Log24

Thursday, December 11, 2014

Jews on Style

Filed under: General — Tags: , — m759 @ 11:00 am

"A window unto  the world"?  "The classical  style"?

Wednesday, December 10, 2014

Broad and Bright

Filed under: General — Tags: — m759 @ 8:23 pm

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

Filed under: General — m759 @ 6:29 pm

The title refers to Brit Marling from the previous post.
The quote, below, refers to today's news.

"Lovely. Just lovely."

Plan 9…

Filed under: General — Tags: — m759 @ 1:00 pm

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

Filed under: General,Geometry — m759 @ 7:59 pm

(Continued… See "I need a photo opportunity…")

From the previous post's Yankee Puzzle link :

Saturday, January 7, 2012

Doodles

Filed under: Uncategorized — Tags:  — m759 @ 7:14 PM 

Today's Google Doodle for the 100th birthday of Charles Addams—

http://www.log24.com/log/pix12/120107-GoogleDoodle-AddamsFamily.jpg

A doodle from this year's Feast of the Epiphany

http://www.log24.com/log/pix12/120106-CathyHull-Hillman-Detail.jpg

A doodle based on today's previous post and on a post for Twelfth Night, 2003

IMAGE- Quilt blocks- Devil's Claws and Yankee Puzzle

IMAGE- 'I'm a Yankee Doodle Dandy' musical notes

"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

Filed under: General — m759 @ 12:01 pm

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

Filed under: General — m759 @ 9:00 pm

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

Filed under: General — m759 @ 11:09 am

See a Log24 search for kernel .

From that search, an image for cypher enthusiasts :

Robert De Niro as Louis Cyphre in 'Angel Heart'

The Nutshell Suite

Filed under: General — m759 @ 10:30 am

See posts tagged The Nutshell.

Saturday, December 6, 2014

Six-Point Theology

Filed under: General,Geometry — m759 @ 12:00 pm

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

Language Game

Filed under: General — m759 @ 8:23 pm

Note the mace.

Space Craft

Filed under: General — m759 @ 7:59 pm

See also Space + Craft.

Wittgenstein’s Picture

Filed under: General,Geometry — m759 @ 12:00 pm

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.

Filed under: General — m759 @ 11:00 am

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

Filed under: General — Tags: — m759 @ 7:00 pm

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

Filed under: General — Tags: — m759 @ 11:11 am

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 —

Great line reading in 'Angels and Demons'- 'The God PARTICLE?'

Follow This

Filed under: General — Tags: — m759 @ 10:30 am

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

Filed under: General,Geometry — Tags: , — m759 @ 10:00 am

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)

IMAGE- 'The geometry of the dance' is that of a tetrahedron, according to Peter Pesic

I prefer a different, Norwegian, interpretation of "the dance of four."

Related material:
The clash between square and tetrahedral versions of PG(3,2).

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) —

http://www.log24.com/log/pix11A/110505-ThemeAndVariations-Hofstadter.jpg

http://www.log24.com/log/pix11A/110505-BlockDesignTheory.jpg

Mathematics

http://www.log24.com/log/pix11A/110505-WikipediaFanoPlane.jpg

The Fano plane block design

Magic

http://www.log24.com/log/pix11A/110505-DeathlyHallows.jpg

The Deathly Hallows  symbol—
Two blocks short of  a design.

 

(Updated at about 7 PM ET on Dec. 3.)

Tuesday, December 2, 2014

Models

Filed under: General,Geometry — m759 @ 6:45 pm

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

Filed under: General — m759 @ 11:09 am

Reese Witherspoon in "Wild" (Click to enlarge.)

Witherspoon and Wiggins Streets, Princeton, NJ:

"When you come to a fork in the road…

Borderline Metaphysics

Filed under: General — m759 @ 10:25 am

See also Ennead Boo.

Colorful Tale

Filed under: General — Tags: — m759 @ 9:45 am

Continued.

"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

Filed under: General — m759 @ 8:31 pm

"A friend asked why I am saying kaddish.
 A good question."

Kaddish , by Leon Wieseltier, Chapter One

Scarlett Johansson and Natalie Portman

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 :

December 2, 2014

  • "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."

Red Dawn

Filed under: General — Tags: — m759 @ 12:00 pm

Change Arises

Filed under: General,Geometry — Tags: — m759 @ 11:00 am

Flashback to St. Andrew's Day, 2013 —

Saturday, November 30, 2013

Waiting for Ogdoad

Filed under: Uncategorized — Tags:  — m759 @ 10:30 AM 

Continued from October 30 (Devil's Night), 2013.

“In a sense, we would see that change
arises from the structure of the object.”

