Tuesday, March 31, 2015

Flame Diary

Filed under: General — m759 @ 1:00 PM

Last Saturday's post Against Dryness quoted "Gone Girl,"
a recent film about an untypical couple. 

Other works of interest:

The Flame Alphabet  (Ben Marcus, 2012) and
The Folded Clock  (Heidi Julavits, 2015).

Marcus and Julavits are husband and wife. As in
"Gone Girl," both are very bright, and the wife
writes a diary. (No other resemblance between
the couples is apparent.)

Update of 6:40 PM ET March 31:

A 1983 review by the parents of Ben Marcus —

Update of 7:09 PM March 31:


Filed under: General — Tags: , — m759 @ 12:00 PM

See also Würfel in this journal.

Sunday, March 29, 2015

Mathematics for Jews*

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

Headline at the Toronto Star  on Friday, March 27, 2015:

Robert Langlands: The Canadian
who reinvented mathematics

“He’s like a modern-day Einstein.”

Apparently, unlike God, Langlands würfelt .

* See also Blockheads  in this journal.

Death in East Hampton

Filed under: General — Tags: — m759 @ 1:28 PM

See also Deathtrap in this journal.

Saturday, March 28, 2015

Against Dryness

Filed under: General — Tags: — m759 @ 3:24 PM


"July 5, 2012, begins normally enough —
Ben Affleck’s character goes for a drink
at the bar he co-owns with his hilariously
sarcastic twin sister Margo …."

Margo Dunne: Well, the Irish prince graces us
with his presence. [she flicks water in his face]
Nick Dunne: His majesty prefers not to be moistened.

Margo and Nick go on to discuss what Nick should get
his wife as a fifth ("wood") anniversary present.

One possibility, from the German website EinsteinSpiele.de —

(Suggested by the word Legespiel  in yesterday's link Tribute.)

See also the above date — July 5, 2012 — in this journal.

The Esthetic Question

Filed under: General — m759 @ 4:00 AM

From James Joyce's  A Portrait of the Artist as a Young Man —

As he came back to the hearth, limping slightly but with a brisk step, Stephen saw the silent soul of a jesuit look out at him from the pale loveless eyes. Like Ignatius he was lame but in his eyes burned no spark of Ignatius’s enthusiasm. Even the legendary craft of the company, a craft subtler and more secret than its fabled books of secret subtle wisdom, had not fired his soul with the energy of apostleship. It seemed as if he used the shifts and lore and cunning of the world, as bidden to do, for the greater glory of God, without joy in their handling or hatred of that in them which was evil but turning them, with a firm gesture of obedience, back upon themselves: and for all this silent service it seemed as if he loved not at all the master and little, if at all, the ends he served. Similiter atque senis baculushe was, as the founder would have had him, like a staff in an old man’s hand, to be leaned on in the road at nightfall or in stress of weather, to lie with a lady’s nosegay on a garden seat, to be raised in menace.

The dean returned to the hearth and began to stroke his chin.

— When may we expect to have something from you on the esthetic question? — he asked.

Friday, March 27, 2015


Filed under: General — m759 @ 11:32 PM

IMAGE- On awakening, a wife sees her husband's cane.

See also the previous post on "spare yet evocative imagery."


Filed under: General — m759 @ 10:32 PM

See also Sequel, Lumet's "a full half-hour" and Tribute.

The Prequel

Filed under: General — m759 @ 9:00 PM

The McEvoy Rite

Filed under: General — m759 @ 8:00 PM

Nan Tucker McEvoy, last of founding family
to run Chronicle, dies

By Sam Whiting at SFGate.com, Friday, March 27, 2015 

From the story —

"After graduating from Dominican Convent Upper School 
in San Rafael in 1937, she was discouraged from attending college
by family members who wanted her to be a socialite."

Related material —

A school, a tweet, and a post.

Pursuit of Gestalt*

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

The art above is by the Copenhagen studio
Hvass & Hannibal. For a photo of the artists,
see a webpage on Beijing Design Week 2011.

Hvass and Hannibal were apparently in Beijing
for the "open workshop," Sept. 17-23, 2011.

Gestalt-related material from this journal that week —

* Title suggested by that of a book by Quine.

Thursday, March 26, 2015

When Death Tells a Story…

Filed under: General — m759 @ 1:21 AM

See the title phrase and "working backward" in this journal.

