Tuesday, May 31, 2016

Galois Space —

Filed under: General,Geometry — Tags: — m759 @ 7:00 PM

A very brief introduction:

Seven is Heaven...

Und Dann …

Filed under: General — m759 @ 5:48 PM

In memory of CBS TV programmer Michael Dann,
who reportedly died at 94 on Friday, May 27 —

Don't Forget Hoss

Judy Carne and Hoss in NBC's "Bonanza,"  a nemesis
of CBS Sunday programming.

In other entertainment news

Cartoonist Frank Modell reportedly died at 98, 
also on Friday, May 27.

In his  memory, part of a Weird Tale from 1948 that is
illustrated (sort of) by a more recent Modell drawing —

Wild Devising

"No one ever found out who the dead man was.
He had no luggage and no identification;
he had been hitchhiking, and he had
over ninety dollars in his pocket.
He might have been anybody—
someone from show business, or a writer perhaps,
on a haywire vacation of his own wild devising.
I suppose that doesn't matter either.
What does matter is that he died while
Grace was in a very close communion
with what he was doing, and her mind was
wide open for his fantasy. …. "

— Theodore Stugeon, "The Perfect Host,"
Weird Tales , November 1948, page 15

Some context:  This morning's post
"Entertainment in Plato's Cave," and
a few titles from my Kindle library —

Entertainment in Plato’s Cave

Filed under: General — m759 @ 9:00 AM

"Plato's allegory of the cave describes prisoners,
inhabiting the cave since childhood, immobile,
facing an interior wall. A large fire burns behind
the prisoners, and as people pass this fire their
shadows are cast upon the cave's wall, and
these shadows of the activity being played out
behind the prisoner become the only version of
reality that the prisoner knows."

From the Occupy Space gallery in Ireland

IMAGE- Patrick McGoohan as 'The Prisoner,' with lapel button that says '6.'

See also the number 6 in yesterday's posts,
Perfect Number and Perfect Universe.

Monday, May 30, 2016

Perfect Universe

Filed under: General,Geometry — Tags: — m759 @ 7:00 PM

(A sequel to the previous post, Perfect Number)

Since antiquity,  six has been known as
"the smallest perfect number." The word "perfect"
here means that a number is the sum of its 
proper divisors — in the case of six: 1, 2, and 3.

The properties of a six-element set (a "6-set") 
divided into three 2-sets and divided into two 3-sets
are those of what Burkard Polster, using the same 
adjective in a different sense, has called 
"the smallest perfect universe" — PG(3,2), the projective
3-dimensional space over the 2-element Galois field.

A Google search for the phrase "smallest perfect universe"
suggests a turnaround in meaning , if not in finance, 
that might please Yahoo CEO Marissa Mayer on her birthday —

The semantic  turnaround here in the meaning  of "perfect"
is accompanied by a model  turnaround in the picture  of PG(3,2) as
Polster's tetrahedral  model is replaced by Cullinane's square  model.

Further background from the previous post —

See also Kirkman's Schoolgirl Problem.

Perfect Number

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

"Ageometretos me eisito."—
"Let no one ignorant of geometry enter."—
Said to be a saying of Plato, part of the
seal of the American Mathematical Society—

For the birthday of Marissa Mayer, who turns 41 today —

VOGUE Magazine,
AUGUST 16, 2013 12:01 AM

"As she works to reverse the fortunes of a failing Silicon Valley
giant, Yahoo’s Marissa Mayer has fueled a national debate
about the office life, motherhood, and what it takes to be the
CEO of the moment.

'I really like even numbers, and
I like heavily divisible numbers.
Twelve is my lucky number—
I just love how divisible it is.
I don’t like odd numbers, and
I really don’t like primes.
When I turned 37,
I put on a strong face, but
I was not looking forward to 37.
But 37 turned out to be a pretty amazing year.
Especially considering that
36 is divisible by twelve!'

A few things may strike you while listening to Marissa Mayer
deliver this riff . . . . "

Yes, they may.

A smaller number for Marissa's meditations:

Six has been known since antiquity as the first "perfect" number.
Why it was so called is of little interest to anyone but historians
of number theory  (a discipline that is not, as Wikipedia notes, 
to be confused with numerology .)

What part geometry , on the other hand, played in Marissa's education,
I do not know.

Here, for what it's worth, is a figure from a review of posts in this journal
on the key role played by the number six in geometry —

Sunday, May 29, 2016

The Ideogram Principle …

Filed under: General,Geometry — Tags: , , — m759 @ 4:23 PM

According to McLuhan

Marshall McLuhan writing to Ezra Pound on Dec. 21, 1948—

"The American mind is not even close to being amenable
to the ideogram principle as yet.  The reason is simply this.
America is 100% 18th Century. The 18th century had
chucked out the principle of metaphor and analogy—
the basic fact that as A is to B so is C to D.  AB:CD.   
It can see AB relations.  But relations in four terms are still
verboten.  This amounts to deep occultation of nearly all
human thought for the U.S.A.