— Theoretical physicist quoted in a
Simons Foundation article of Sept. 17, 2013

This suggests a review of mathematics and the
"Classic of Change ," the I Ching .

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 —

Spaces as Hypercubes

A different representation of the unit cell of
the hyperspace H (and of the I Ching ) —

Child Buyer

Filed under: General — Tags: — m759 @ 4:02 am

Sunday, November 30, 2014

Agents of a Great Despair

Filed under: General,Geometry — Tags: — m759 @ 6:00 pm

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

Filed under: General — Tags: — m759 @ 12:31 pm

Continued from Black Friday 

"Tell me no secrets, tell me some lies."

Don't It Make My Brown Eyes Blue

View from the Bottom

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm

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

Thomas Mann on the deathly precision of snowflakes

Britannica article, 'Flounder'

Back to the Real

Filed under: General — Tags: — m759 @ 4:30 am

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

Filed under: General,Geometry — Tags: — m759 @ 4:00 am

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

Filed under: General,Geometry — Tags: , , — m759 @ 1:23 am

The Regular Tetrahedron

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.)

The Cube

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

Mark Strand

Filed under: General — m759 @ 2:14 pm

Something Missing?

Filed under: General — m759 @ 7:59 am

The title refers to this morning's previous post.

The above links from today's aldaily.com :  Cubism,  Bernstein,  Hell.

Mountain, Fountain

Filed under: General — m759 @ 6:29 am

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

Filed under: General — m759 @ 6:00 pm

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)—

IMAGE- Marissa Mayer on numbers in Vogue magazine

Religion for Academics

Filed under: General — m759 @ 5:35 pm

From PhDTree.org —

“Paradox lust”: the fortunate fall
according to Joyce in finnegans wake

Gerald Gillespie

Journal Article Neohelicon 38(1) 161-175 (2011)

No abstract.

DOI: 10.1007/s11059-011-0092-y

Download: Full Text PDF

A Key for the Twins*

Filed under: General — m759 @ 5:02 pm

* Id est , The Skeleton Twins.

Former-Day Saint

Filed under: General — Tags: — m759 @ 4:35 pm

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

Filed under: General — m759 @ 10:10 am

Kristen Wiig, Girl Reporter…

.. in The Skeleton Twins

"I've got news for you."

Co-starring Bill Hader as Her —

Words and Pictures

Filed under: General — m759 @ 8:07 am

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 —

Snow globe

"Rosebud."

Off the Map

Filed under: General — m759 @ 6:07 am

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 :

November Seventh, 2013 :

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

Filed under: General,Geometry — m759 @ 1:01 pm

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

Filed under: General — m759 @ 5:31 am

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

Filed under: General,Geometry — Tags: — m759 @ 10:00 pm

Mathematics:  Galois-Plane Models.

Narrative: "The Dreaming Jewels."

A Tetrahedral Fano-Plane Model

Filed under: General,Geometry — Tags: , — m759 @ 5:30 pm

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

Filed under: General,Geometry — Tags: , — m759 @ 7:18 am

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,
California State University, Northridge, 
"Pythagorean and Platonic Bridges between
Geometry and Algebra," in BRIDGES: Mathematical
Connections in Art, Music, and Science 
, 1998,
archive.bridgesmathart.org/1998/bridges1998-121.pdf

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

Filed under: General,Geometry — Tags: , , — m759 @ 11:00 am

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.

Oxley's 2004 drawing of the 13-point projective plane

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)).

http://www.log24.com/log/pix11A/110427-Cube27.jpg

   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?”

Filed under: General — m759 @ 10:00 pm

Creating new realities in DeLillo's 'Point Omega'

"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

Filed under: General — m759 @ 12:48 pm

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

Filed under: General — Tags: , — m759 @ 1:00 am

Continued from Friday, November 21:

Sunday, November 23, 2014

Remarks on Reality

Filed under: General — Tags: — m759 @ 5:09 pm

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

Filed under: General — Tags: — m759 @ 6:00 am

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.

Stevens on 'the Ruler of Reality'

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

Filed under: General — m759 @ 8:00 am

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

Filed under: General — Tags: — m759 @ 5:24 am

Welcome to the Garden Club, Pilgrim

http://www.log24.com/log/pix08/080520-GardenClub2.jpg

"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

Filed under: General — Tags: , — m759 @ 9:00 am

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

Filed under: General — m759 @ 12:12 pm

In memory of Mike Nichols

"Let me put you in this unit." — John Calley

Graduate Director

Filed under: General — m759 @ 11:00 am

The Manchurian Candidate

Filed under: General — m759 @ 12:59 am

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

Filed under: General,Geometry — Tags: — m759 @ 10:25 am

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

Filed under: General — Tags: , — m759 @ 9:13 am

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.”