The Möbius Hypercube

Filed under: General,Geometry — Tags: , — m759 @ 12:31 AM

The incidences of points and planes in the
Möbius 8 configuration (8 points and 8 planes,
with 4 points on each plane and 4 planes on each point),
were described by Coxeter in a 1950 paper.* 
A table from Monday's post summarizes Coxeter's
remarks, which described the incidences in
spatial terms, with the points and planes as the vertices
and face-planes of two mutually inscribed tetrahedra —

Monday's post, "Gallucci's Möbius Configuration,"
may not be completely intelligible unless one notices
that Coxeter has drawn some of the intersections in his 
Fig. 24, a schematic representation of the point-plane
incidences, as dotless, and some as hollow dots.  The figure,
"Gallucci's version of Möbius's 84," is shown below.
The hollow dots, representing the 8 points  (as opposed
to the 8 planes ) of the configuration, are highlighted in blue.

Here a plane  (represented by a dotless intersection) contains
the four points  that are represented in the square array as lying
in the same row or same column as the plane. 

The above Möbius incidences appear also much earlier in
Coxeter's paper, in figures 6 and 5, where they are shown
as describing the structure of a hypercube. 

In figures 6 and 5, the dotless intersections representing
planes have been replaced by solid dots. The hollow dots
have again been highlighted in blue.

Figures 6 and 5 demonstrate the fact that adjacency in the set of
16 vertices of a hypercube is isomorphic to adjacency in the set
of 16 subsquares of a square 4×4 array, provided that opposite
sides of the array are identified, as in Fig. 6. The digits in 
Coxeter's labels above may be viewed as naming the positions 
of the 1's in (0,1) vectors (x4, x3, x2, x1) over the two-element
Galois field.  In that context, the 4×4 array may be called, instead
of a Möbius hypercube , a Galois tesseract .

*  "Self-Dual Configurations and Regular Graphs," 
    Bulletin of the American Mathematical Society,
    Vol. 56 (1950), pp. 413-455

The subscripts' usual 1-2-3-4 order is reversed as a reminder
    that such a vector may be viewed as labeling a binary number 
    from 0  through 15, or alternately as labeling a polynomial in
    the 16-element Galois field GF(24).  See the Log24 post
     Vector Addition in a Finite Field (Jan. 5, 2013).

Tuesday, March 24, 2015


Filed under: General,Geometry — m759 @ 1:00 PM

(Continued from July 16, 2014.)

Some background from Wikipedia:

"Friedrich Ernst Peter Hirzebruch  ForMemRS[2] 
(17 October 1927 – 27 May 2012)
was a 
German mathematician, working in the fields of topology
complex manifolds and algebraic geometry, and a leading figure
in his generation. He has been described as 'the most important
mathematician in Germany of the postwar period.'


A search for citations of the A. E. Brouwer paper in
the previous post yields a quotation from the preface
to the third ("2013") edition of Wolfgang Ebeling's
Lattices and Codes: A Course Partially Based
on Lectures by Friedrich Hirzebruch
, a book
reportedly published on September 19, 2012 —

"Sadly, on May 27 this year, Friedrich Hirzebruch,
on whose lectures this book is partially based,
passed away. I would like to express my gratitude
and my admiration by dedicating this book
to his memory.

Hannover, July 2012               Wolfgang Ebeling "

(Prof. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry,
Leibniz Universität Hannover, Germany)

Also sadly

Brouwer on the Galois Tesseract

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

Yesterday's post suggests a review of the following —

Andries Brouwer, preprint, 1982:

"The Witt designs, Golay codes and Mathieu groups"
(unpublished as of 2013)

Pages 8-9:

Substructures of S(5, 8, 24)

An octad is a block of S(5, 8, 24).

Theorem 5.1

Let B0 be a fixed octad. The 30 octads disjoint from B0
form a self-complementary 3-(16,8,3) design, namely 

the design of the points and affine hyperplanes in AG(4, 2),
the 4-dimensional affine space over F2.


… (iv) We have AG(4, 2).

(Proof: invoke your favorite characterization of AG(4, 2) 
or PG(3, 2), say 
Dembowski-Wagner or Veblen & Young. 

An explicit construction of the vector space is also easy….)

Related material:  Posts tagged Priority.

Monday, March 23, 2015

Gallucci’s Möbius Configuration

Filed under: General,Geometry — Tags: — m759 @ 12:05 PM

From H. S. M. Coxeter's 1950 paper
"Self-Dual Configurations and Regular Graphs," 
a 4×4 array and a more perspicuous rearrangement—

(Click image to enlarge.) 