I am trying to devise a way of stating this difficulty as it exists.  
Until stated and publicly recognized for what it is, poetry and
the arts can’t exist in America."

For context, see Cameron McEwen,
"Marshall McLuhan, John Pick, and Gerard Manley Hopkins."
(Renascence , Fall 2011, Vol. 64 Issue 1, 55-76)

A relation in four terms

A : B  ::  C : D   as   Model : Crutch  ::  Metaphor : Ornament —

See also Dueling Formulas and Symmetry.

Sunday School

Filed under: General — Tags: — m759 @ 8:00 AM


Saturday, May 28, 2016

Plan 4

Filed under: General — Tags: , — m759 @ 2:45 AM

See a search in this journal for "As Is."

Friday, May 27, 2016

Plan 9

Filed under: General — m759 @ 9:00 AM


Raiders of the Lost Crucible…

Filed under: General — m759 @ 8:00 AM

Continues .

Number and Time, by Marie-Louise von Franz

For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.

The above passage suggests a meditation on this morning's
New York Times * —

"When shall we three meet again?" — William Shakespeare

“We three have scattered, leaving only me behind
to clean up the scene,” Ms. Yang wrote.
“I am alone, missing us three.” — Amy Qin

Peer Review

Filed under: General — m759 @ 7:00 AM

A review of the phrase "Innermost Kernel" in this journal
suggests the following meditation

"Who am I?" — Existential cry
in "Zoolander" and "Zoolander 2."

A similar question occurs in "Peer Gynt" —

Ben Brantley in yesterday morning's print New York Times *
expressed a nihilistic view of Peer as an onion-peeler —

"Toward the end of Ibsen’s 'Peer Gynt,' a saga of self
under siege, the title character is discovered peeling
an onion, finding in the layers of that humble vegetable
a symbol for the chapters of an eventful life . . . .

[the director’s] approach is the same one that Peer
applies to the onion: Keep stripping until you find the core.
Of course in Peer’s case what is finally found is
plenty of nothing, an apt conclusion for a man
for whom a solid self remains elusive."

I prefer a view from what Fitzgerald called
"the dark fields of the republic" — the Dordt College view —

* The Times — "A version of this review appears in print on May 26, 2016, 
on page C3 of the New York edition with the headline:
'A Saga of Self-Identity, Stripped to Its Core, Still Provokes.' "

Thursday, May 26, 2016


Filed under: General,Geometry — m759 @ 6:40 PM

Images suggested by the previous post

Note the name "Dorje" in the first image above.

Remarks related to the name "Dorje," as well as to
 "Projective Geometry and PT-Symmetric Dirac Hamiltonian,"
a 2009 paper by Y. Jack Ng  and the late Hendrik van Dam —

Dorje C. Brody, 'Consistency of PT-Symmetric Quantum Mechanics'

Remarks for the Church of Synchronology from December 16, 2015,
the date of the above Dorje  arXiv upload —

Expanding the Spielraum

Filed under: General — m759 @ 1:45 AM


The physicist Hendrik van Dam was mentioned in recent posts.

He reportedly died at 78 on February 11, 2013.

A post from that date, and a followup —

Wednesday, May 25, 2016


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

"Studies of spin-½ theories in the framework of projective geometry
have been undertaken before." — Y. Jack Ng  and H. van Dam
February 20, 2009

For one such framework,* see posts from that same date 
four years earlier — February 20, 2005.

* A 4×4 array. See the 19771978, and 1986 versions by 
Steven H. Cullinane,   the 1987 version by R. T. Curtis, and
the 1988 Conway-Sloane version illustrated below —

Cullinane, 1977

IMAGE- Hypercube and 4x4 matrix from the 1976 'Diamond Theory' preprint, as excerpted in 'Computer Graphics and Art'

Cullinane, 1978

Cullinane, 1986

Curtis, 1987

Update of 10:42 PM ET on Sunday, June 19, 2016 —

The above images are precursors to

Conway and Sloane, 1988

Update of 10 AM ET Sept. 16, 2016 — The excerpt from the
1977 "Diamond Theory" article was added above.


Filed under: General — m759 @ 11:30 AM

For the Church of Synchronology

Marissa Mayer, as illustrated on the cover
of the current issue of Variety , and
Mira Sorvino, as discussed in posts of
Feb. 20, 2009 (a date suggested by the
arXiv upload date in the previous post).

