, May 18, 2014.
A sequel to this afternoon's Rubik Quote:
"The Cube was born in 1974 as a teaching tool
to help me and my students better understand
space and 3D. The Cube challenged us to find
order in chaos."
— Professor Ernő Rubik at Chrome Cube Lab
(Click image below to enlarge.)
“The Cube was born in 1974 as a teaching tool
to help me and my students better understand
space and 3D. The Cube challenged us to find
order in chaos."
— Professor Ernő Rubik at Chrome Cube Lab
For a Chinese approach to order and chaos,
see I Ching Cube in this journal.
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