The above rearrangement brings Coxeter's remarks into accord
with the webpage The Galois Tesseract.

Update of Thursday, March 26, 2015 —

For an explanation of Coxeter's Fig. 24, see Thursday's later
post titled "The Möbius Hypercube."

Sunday, March 22, 2015


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

In memory of a film enthusiast who reportedly
died on February 23, 2015:

"We wanted the film to go through a very subtle
and nuanced visual metamorphosis." 

— Nenad Cicin-Sain on The Time Being

See also February 23, 2015 in this journal.

The Forking (continued)

Filed under: General — Tags: , , — m759 @ 12:18 PM

IMAGE- Definition of 'forking' at GitHub

A film —

A weblog post —

Friday, March 20, 2015

The Forking

Filed under: General — m759 @ 10:02 PM


An article in the new April issue of Notices of the American
Mathmatical Society 
suggests a search for connections
between the Calkin-Wilf tree and the modular group.

The search yields, for instance (in chronological order)

"Cutting sequences for geodesic flow on the modular surface
and continued fractions
," David J. Grahinet, Jeffrey C. Lagaria,
arXiv, 2 April 2001

"Orderings of the rationals and dynamical systems,"
Claudio Bonanno, Stefano Isola, arXiv, 14 May 2008.

"Periods of negative-regular continued fractions. Rational numbers."
Sergey Khrushchev and Michael Tyaglov, slides PDF, 11 Sept. 2012

"The Minkowski ?(x) function, a class of singular measures,
theta-constants, and mean-modular forms
," Giedrius Alkauskas,
arXiv, 20 Sept. 2012

"Forests of complex numbers,"
Melvyn B. Nathanson, arXiv, 1 Dec. 2014

Update of March 21, 2015:

For many more related papers, search by combining the
phrase "modular group" with phrases denoting forking structures
other than Calkin-Wilf, such as "cubic tree," "Stern-Brocot tree,"
and "Farey tree" (or "Farey sequence" or "Farey series" or
"Farey graph" ).


Filed under: General — Tags: — m759 @ 2:48 PM

Compare and contrast yesterday's quotation from Jeffrey Kipnis
with the following quotation from Robert Bringhurst —

Related material — Jews on Style.

Thursday, March 19, 2015

“Divisive Rhetoric”

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

I Ching hexagram 14, box style

An example for 'Jews on Style'- Kipnis on the separatrix

     — Jeffrey Kipnis, "Twisting the Separatrix"
     Assemblage  No. 14 (Apr., 1991), pp. 30-61
     Published by: The MIT Press
     Article Stable URL: http://www.jstor.org/stable/3171098

Midnight in the Garden continues…

Filed under: General — m759 @ 12:00 AM

See also Icon and a fresh New York Times  obituary.

Happy birthday to Jill Abramson.

Wednesday, March 18, 2015

Natural History

Filed under: General — m759 @ 10:10 PM

Copyrighted images, intended only for scholarly personal use.

See also Witch Ball and City of Bones .

Logo Design

Filed under: General — m759 @ 9:11 PM

See also today's previous post and Cartoon Graveyard.

Burning Bright

Filed under: General — m759 @ 2:01 PM

For Mark Steinberg, sports agent .

From Field Notes (9:29 AM ET Saturday, Nov. 28, 2009) —

Elements of Story, by Francis Flaherty

From the heraldic crest of Steinberg's fraternity :

"Remember me to Herald Square."

Play Is Not Playing Around

Filed under: General — m759 @ 1:00 PM

(A saying of Friedrich Fröbel)

See also the previous two posts,      
        Dude!  and Focus! .

Tuesday, March 17, 2015


Filed under: General,Geometry — Tags: , , — m759 @ 11:30 AM

A sequel to Dude!

See also "Triangles are Square."

Monday, March 16, 2015


Filed under: General — Tags: , — m759 @ 1:26 PM

Twelve years ago on this date —

Sunday, March 15, 2015

Nicht Spielerei

Filed under: General — m759 @ 1:00 AM


See Brian Sutton-Smith in today's New York Times
obituaries and Jerome Kagan in this journal.

See also a post from March 7, 2015, the reported
date of Sutton-Smith's death.

Saturday, March 14, 2015

Unicode Diamonds

Filed under: General,Geometry — m759 @ 9:16 PM

The following figure, intended to display as
a black diamond, was produced with
HTML and Unicode characters. Depending
on the technology used to view it, the figure
may contain gaps or overlaps.