Kummer and Dirac

From "Projective Geometry and PT-Symmetric Dirac Hamiltonian,"
Y. Jack Ng  and H. van Dam, 
Physics Letters B , Volume 673, Issue 3,
23 March 2009, Pages 237–239

(http://arxiv.org/abs/0901.2579v2, last revised Feb. 20, 2009)

" Studies of spin-½ theories in the framework of projective geometry
have been undertaken before. See, e.g., Ref. [4]. 1 "

1 These papers are rather mathematical and technical.
The authors of the first two papers discuss the Dirac equation
in terms of the Plucker-Klein correspondence between lines of
a three-dimensional projective space and points of a quadric
in a five-dimensional projective space. The last paper shows
that the Dirac equation bears a certain relation to Kummer’s
surface, viz., the structure of the Dirac ring of matrices is 
related to that of Kummer’s 166 configuration . . . ."


O. Veblen
Proc. Natl. Acad. Sci. USA , 19 (1933), p. 503
Full Text via CrossRef

E.M. Bruins
Proc. Nederl. Akad. Wetensch. , 52 (1949), p. 1135

F.C. Taylor Jr., Master thesis, University of North Carolina
at Chapel Hill (1968), unpublished

A remark of my own on the structure of Kummer’s 166 configuration . . . .

See that structure in this  journal, for instance —

See as well yesterday morning's post.

Nothing Illustrated

Filed under: General — m759 @ 3:33 AM

Illustration by Javier Jaén

See also "Box of Nothing" in this journal.

Tuesday, May 24, 2016

Rosenhain and Göpel Revisited

The authors Taormina and Wendland in the previous post
discussed some mathematics they apparently did not know was
related to a classic 1905 book by R. W. H. T. Hudson, Kummer's
Quartic Surface

"This famous book is a prototype for the possibility
of explaining and exploring a many-faceted topic of
research, without focussing on general definitions,
formal techniques, or even fancy machinery. In this
regard, the book still stands as a highly recommendable,
unparalleled introduction to Kummer surfaces, as a
permanent source of inspiration and, last but not least, 
as an everlasting symbol of mathematical culture."

— Werner Kleinert, Mathematical Reviews ,
     as quoted at Amazon.com

Some 4×4 diagrams from that book are highly relevant to the
discussion by Taormina and Wendland of the 4×4 squares within
the 1974 Miracle Octad Generator of R. T. Curtis that were later,
in 1987, described by Curtis as pictures of the vector 4-space over
the two-element Galois field GF(2).

Hudson did not think of his 4×4 diagrams as illustrating a vector space,
but he did use them to picture certain subsets of the 16 cells in each
diagram that he called Rosenhain and Göpel tetrads .

Some related work of my own (click images for related posts)—

Rosenhain tetrads as 20 of the 35 projective lines in PG(3,2)

IMAGE- Desargues's theorem in light of Galois geometry

Göpel tetrads as 15 of the 35 projective lines in PG(3,2)

Anticommuting Dirac matrices as spreads of projective lines

Related terminology describing the Göpel tetrads above

Ron Shaw on symplectic geometry and a linear complex in PG(3,2)

Monday, May 23, 2016


Filed under: General — m759 @ 10:00 AM

In memory of the late mathematician John Nash
and of the late actor Alan Young ...

A Talking Horse — 

What the horse says: "First online: 28 August 2013."

See also OverarchingPsychonauts, and Spider Tale in this journal.


Filed under: General,Geometry — m759 @ 8:25 AM

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

Keywords: Golay, Mathieu, Steiner system, Carmichael, Harvard

Sunday, May 22, 2016


Filed under: General — m759 @ 7:30 PM

"(CBS News) Two decades after Morley Safer took
a critical look at contemporary art in his 60 Minutes
story  'Yes…But is it Art?'  he has found the definitive
answer to his snide question . . . ."

— March 30, 2012, introduction to a "60 Minutes" piece 
dated April 1, 2012

Sunday School

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

From 'The Politics of Experience,' by R.D. Laing

A less metaphysical approach to a "pre-form" —

From Wallace Stevens, "The Man with the Blue Guitar":


And the color, the overcast blue
Of the air, in which the blue guitar
Is a form, described but difficult,
And I am merely a shadow hunched
Above the arrowy, still strings,
The maker of a thing yet to be made . . . .

"Arrowy, still strings" from the diamond theorem

See also "preforming" and the blue guitar
in a post of May 19, 2010.

Update of 7:11 PM ET:
More generally, see posts tagged May 19 Gestalt.

