See also a July 19 death, this journal on that date, and
Down the Up Staircase.
See also a July 19 death, this journal on that date, and
Down the Up Staircase.
Judy Davis in the Marabar Caves
The above image is from this journal on Sunday, April 13, 2008.
The preceding cover of a book by Northrop Frye was suggested
by material in this journal from February 2003.
See also Yankee Puzzle and Doodle Dandy.
Related material:
Frank J. Prial on the late singer Tony Martin—
— and, on Jan. 1, 2005, on beverage marketing:
Happy birthday to Hilary Swank.
A Necessary Truth—
James Singer, "A Theorem in Finite Projective Geometry
and Some Applications to Number Theory," Transactions
of the American Mathematical Society 43 (1938), 377-385.
A Contingent Truth—
Singer Tony Martin reportedly died Friday evening, July 27, 2012.
In his memory, some references to a "Singer 7-Cycle."
See also this journal 7 years prior to Martin's death.
Eric M. Friedlander, President of the
American Mathematical Society (AMS),
in the March 2011 AMS Notices —
"I think the best thing the AMS does by far is the Notices .
It could easily be in all doctors’ and dentists’ offices."
Notices : "Really?"
Friedlander: "It could be."
Related material from this journal:


— Annals of Art Education:
Geometry and Death
"There is no question about what arithmetic is for
or why it is supported. Society cannot proceed
without it. Addition, subtraction, multiplication,
division, percentages: though not all citizens can
deal fluently with all of them, we make the
assumption that they can when necessary.
Those who cannot are sometimes at a disadvantage.
Algebra, though, is another matter."
— Underwood Dudley in the Notices of the
American Mathematical Society, May 2010:
"What Is Mathematics For?"
A less nuanced remark from the American
Mathematical Society (AMS) today—
"The answer to the recent Op-Ed piece
in The New York Times entitled
'Is Algebra Necessary?'
is resoundingly YES!"
— Eric Friedlander, AMS president
* A review of philosophical terminology—
"The distinction between necessary truth
and contingent truth is a version of Leibniz 's
distinction between truths of reason and truths
of fact. A necessary truth must be true and
could not be false, whatever way the world is.
It is true in itself. A contingent truth, on the other
hand, depends upon the empirical world and might
have been false had the world been different."
The three parts of the figure in today's earlier post "Defining Form"—

— share the same vector-space structure:
| 0 | c | d | c + d |
| a | a + c | a + d | a + c + d |
| b | b + c | b + d | b + c + d |
| a + b | a + b + c | a + b + d | a + b + c + d |
(This vector-space a b c d diagram is from Chapter 11 of
Sphere Packings, Lattices and Groups , by John Horton
Conway and N. J. A. Sloane, first published by Springer
in 1988.)
The fact that any 4×4 array embodies such a structure was implicit in
the diamond theorem (February 1979). Any 4×4 array, regarded as
a model of the finite geometry AG(4, 2), may be called a Galois tesseract.
(So called because of the Galois geometry involved, and because the
16 cells of a 4×4 array with opposite edges identified have the same
adjacency pattern as the 16 vertices of a tesseract (see, for instance,
Coxeter's 1950 "Self-Dual Configurations and Regular Graphs," figures
5 and 6).)
A 1982 discussion of a more abstract form of AG(4, 2):

Source:

The above 1982 remarks by Brouwer may or may not have influenced
the drawing of the above 1988 Conway-Sloane diagram.
Background: Square-Triangle Theorem.
For a more literary approach, see "Defining Form" in this journal
and a bibliography from the University of Zaragoza.
On painter Karl Benjamin of Claremont, California,
who reportedly died on Thursday—
He played them music
and everything was concentrated and timeless
and all were artists 'til the bell rang.
Another remark from Claremont—
"'Once upon a time' used to be a gateway to
a land that was inviting precisely because
it was timeless, like the stories it introduced
and their ageless lessons about the human condition."
– Dorothea Israel Wolfson,
Claremont Review of Books, Summer 2006
Benjamin was a professor emeritus at Pomona College.
The end of the beginning of the London Games
suggests other games —
Shadows (July 14) —
A Game of Shadows — "You know my methods."
Related religious material —
The Feast of Saint Jude, 2011.
Wikipedia on a magical ring—
Background— The Ring and the Stone, a story linked to here Wednesday.
"By then he was familiar with the work of the Vienna Actionists….
He once said that he had his first taste of the movement
when he heard the screams of his mother’s dental patients
from her office next door to the family’s apartment."
— Obituary of a Viennese artist who reportedly died Wednesday
(Mathematics and Narrative, continued)
Narrative—
The Ring and The Stone from yesterday's post, and…
"In Medieval Jewish, Christian and Islamic legends,
the Seal of Solomon was a magical signet ring
said to have been possessed by King Solomon…."
— Wikipedia article, Seal of Solomon
Mathematics—
A fact related to the mathematical
"Solomon's seal" described above by Bell:
The reference to Edge is as follows—
[3] Edge, W. L., Quadrics over GF(2) and
their relevance for the cubic surface group,
Canadian J. Maths. 11 (1959) ….
(This reference relates Hirschfeld's remarks
quoted above to the 64-point affine space
illustrated below (via the associated
63-point projective space PG (5, 2)).
As for the narrative's Stone…
(Continued from July 22)
Manhattan, July 22, 2012 — "Once upon a time, in a quiet corner
of the Middle East, there lived a shepherd named Gyges. Despite
the hardships in his life Gyges was relatively satisfied with his meager
existence. Then, one day, he found a ring buried in a nearby cave."
Read more…
"I want you on the Swansea lathe today."
— Boss of the Christ figure in "The Machinist" (2004)
Related material in this journal—
Dylan Thomas and Modern Times—
IMDb trivia page on "The Machinist" (2004)—
"The time of 1:30 AM is significant throughout the movie.
Trevor often notices something out of the ordinary at this time.
During the 1 hour 30 minute mark in the movie,
the major plot twist is revealed."
As for the date 1/30… See Tolkien on telepathy.
(Backstory: The Gospel According to Father Hardon )