Some variations:





Such combined Unicode characters —

◢  black lower right triangle,
◣  black lower left triangle,
᭘  black upper left triangle,
᭙  black upper right triangle 

— might be used for a text-only version of the Diamond 16 Puzzle
that is more easily programmed than the current version.

The tricky part would be coding the letter-spacing and
line-height to avoid gaps or overlaps within the figures in
a variety of browsers. The w3.org visual formatting model
may or may not be helpful here.

Update of 11:20 PM ET March 15, 2015 — 
Seekers of simplicity should note that there is
a simple program in the Processing.js  language, not  using
such Unicode characters, that shows many random affine
permutations of a 4×4 diamond-theorem array when the
display window is clicked.

Eating Club

Filed under: General — m759 @ 1:06 PM

From Wikipedia's Eating Clubs at Princeton University —

"Princeton's eating clubs are the primary setting in 
F. Scott Fitzgerald's 1920 debut novel, This Side of Paradise ,
and more recently, the clubs appeared prominently in the
2004 novel, The Rule of Four . In her most recent novel, 
The Accursed , Joyce Carol Oates repeatedly refers to the
Eating Clubs …."

See as well Eating Club  in this journal.

Introduction to Yau

Filed under: General — m759 @ 12:00 PM

Home page of Doctor Yau

This is related somewhat distantly to Mathieu moonshine.

Friday, March 13, 2015

Good Vibrations

Filed under: General — m759 @ 10:16 PM

Springtime for Princeton  continues

Springtime for Princeton

Filed under: General — m759 @ 5:01 PM

Mathieu Moonshine

Filed under: General — m759 @ 1:26 PM

(Continued from yesterday's "earlier references" link.)

Yesterday at the Simons Foundation's Quanta Magazine :

See also earlier Log24 references to Mathieu moonshine .
I do not know the origin of this succinct phrase, taken from
an undated web page of Anne Taormina.

Stranger than Dreams

Filed under: General — m759 @ 10:33 AM


For further details, see USA Today.

Thursday, March 12, 2015

For Stephen King

Filed under: General — Tags: — m759 @ 3:12 PM

Doctor Steam

"Everybody's doin'
a brand new dance now…"

     "A corpse will be
transported by express!"
Under the Volcano

Overarching Symmetry*

Filed under: General — m759 @ 6:29 AM

for fans of the late C. P. Snow

* See earlier references here to that phrase.

Wednesday, March 11, 2015

World Time

Filed under: General — m759 @ 1:46 AM

1:46 AM March 11, 2015 EDT
(Eastern Daylight Time in USA) is
5:46 AM March 11, 2015 UTC
(Coordinated Universal Time worldwide).

"On March 11, 2011 at 5:46 a.m.
Coordinated Universal Time (UTC),
a magnitude 8.9 earthquake occurred
off the East Coast of Japan…."

Tuesday, March 10, 2015


Filed under: General — Tags: — m759 @ 9:14 PM

Backstory for the "Surf's Up!" in the previous post:

"A Dante for Our Times," Part I and Part II.

An Obit for Dooley

Filed under: General — Tags: — m759 @ 2:48 PM

Related material:

According to Emory University, Sitton
"graduated from Emory in 1949, where he served as
editor in chief of the Emory Wheel. Sitton returned to
Emory to teach from 1991 to 1994, served as a
member of the Board of Counselors of Emory's
Oxford College from 1993 to 2001, and was
instrumental in establishing Emory's journalism
program in the mid-1990s." 

See as well an Emory mascot:

The Big Screw

Filed under: General — Tags: , — m759 @ 12:00 PM

"… sometimes the best path to short-term goals
is through the unplanned byways of
the long-term perspective."
Harvard President Drew Faust

For one such byway, see the bottom line 
of the image search in Monday's post.

Literary Notes

Filed under: General — Tags: , , — m759 @ 12:00 AM

From an interview by Glen Duncan with author
Susanna Moore published on January 29, 2013 —

When did you first realize that you wanted to write fiction? Was there an epiphanic moment?

I was a voracious reader as a child, clearing out the local library (my mother had given me a letter for the librarian, attesting that the books that I borrowed were for her reading alone), and I began to write plays, usually starring myself, when I was 9 or 10. There were years of bad poetry. I was features editor of the Punahou school newspaper. But at no moment did I clearly decide that I was going to be a writer, nor did it feel as if I had always been one. I left home for the mainland (I grew up in Hawaii) when I was 17 with no money or education beyond Punahou and the books that I’d read, and knew that I had to earn my living. I had a fantasy that I’d be a reporter and was sent by an equally naïve friend to Walter Annenberg, the owner of The Philadelphia Inquirer , who promptly sent me to the classified ad room, where I became an ad-taker. I’ve always thought that it was very good training: A man would call to place an ad in the hope of selling his used bed, and I would have to write a convincing few sentences on his behalf. I later read scripts for Jack Nicholson and oddly enough had to do the same thing – condense a complicated proposal into a statement of a dozen words.