Saturday, May 21, 2016

Meet the Fitzgeralds

Filed under: General — m759 @ 10:54 PM


Filed under: General — m759 @ 12:00 PM

Related material:  The Lindbergh Manifesto and The Leibniz Medal.

Fitzgerald and Paris

Filed under: General — m759 @ 10:08 AM

The previous post suggests two images

The date of the above Promoted Tweet is October 19, 2015.

For the Church of Synchronology, an image from Log24 on that date:

"So we beat on, boats against the current " — F. Scott Fitzgerald

New Base

Filed under: General — m759 @ 12:48 AM

Three reflections suggested by the previous post

1. A Whit Stillman film mentions favorably Scrooge McDuck —

2. A "promoted tweet" at the Twitter of the previous post's author leads to

3. The above phrase "New Base" suggests a related literary note —

Friday, May 20, 2016

Well Received

Filed under: General — m759 @ 11:25 PM

Steve Almasy, CNN

Updated 10:46 PM ET, Fri., May 20, 2016

" (CNN)  Alan Young, who played the hapless yet protective
owner of a talking horse on the popular television comedy
'Mister Ed,' has died at age 96, according to officials at the
Motion Picture & Television Home in Woodland Hills, California.

He died Thursday of natural causes with his children at his side,
the organization said.

Young also was a well-received voice actor, with appearances
as Scrooge McDuck in many Disney productions . . . ."

[McDuck link added.]

Plan 9 Revival

Filed under: General — m759 @ 12:00 PM

Amy Adams as Amelia Earhart in 'Night at the Museum: Battle of the Smithsonian'

It from Bit*

Filed under: General — m759 @ 11:00 AM

For Galatea 2.2 on Eliza Doolittle Day

My Google searches are set to ignore my own private
search history. Still, I am not sure whether others would
see the same results as those below, which do  seem to
reflect rather closely my own interests.  Google-as-Galatea
perhaps based the search results partly on associations
from this weblog. An exception: the "Family Circus " novel
in the list below. I have not heard of this book before, but
it seems to be a tale analogous to Stephen King's It ,
from which the searched-for quotation below is drawn.

I prefer a different Family Circus.

* A phrase coined by the late John Archibald Wheeler.


Filed under: General — Tags: — m759 @ 2:14 AM

"… Thursday morning at 7:30 a.m. at a hospice
      in Danvers, Massachusetts."

Read more:  http://www.rollingstone.com/music/news/

From a search for Danvers in this journal, two quotations
for Stephen King fans

"Danvers is a town in Essex County, Massachusetts, 
United States, located on the Danvers River near the
northeastern coast of Massachusetts. Originally known
as Salem Village, the town is most widely known for its
association with the 1692 Salem witch trials. It is also
known for the Danvers State Hospital, one of the state's
19th-century psychiatric hospitals, which was located here." 

"The summer's gone and all the roses fallin' "

In a world gone mad it's hard to think right

Read more:  Beastie Boys – In A World Gone Mad Lyrics

Illustrations: Thursday's 3:28 AM ET post and

    (Sketch for a favicon)

Thursday, May 19, 2016

I have seen it, I have seen it!

Filed under: General — Tags: — m759 @ 3:28 AM

The title is a quote from Sir Galahad in
"Monty Python and the Holy Grail."

Immediately following these words

Note also posts on The Hourglass Code .

This  post was suggested by an album cover 
mentioned in tonight's New York Times  story 
on the May 11 death at 73 in London of one
David King , a graphic designer and design historian — 

"For the third Hendrix album, 'Electric Ladyland,'
Mr. King commissioned a photograph of 19
nude women, in various sizes and shapes, which
he intended as a rebuttal to the Playboy image of
women. In the United States, it was regarded as
risqué and was replaced with a head shot of Hendrix."

— William Grimes


Filed under: General,Geometry — m759 @ 2:27 AM

From a check tonight of The New York Review of Books

These NYRB  stories from May 15 and May 13 suggest a
review of images on Ratner's Star  and on the Eye of God.

IMAGE- 'Ratner's Star,' by Don DeLillo (1976)

Above image reposted from Jan. 10, 2014

I. The structures in the Diamond Puzzle

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

Click on image for Jungian background.

II: The structure on a recent cover of Semiotica

'Semiotica' cover and article by Solomon Marcus on Levi-Strauss's 'canonic formula' of myth

Above images reposted from May 5, 2016

Related material:  The previous post, Dueling Formulas.

Wednesday, May 18, 2016

Dueling Formulas

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

Jung's four-diamond formula vs. Levi-Strauss's 'canonical formula'

Note the echo of Jung's formula in the diamond theorem.