Part I:
Christian Bale as a Spanish Christ-parody in "The Machinist" (2004)
Part II:
"The expression 'the devil is in the details'
is turned on its head in the exhibit 'The Sacred Made Real'
at Washington's National Gallery of Art…."
— Catholic News Service, 2010
Part III:
Tonight's New York Times obituaries
Part IV:
"My goodness, there must be a hole in this glass."
— Maria in "The Machinist" (2004)
For those who like puzzles—
What film's page at IMDb recommends
the following "also liked" choices?

The Interpreter (2005), Identity (2003), The Game (1997),
The Ghost Writer (2010), The Machinist (2004), The Number 23 (2007)
A similar puzzle: Related Books
For art collector Herbert Vogel,
who reportedly died today
Philip Kennicott in The Washington Post , July 3, 2009—
"The Vogels help allay deep cultural fears
within the art world— fears that art is elitist,
or some kind of confidence game,
or not a serious endeavor (a fear that has
dogged art since at least the time of Plato)."
Some related material from finitegeometry.org,
offered without comment—
"One ring to bring them all…"
— J. R. R. Tolkien, Catholic author
Today in History, July 22, by The Associated Press—
"In 1934, bank robber John Dillinger was shot to death
by federal agents outside Chicago's Biograph Theater,
where he had just seen the Clark Gable movie
'Manhattan Melodrama.'"
From a Manhattan Melodrama—
"Follow the Ring"
Piatigorsky died on Sunday, July 15. Notes in this journal from that date—
Backstory—
Colin Moynihan on the late Alexander Cockburn—
"His attachment to left-wing journalism— and controversy—
was forged very early on. His father, Claud Cockburn, while
covering the Spanish Civil War for The Daily Worker , joined
the Republican forces fighting the rebellion of Francisco
Franco. (Claud Cockburn, under a pseudonym, also wrote
novels, including Beat the Devil , which was made into a
film with Humphrey Bogart and which his son used as the
title of his column in The Nation .)"
A video linked to in this evening's earlier post suggests
an antidote to the film oeuvre of Guillermo del Toro—
in particular, to Pan's Labyrinth.

Here's your ticket, pack your bags,
time for jumpin' overboard
Transportation is here
The New York Times online front page
update of 10:11 this morning provides
a sort of antidote to Saturday morning
cartoons.
The update's time suggests a check
of this journal's most recent post
with the date 10/11. It turns out
to be a meditation on art and
the speed of perception.
Related material:
A linked-to post, Twenty-Four.
"A Saturday morning cartoon is the colloquial term
for the animated television programming that has
typically been scheduled on Saturday mornings
on the major American television networks from
the 1960s to the present…." —Wikipedia
Martin Gardner in the Notices of the
American Mathematical Society ,
June/July 2005:
“I did a column in Scientific American
on minimal art, and I reproduced one of
Ed Rinehart’s [sic ] black paintings.
Of course, it was just a solid square of
pure black.”
Click on picture for details.
For a cartoon graveyard—

http://www.latimes.com/news/politics/ la-pn-romney-colorado-shooting-is- unspeakable-tragedy-20120720,0,1226295.story Romney: Colorado shooting is 'unspeakable tragedy' By Seema Mehta July 20, 2012, 11:15 a.m. BOW, N.H.—Hours after a shooter killed a dozen people in a Colorado cinema, Mitt Romney scrubbed a scheduled campaign rally Friday and instead offered his somber condolences and prayers to the victims and their families. “Our hearts break with the sadness of this unspeakable tragedy. Ann and I join the president and first lady and all Americans in offering our deepest condolences to those whose lives were shattered in a few moments, a few moments of evil in Colorado,” Romney told a few hundred people gathered at a lumber yard here. “I stand before you today not as a man running for office but as a father and grandfather, a husband, an American. This is a time for each of us to look into our hearts and remember how much we love one another and how much we love and how much we care for our great country. There’s so much love and goodness in the heart of America.” Romney, wearing a navy blue suit and blue tie, spoke for four minutes. The trademark campaign banners with slogans such as “Believe in America” or “Obama’s Upside- Down Economy” were gone, leaving a handful of American flags as the backdrop. Before Romney spoke, Father Christian Tutor, an Anglican Catholic priest, led a prayer. ... |

See also related juvenile humor, as well as Aurora in this journal.

For those who prefer fiction:
"Many Dimensions (1931) — An evil antiquarian illegally purchases
the fabled Stone of Suleiman (Williams uses this Muslim form
rather than the more familiar King Solomon) from its Islamic guardian
in Baghdad and returns to England to discover not only that the Stone
can multiply itself infinitely without diminishing the original, but that it
also allows its possessor to transcend the barriers of space and time."
— Wikipedia article on the author Charles Williams
Powered by WordPress