We’ve talked before about how feeling different from the people around us – “mutant” was the word you used – informs or underpins the burgeoning writer’s mentality. Could you expand on that?

By mutant, I mean that state in childhood and adolescence of isolation, sometimes blissful, often bewildering, when you realize that you have little in common with the people closest to you – not because you are superior in intelligence or sensitivity, but because you perceive the world in an utterly different way, which you assume to be a failing on your part. It was only through reading and discovering characters who shared that feeling that I realized when I was about 14 that I wasn’t insane. And yes, I think that the sensation, the awareness and then the conviction that your perception of the world is not what might be called conventional, is essential to the making of an artist. It is a little like speaking a different language from the people around you – it affords you solitude, but it also means that you are sometimes misunderstood.

Related material:

Midnight Politics,  X-Woman,  "Welcome to Me,"  and
the following meditation on the word "binder"—

Monday, March 9, 2015

Philosophy of Jurisprudence

Filed under: General — Tags: — m759 @ 3:11 PM

"Program or Be Programmed:
Ten Commands for a Digital Age"

— Title of a book by Douglas Rushkoff, quoted here on Jan. 18, 2015

"Cultural Software: 
A Theory of Ideology"

— Title of a book by Yale Law School professor J. M. Balkin

Related image search:

See as well some related Bible verses.

Saturday, March 7, 2015

Film and Phenomenology

Filed under: General,Geometry — m759 @ 1:18 PM

Continued from All Hallows' Eve, 2014.

Last year's Halloween post displayed the
Dürer print Knight, Death, and the Devil 
(illustrated below on the cover of the book
Film and Phenomenology  by Allan Casebier).

Cover illustration: Durer's 'Knight, Death, and the Devil'

Cover illustration: Knight, Death, and the Devil
by Albrecht Dürer

Some mathematics related to a different Dürer print —

Friday, March 6, 2015

Cinéma Vérité

Filed under: General — m759 @ 7:11 PM

Three Colorful Tales —

See also the recent film Nightcrawler .

Thursday, March 5, 2015

Purim Play for St. Paul’s

Filed under: General — m759 @ 2:45 PM

"The study of the diverse ways in which
people of different cultures approach problems
provides students with a more comprehensive
understanding of topics introduced in previous courses."

From today's diplomatic news:


Log24 posts tagged Frenkel-Metaphors, as well as
For Turing's Cathedral and Philadelphia Story.

Wednesday, March 4, 2015

Frenkel’s Rashomon

Filed under: General — Tags: — m759 @ 2:02 PM

Tuesday, March 3, 2015

Blues View

Filed under: General — m759 @ 9:00 AM

End of the Line Blues

IMAGE- YouTube statistics: 384 views, 3 thumbs up, 0 down.

A film with a related title had a limited
USA theatrical release on Feb. 27, 2015.

See also some New Yorker  theology .

Monday, March 2, 2015

For Turing’s Cathedral

Filed under: General — m759 @ 10:30 PM

Item from the British press on Oct. 17, 2014:

Item from this journal on that same date:

Raiders of the Inarticulate.

A related "slash" —

Elementary, my dear Watson.

High Concepts of Space

Filed under: General — m759 @ 3:05 PM

Related material:

Agents of a Great Despair and A Kirk for Spock —

Shades of Grey (1949)

Filed under: General — m759 @ 9:45 AM

Or:  Elements of Design  Continued

"Show me all  the blueprints."

Elements of Design

Filed under: General — m759 @ 1:28 AM

From "How the Guggenheim Got Its Visual Identity,"
by Caitlin Dover, November 4, 2013 —

For the square and half-square in the above logo
as independent design elements, see 
the Cullinane diamond theorem.

For the circle and half-circle in the logo,
see Art Wars (July 22, 2012).

For a rectangular space that embodies the name of
the logo's design firm 2×4, see Octad in this journal.

Sunday, March 1, 2015

Sunday School

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

The previous post suggests a review of
the phrase "strange loop" in this journal.

The Knight's Move, by Loder and Neidhardt

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