An attempt by Lévi-Strauss to defend his  formula —

"… reducing the life of the mind to an abstract game . . . ." —

For a fictional version of such a game, see Das Glasperlenspiel .

Tuesday, May 17, 2016

Death on May Day

Filed under: General — Tags: — m759 @ 2:45 AM

So set 'em up, Joe  . . . .

Bullshit Studies

Filed under: General,Geometry — Tags: , , , — m759 @ 1:06 AM

The originator of the phrase 'Fab Four' reportedly
died at 80 on Saturday, May 14, 2016.

This suggests a review of another noted four-set.

The above image is from a study of Lévi-Strauss's "Canonical Formula"

Midrash —

Log24 post titled 'As Is'

[Above photo of Lévi-Strauss and formula added June 6, 2016.]

Monday, May 16, 2016


Filed under: General — m759 @ 1:06 PM

Click the tweets below for a related news story.

See also this  journal on the same weekend —

Friday, March 11, through Monday, March 14, 2016.

A sample —

From the Wikipedia article Bauhaus (band) —

"On 31 October 2013 (Halloween), 
David J and Jill Tracy released 
'Bela Lugosi's Dead (Undead Is Forever),' 
a cinematic piano-led rework of
'Bela Lugosi's Dead.'"

Fake Religion

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

(A companion-piece to Fake Eliot.)

The President at Rutgers on Sunday

Point number one

When you hear someone longing for the ‘good old days,’
take it with a grain of salt.  (Laughter and applause.)
Take it with a grain of salt.”

Boris Karloff as a modernist architect in a 1934 horror film —

Cum grano salis.

Jew at the Glitter Ball

Filed under: General — m759 @ 12:00 AM

The title refers to Frederick Seidel and
to a post of April 29, "At the Still Point."

Sunday, May 15, 2016

Fake Eliot

Filed under: General — Tags: , — m759 @ 11:30 PM

The New Yorker

Poems | September 3, 2012 issue

House Master


. . . .

“I remember everything.
I remember nothing.
I remember ancient Greek sparkles like a diamond ring.”

. . . .

See also posts now tagged “One Ring
and a search in this journal for “Glitter.”

One Ring

Filed under: General,Geometry — Tags: , — m759 @ 5:06 PM

(Continued from May 11 and May 15.)

Poem by Eleanor Wilner from 'Reversing the Spell' speaks of diamonds and 'glitter.' (Pbk. publ. Nov. 1, 1997)

Quarter to Three

Filed under: General — Tags: , — m759 @ 2:45 PM

Hilary Swank in 'Million Dollar Baby'


The "O.C.D." does not refer to obsessive-
compulsive disorder, but to "Our Class, Dear."


Filed under: General — Tags: , — m759 @ 2:09 AM

A college girl's remarks in the previous post suggested
a search in this journal for "vulgar and stupid."
That search yielded date — March 2, 2014.

In the spirit of the Church of Synchronology, a further search —
for that date — yielded, in a March 2, 2014, post, the following —

Square Dance

From The Telegraph —

And no fact of Alain Resnais’s life seemed to strike a stranger note than his assertion that the films which first inspired his ambition to become a film director were those in which Fred Astaire and Ginger Rogers danced. Or was it Dick Powell and Ruby Keeler? He could never be sure. “I wondered if I could find the equivalent of that exhilaration,” he recalled.

If he never did it was perhaps because of his highly cultivated attitude to serious cinema. His character and temperament were more attuned to the theory of film and a kind of intellectual square dance* which was far harder to bring to the screen with “exhilaration” than the art of Astaire and Rogers.

*See today's 11 AM ET Sermon.

"Heaven, I'm in Heaven!"

The college girl, who reportedly died at 70 on May 11, was
Katherine Dunn, author of the book One Ring Circus  quoted
above. She apparently improved with age.

Saturday, May 14, 2016

Yeah, Art, Beauty

Filed under: General — Tags: , — m759 @ 11:17 PM

From a New York Times  obituary this evening —

"She entered Reed College in Portland as a philosophy major.

'I enjoyed it until I ran aground in an aesthetics class,' 
Ms. Dunn told Wired  magazine. 'I went in thinking, yeah,
art, beauty — my meat, drink and air. But on the first day,
I didn’t understand a word that was said in class, so I
marched out and changed my major to psychology.' "

Could have marched out and bought a dictionary .

