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
Continued from Black Friday …
"Tell me no secrets, tell me some lies."
— Don't It Make My Brown Eyes Blue
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
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."
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.
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.)
The title refers to this morning's previous post.
The above links from today's aldaily.com : Cubism, Bernstein, Hell.
For the late Vladimir Nabokov, author of Pale Fire :
He took his article from a steel file:
"It's accurate. I have not changed her style.
There's one misprint–not that it matters much:
Mountain, not fountain. The majestic touch."
Click for a related Hollywood Reporter story.
A search for background on the academic
author cited in the previous post yields…
"The debate is, in the words of one professor,
'a struggle for the intellectual soul of Stanford.'"
Some may doubt there is such a thing.
See Marissa Mayer in this journal…
and in Vogue (a story dated August 16, 2013)—
From PhDTree.org —
Journal Article Neohelicon 38(1) 161-175 (2011)
No abstract.
DOI: 10.1007/s11059-011-0092-y
Download: Full Text PDF
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.
Kristen Wiig, Girl Reporter…
.. in The Skeleton Twins—
"I've got news for you."
Co-starring Bill Hader as Her —
Continued from Finder (Sept. 23, 2014)
"I wrote another book!" — Harlan Kane
From an online NY Times obituary this morning :
"At Newsweek, Mr. Bernstein and other top editors
became known as the Flying Wallendas for
managing tasks on deadline with the seeming ease
of the famed trapeze artists. In a tribute, staff
members framed a circus poster of the high-wire
troupe and hung it in his office."
Wikipedia on Bernstein's son-in-law :
"Married to New York Times correspondent Nina Bernstein,
Huyssen is also a longtime friend of Nobel Prize-winning
Turkish novelist Orhan Pamuk, and often hosts him when
the writer comes to the US. The two teach an undergraduate
class together at Columbia called 'Words and Pictures,'
which examines problems of visual representation in literature,
particularly theories of ekphrasis."
Ekphrasis for Bernsteins:
The Wonder Show of the World!
See also Miniature Prize —
"Rosebud."
Alexander Grothendieck, Récoltes et Semailles , 18.5.9.5. e, p. 1181 :
Pour mettre la joie à son comble, j’ajoute que le dénommé Saavedra
semble avoir disparu de la circulation sans plus laisser aucune trace….
Du coup, l’histoire prend des allures de sombre intrigue policière.
Man of La Mancha :
"Who knows where madness lies?"
An author quoted here at 10 PM ET Monday, Nov. 24, 2014 :
And then there is author Dan McGirt :
|
It sounded fun, so I signed up — and soon learned writing a story set in someone else’s fictional world presents certain … challenges. It was an enjoyable experience, yet very different than being able to write and run with whatever crazy idea pops into my head. Trying to capture the feel of a game that is more based on action and blowing stuff up than on deep character moments (not that I would know much about that … ) was also a challenge. I experimented with things like using comic book sound effects, lean descriptions (do I really need to describe a fireball spell in detail?) and other tricks to keep things moving. I also got to add to Magicka lore. Often the answer to my questions about some bit of in-world history or “fact” was “Make something up.” So I did! (Often getting a response of … “Odin’s onions, no! You can’t do that!”) So I was thrilled and excited to contribute in a small way to the development of Midgård. The result is Magicka: The Ninth Element , in which four young Wizards are sent on a quest to pursue the mysterious Purple Wizard who has stolen a powerful artifact from the Order of Magick. Which powerful artifact? No one is quite sure (for reasons explained in the story). What does it do? Again, unclear. But it can’t be good. Thus our heroes Davlo, Grimnir, Fafnir and Tuonetar set out on their quest — and promptly go off the map. (I’m not even kidding. The Midgård map in the front of the book will of little use to you. But it’s pretty!) Will they survive the dangers of the Unmapped Lands? Will they catch the Purple Wizard in time? Will they save the world? Read the book to find out! |
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
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.)
Mathematics: Galois-Plane Models.
Narrative: "The Dreaming Jewels."
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.
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.
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.
"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
Continued from Tuesday, November 18, 2014
International poster for the 2010 film "Black Swan"—
"Death is a black swan." — Graciela Chichilnisky
Continued from Friday, November 21:
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) —
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.
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.
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.
“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“
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