— TheArtStory.org

Lectures at Bennington, 1971

For example:

Art adapted today from the Google search screen. Discuss.

The Abacus Conundrum…

Filed under: General — Tags: — m759 @ 1:44 am

Continues.

http://www.log24.com/log/pix10B/101206-AbacusConundrum.jpg

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

Filed under: General — Tags: — m759 @ 12:45 am

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

Filed under: General — m759 @ 9:00 am

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

Filed under: General — m759 @ 5:20 am

“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

See also, in this journal,  528,  1963,  522, and  3273.

Saturday, November 15, 2014

A Dark Detective Story

Filed under: General — m759 @ 7:20 pm

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

Filed under: General — m759 @ 7:59 am

(Continued)

A Math Enigma

Grothendieck reportedly died on Thursday, November 13, 2014.
From this  journal a year earlier:

A German Enigma 

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

Filed under: General,Geometry — m759 @ 9:00 pm

“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:

Some Symplectic History

Filed under: General,Geometry — m759 @ 1:28 am

A paper from 1976 on symplectic torsors  and finite geometry:

IMAGE- Saavedra-Rivano, 'Finite Geometries in the Theory of Theta Characteristics' (1976)

A pdf is now available:

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

Filed under: General — m759 @ 5:55 pm

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:

IMAGE- Massimo Vignelli, his wife Lella, and cube

Progressive Matrix

Filed under: General,Geometry — Tags: , — m759 @ 6:00 am

Yesterday's post and recent Hollywood news suggest
a meditation on a Progressive Matrix —

Oct. 12-14, 2005:

'A Poem for Pinter,' conclusion: 'Tick Tick Hash.'

'The Interpreter'-- Sean Penn to Nicole Kidman-- 'My Card.'

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):

IMAGE- Raven's Progressive Matrices item with symbols from Cullinane's box-style I Ching

Structural background —

Wednesday, November 12, 2014

Harrowing Cuteness

Filed under: General — Tags: — m759 @ 10:22 am

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

Vonnegut’s Birthday

Filed under: General — Tags: — m759 @ 11:00 am

Monday, November 10, 2014

Meanwhile, Back in 1962…

Filed under: General — Tags: — m759 @ 11:59 pm

Remember him to Herald Square.

Narrative Line

Filed under: General,Geometry — Tags: , , — m759 @ 11:02 pm

"We live entirely, especially if we are writers, by the imposition
of a narrative line upon 
disparate images…." — Joan Didion

Narrative Line:

IMAGE- R. D. Carmichael's 1931 construction of the Steiner system S(5, 8, 24)

IMAGE- Harvard senior Jeremy Booher in 2010 discusses Carmichael's 1931 construction of S(5, 8, 24) without mentioning Carmichael.

Disparate images:

Exercise:

Can the above narrative line be imposed in any sensible way
upon the above disparate images?

Sunday, November 9, 2014

Sermon

Filed under: General — Tags: , , , — m759 @ 11:00 am

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

Filed under: General,Geometry — Tags: , — m759 @ 1:00 am

“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*

Filed under: General — m759 @ 11:59 pm

Fantasy and the Buffered Self.”

*For the title, see Enormous Changes.

Friday, November 7, 2014

The Missing ART

Filed under: General,Geometry — m759 @ 7:31 am

IMAGE- Harvard art museum director: 'This is brand new museum.'

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.

Geometry was very important to us in this movie.”

The Crosswicks Curse…

Filed under: General — m759 @ 7:00 am

Continues.

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

Filed under: General — Tags: — m759 @ 1:44 pm

(Continued)

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…

Filed under: General — Tags: — m759 @ 1:06 am

Continues.

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…

Filed under: General — m759 @ 10:00 pm

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*

Filed under: General — Tags: — m759 @ 8:59 pm

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

Filed under: General — Tags: — m759 @ 2:01 pm

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

Filed under: General,Geometry — Tags: — m759 @ 12:48 pm

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….”

Symplectic :

IMAGE- A symplectic structure -- i.e. a structure that is symplectic (meaning plaited or woven)

— Steven H. Cullinane,
diamond theorem illustration

Sunday, November 2, 2014

A Singular Place

Filed under: General,Geometry — m759 @ 5:09 pm

"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:

Makeover on 34th Street .

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 …

http://www.diamondspace.net/about.html:

IMAGE - The Diamond Theorem

Right Through Hell

Filed under: General — m759 @ 8:28 am

… there is a path. — Malcolm Lowry

Saturday, November 1, 2014

Tonic

Filed under: General — Tags: — m759 @ 10:00 pm

Related posts:
New Key and The Well-Tempered Monolith.

Hold the gin.