The Hourglass Code

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

version of the I Ching’s Hexagram 19:

I Ching Hexagram 19, 'Approach,' the box-style version

From Katherine Neville's The Eight , a book on the significance
of the date April 4 — the author's birthday —

Axe image from Katherine Neville's 'The Eight'

The Eight  by Katherine Neville —

    “What does this have to do with why we’re here?”
    “I saw it in a chess book Mordecai showed me.  The most ancient chess service ever discovered was found at the palace of King Minos on Crete– the place where the famous Labyrinth was built, named after this sacred axe.  The chess service dates to 2000 B.C.  It was made of gold and silver and jewels…. And in the center was carved a labrys.”
… “But I thought chess wasn’t even invented until six or seven hundred A.D.,” I added.  “They always say it came from Persia or India.  How could this Minoan chess service be so old?”
    “Mordecai’s written a lot himself on the history of chess,” said Lily…. “He thinks that chess set in Crete was designed by the same guy who built the Labyrinth– the sculptor Daedalus….”
    Now things were beginning to click into place….
    “Why was this axe carved on the chessboard?” I asked Lily, knowing the answer in my heart before she spoke.  “What did Mordecai say was the connection?”….
    “That’s what it’s all about,” she said quietly.  “To kill the King.”
     The sacred axe was used to kill the King.  The ritual had been the same since the beginning of time. The game of chess was merely a reenactment.  Why hadn’t I recognized it before?

Related material:  Posts now tagged Hourglass Code.

See also the hourglass in a search for Pilgrim's Progress Illustration.

Friday, May 13, 2016

Geometry and Kinematics

Filed under: General,Geometry — Tags: — m759 @ 10:31 PM

"Just as both tragedy and comedy can be written
by using the same letters of the alphabet, the vast
variety of events in this world can be realized by
the same atoms through their different arrangements
and movements. Geometry and kinematics, which
were made possible by the void, proved to be still
more important in some way than pure being."

— Werner Heisenberg in Physics and Philosophy

For more about geometry and kinematics, see (for instance)

"An introduction to line geometry with applications,"
by Helmut Pottmann, Martin Peternell, and Bahram Ravani,
Computer-Aided Design  31 (1999), 3-16.

The concepts of line geometry (null point, null plane, null polarity,
linear complex, Klein quadric, etc.) are also of interest in finite  geometry.
Some small finite spaces have as their natural models arrays of cubes .

The Zorro of Mark

Filed under: General — m759 @ 3:57 PM

(Continued from Code Name Zero .)

Also on May 2, 2014 — Cross Quote .

Code Name Zero

Filed under: General — Tags: — m759 @ 3:09 PM

NY Times  obit for Mark Lane with erroneous book title:

NY Times obit for Mark Lane with erroneous book title

Sounds like a case for Zimbalist.

For the Late Mark Lane

Filed under: General — Tags: — m759 @ 5:01 AM

Sixties conspiracy theorist Mark Lane reportedly
died at 89 on Tuesday night.

From the previous post, But Seriously . . .  —

"Today, we are excited to share the fruits of our research
with the broader community . . . ."

Thursday, May 12, 2016

But Seriously …

Filed under: General — m759 @ 7:31 PM

Google today released on GitHub an English parser,
Parsey McParseface .  From Google Research Blog

"Today, we are excited to share the fruits of our research
with the broader community by releasing SyntaxNet,
an open-source neural network framework implemented in 
TensorFlow that provides a foundation for 
Natural Language Understanding (NLU) systems.
Our release includes all the code needed to train new
SyntaxNet models on your own data, as well as 
Parsey McParseface , an English parser that we have
trained for you and that you can use to analyze English text."

"While the accuracy is not perfect, it’s certainly high enough
to be useful in many applications. The major source of errors
at this point are examples such as the prepositional phrase
attachment ambiguity described above, which require real
world knowledge (e.g. that a street is not likely to be located
in a car) and deep contextual reasoning. Machine learning
(and in particular, neural networks) have made significant
progress in resolving these ambiguities. But our work is still
cut out for us: we would like to develop methods that can
learn world knowledge and enable equal understanding of
natural language across all  languages and contexts."

But seriously

For some historical background, see (for instance) a book by
Ekaterina Ovchinnikova —

Integration of World Knowledge for
Natural Language Understanding
Atlantis Press, Springer, 2012.

A PDF of Chapter 2, "Natural Language Understanding
and World Knowledge," is available for download.

The philosophical background is the distinction between
syntax  and semantics . See (for instance)

Gian-Carlo Rota on Syntax and Semantics

Wednesday, May 11, 2016

Null Point

Filed under: General — Tags: — m759 @ 7:59 PM

This evening's previous post links to an earlier post
on a book by DeLillo.  This suggests a review
of DeLillo's most recent book, Zero K .

A title I prefer: that of this post, Null Point. *
For related mathematics, see Zero System .

Wikipedia — 

The Kelvin scale is an absolute, 
thermodynamic temperature scale 
using as its null point  absolute zero,
the temperature at which
all thermal motion ceases in the
classical description of thermodynamics.

Hear Ye*

Filed under: General — m759 @ 7:31 PM

* Here the "Ye" may be interpreted in light of the "Yi"
   of today's noon post. See also Ratner in this journal.

Jewel of Odin

Filed under: General — m759 @ 1:00 PM

The tesseract in last night's post Game Theory
suggests a search in Log24 for "Jewel of Odin."

See also Trinkets.

By Diction Possessed

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

Continued from Saturday, May 7, 2016 .

From an obituary in yesterday evening's online New York Times —

"I was writing plays, one-acters, about musicians
who were speakers of the idiom I loved most:
black American male speech, full of curse words,"
he wrote in an autobiographical essay. . . .

The obituary is for a poet who reportedly died on Saturday, May 7.

This  journal on that day ("By Diction Possessed") recalled the death
(on Valentine's Day 2015) of an English actor who was the voice of
the Ring in two of the "Lord of the Rings" films —

Backstory from Wikipedia — See Black Speech —

"The only example of 'pure' Black Speech is
the inscription upon the One Ring . . .

One Ring to rule them all,
One Ring to find them,
One Ring to bring them all
And in the darkness bind them. 

Tuesday, May 10, 2016

Game Theory

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

The following passage appeared in this journal
on the night of May 23-24, 2015.

IMAGE- A fictional vision of resurrection within a tesseract

The afternoon  of May 23, 2015, was significant
for devotees of mathematics and narrative.

Monday, May 9, 2016

Requiem for an Authority Figure

Filed under: General — Tags: — m759 @ 2:45 PM

Today's online New York Times  describes an authority
figure who reportedly died on Sunday (May 8, 2016) —

"With his preternaturally mature, intelligent but
(by Hollywood standards) unremarkable looks,
he was cast almost from the beginning as an
authority figure — a father or a teacher, a doctor
or a scientist, a mayor or a judge."

This  journal on Sunday

Manic Monday

Filed under: General — m759 @ 2:00 PM

From the online Harvard Crimson  this afternoon —

"It's just another manic Monday
I wish it was Sunday
'Cause that's my fun day"


Search for the Lost Theorem

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

The three Solomons of the previous post (LeWitt,
Marcus, and Golomb) suggest the three figures
-1, 0, and 1  symbols for the three elements
of the Galois field GF(3).  This in turn suggests a
Search for The Lost Theorem. Some cross-cultural
context:  The First of May, 2010.

Sunday, May 8, 2016

The Three Solomons

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

Earlier posts have dealt with Solomon Marcus and Solomon Golomb,
both of whom died this year — Marcus on Saint Patrick’s Day, and
Golomb on Orthodox Easter Sunday. This suggests a review of
Solomon LeWitt, who died on Catholic Easter Sunday, 2007.

A quote from LeWitt indicates the depth of the word “conceptual”
in his approach to “conceptual art.”

From Sol LeWitt: A Retrospective , edited by Gary Garrels, Yale University Press, 2000, p. 376:

by Sol LeWitt

“The best that can be said for either the square or the cube is that they are relatively uninteresting in themselves. Being basic representations of two- and three-dimensional form, they lack the expressive force of other more interesting forms and shapes. They are standard and universally recognized, no initiation being required of the viewer; it is immediately evident that a square is a square and a cube a cube. Released from the necessity of being significant in themselves, they can be better used as grammatical devices from which the work may proceed.”

Reprinted from Lucy R. Lippard et al ., “Homage to the Square,” Art in America  55, No. 4 (July-August 1967): 54. (LeWitt’s contribution was originally untitled.)”

See also the Cullinane models of some small Galois spaces

Some small Galois spaces (the Cullinane models)


Filed under: General — Tags: , , — m759 @ 10:00 PM

„Ich begriff plötzlich, daß in der Sprache oder doch
mindestens im Geist des Glasperlenspiels tatsächlich
alles allbedeutend sei, daß jedes Symbol und jede
Kombination von Symbolen nicht hierhin oder dorthin,
nicht zu einzelnen Beispielen, Experimenten und
Beweisen führe, sondern ins Zentrum, ins Geheimnis
und Innerste der Welt, in das Urwissen. Jeder Übergang
von Dur zu Moll in einer Sonate, jede Wandlung eines
Mythos oder eines Kultes, jede klassische, künstlerische
Formulierung sei, so erkannte ich im Blitz jenes
Augenblicks, bei echter meditativer Betrachtung,
nichts andres als ein unmittelbarer Weg ins Innere
des Weltgeheimnisses, wo im Hin und Wider zwischen
Ein- und Ausatmen, zwischen Himmel und Erde,
zwischen Yin und Yang sich ewig das Heilige vollzieht.“

— Hermann Hesse, Das Glasperlenspiel .
Berlin:  Suhrkamp Taschenbuch Verlag, 2012, p. 172,
as quoted in a weblog.