Not Saints

Filed under: General — m759 @ 1:00 pm

“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.

All Saints’ Day

Filed under: General — m759 @ 12:06 pm

Friday, October 31, 2014

For the Late Hans Schneider

Filed under: General — Tags: — m759 @ 3:30 am

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

Filed under: General,Geometry — m759 @ 3:00 am

On Devil’s Night

Introducing a group of 322,560 affine transformations of Dürer’s ‘Magic’ Square

IMAGE- Introduction to 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

Filed under: General — Tags: — m759 @ 5:09 pm

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

Filed under: General — Tags: — m759 @ 12:00 pm

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.

Symbology for Harvard

Filed under: General — m759 @ 12:00 am

See also “Satan’s School.”

Tuesday, October 28, 2014

Raiders of the Lost Symbol

Filed under: General,Geometry — Tags: — m759 @ 5:00 pm

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

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

“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

Filed under: General — Tags: — m759 @ 4:00 pm

For Karl Pribram and Katherine Neville,
a sequel to this morning's Figural Processing —

See also Christmas 2013.

Figural Processing

Filed under: General,Geometry — Tags: — m759 @ 4:22 am

Part I:

Six-dimensional hypercube from 'Brain and Perception: Holonomy and Structure in Figural Processing,' by Karl H. Pribram

Part II:

Click images for some context.

Monday, October 27, 2014

Revolutions in Geometry

Filed under: General,Geometry — m759 @ 9:00 am

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

Filed under: General,Geometry — Tags: — m759 @ 12:00 pm

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.

For Chern’s Birthday

Filed under: General — Tags: — m759 @ 11:00 am

The Poem of Pure Reality

Saturday, October 25, 2014

Foundation Square

Filed under: General,Geometry — Tags: , , , — m759 @ 2:56 pm

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…

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

Filed under: General — Tags: — m759 @ 9:00 pm

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

Prime Cut

Filed under: General — m759 @ 7:24 pm

See that phrase in this journal.

Wednesday, October 22, 2014

The Seventh Stage

Filed under: General — Tags: — m759 @ 7:01 pm

Robin Williams at Bunker Hill Community College

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

Claves Regni Caelorum

Filed under: General — Tags: — m759 @ 10:00 am

Continued from Day at the Museum, last Sunday, October 19, 2014.

This post was suggested by…

  1.  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 .
  2. A detail in Day at the Museum— The New York Times ‘s
    appraisal of Joan Rivers: “A Comic Without a Shut-Off Switch.”
  3. 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

Filed under: General,Geometry — m759 @ 9:00 pm

(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.

Commentary:

http://www.log24.com/log/pix11/110219-SquareRootQuaternion.jpg

A star figure and the Galois quaternion.

The square root of the former is the latter.

Art as a Tool

Filed under: General,Geometry — Tags: — m759 @ 12:35 pm

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

Filed under: General,Geometry — Tags: — m759 @ 12:00 am

(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

Filed under: General — Tags: — m759 @ 12:00 pm

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)

Perhaps the I Ching ?

The Writing Desk

Filed under: General — Tags: — m759 @ 11:00 am

Why is  a raven like a writing desk?

Sunday, October 19, 2014

Night at the Museum

Filed under: General — m759 @ 9:00 pm

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

Filed under: General — m759 @ 10:00 am

IMAGE- 'The Final Cut,' 2004, at IMDb

“So it’s the laughter we will remember.”  Speak for yourself, Barbra.

Saturday, October 18, 2014

Elementary Galois Geometry

Filed under: General,Geometry — m759 @ 9:29 pm

The image search (2.26 MB).

Educational Series

Filed under: General,Geometry — Tags: , , — m759 @ 1:01 pm

Barron's Educational Series (click to enlarge):

The Tablet of Ahkmenrah:

IMAGE- The Tablet of Ahkmenrah, from 'Night at the Museum'

 "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):

Image-- Rosalind Krauss and The Ninefold Square

Art theorist Rosalind Krauss and The Ninefold Square

IMAGE- Elementary Galois Geometry over GF(3)

Friday, October 17, 2014

Raiders of the Inarticulate

Filed under: General — m759 @ 9:00 pm

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:

IMAGE- Bletchley Park and the Colossus computer

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:

Filed under: General — Tags: , — m759 @ 2:01 pm

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:

Medal of 9/15/06

Backstory:  Posts tagged Root Circle.

Thursday, October 16, 2014

Seeking Kleos

Filed under: General — Tags: — m759 @ 6:22 pm

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:

Rebecca Goldstein and a Cullinane quaternion

From Argument for the Existence of Rebecca (Feb. 6, 2010)

A Forkèd Tongue

Filed under: General — Tags: — m759 @ 5:20 pm

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.

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