"Only connect." — Howards End

Saturday, May 7, 2016

By Diction Possessed

Filed under: General — Tags: , — m759 @ 3:00 PM

Mr. Howard reportedly died on Valentine's Day, 2015.

Friday, May 6, 2016


Filed under: General,Geometry — Tags: — m759 @ 9:48 PM

 Some small Galois spaces (the Cullinane models)

The Old In and Out

Filed under: General — m759 @ 12:00 PM

And the way in is the way out?

By Syndication

Filed under: General — m759 @ 11:30 AM

Thanks to some British computer foul-up, today's Telegraph 's  
"Latest obituaries by syndication" include election results—

ART WARS continues…

Filed under: General — m759 @ 11:00 AM

"Again, in spite of that, we call this Friday good."
— T. S. Eliot, Four Quartets

From this journal on Orthodox Good Friday, 2016,
an image from New Scientist  on St. Andrew's Day, 2015 —

From an old Dick Tracy strip —

See also meditations from this year's un -Orthodox Good Friday
in a Tennessee weblog and in this  journal

" There is a pleasantly discursive treatment 
of Pontius Pilate’s unanswered question
‘What is truth?’ ”

— Coxeter, 1987, introduction to Trudeau’s
     The Non-Euclidean Revolution

Thursday, May 5, 2016

Solomon’s Seal

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

Excerpt from a post of November 4, 2009

I. The structures in the Diamond Puzzle

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

Click on image for Jungian background.

II: The structure on a recent cover of Semiotica

'Semiotica' cover and article by Solomon Marcus on Levi-Strauss's 'canonic formula' of myth

For some related material, see a search 
for Solomon Marcus in this  journal.

Wednesday, May 4, 2016

Walpurgisnacht Death

Filed under: General — m759 @ 10:30 PM

"Kroto is believed to have died on Saturday, April 30.
Responding to the news on Twitter, Prof Brian Cox
tweeted: 'RIP Harry Kroto – brilliant scientist and a
strong, passionate advocate for science as a vital
part of our culture.' — The Guardian

See also Walpurgisnacht 2016 in this  journal.

Update of 10:45 PM — Some related pure  mathematics :

Hail Affleck

Filed under: General — m759 @ 1:00 PM

Random thoughts suggested by the reference in the
previous post to Aegean Park Press and to stencils

"Stencil’s entire existence is focused on the hunt for V.,
a classic novelistic quest-without-resolution (in fact, V.
might be fiction’s greatest example of a MacGuffin). V.
may be a person, or may be a place, though it could
also be neither: Pynchon calls it, at one point,
'a remarkably scattered concept' and, at another,
'the ultimate Plot Which Has No Name.' "

— Alexander Nazaryan in The New Yorker ,
    article dated March 29, 2013

How about a date ?

From this  journal on Good Friday, March 29, 2013

Golomb and Symmetry

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

From the webpage Diamond Theory Bibliography

Golomb, Solomon W. 
Shift register sequences  (Revised edition)
Aegean Park Press, Laguna Hills, CA, 1982
   The fifteen "stencils" in Golomb's Fig. VIII-8, page 219,
   are the same as the fifteen affine hyperplanes that
   account for patterns' symmetry in diamond theory.
   This figure occurs in a discussion of Rademacher-
   Walsh functions.


Solomon Golomb, 1932-2016

Filed under: General,Geometry — m759 @ 4:00 AM

Material related to the previous post, "Symmetry" —

This is the group of "8 rigid motions
generated by reflections in midplanes"
of "Solomon's Cube."

Material from this journal on May 1, the date of Golomb's death —

"Weitere Informationen zu diesem Themenkreis
finden sich unter http://​www.​encyclopediaofma​th.​org/
http://​finitegeometry.​org/​sc/​gen/​coord.​html ."

Tuesday, May 3, 2016


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

A note related to the diamond theorem and to the site
Finite Geometry of the Square and Cube —

The last link in the previous post leads to a post of last October whose
final link leads, in turn, to a 2009 post titled Summa Mythologica .

Webpage demonstrating symmetries of 'Solomon's Cube'

Some may view the above web page as illustrating the
Glasperlenspiel  passage quoted here in Summa Mythologica 

“”I suddenly realized that in the language, or at any rate
in the spirit of the Glass Bead Game, everything actually
was all-meaningful, that every symbol and combination of
symbols led not hither and yon, not to single examples,
experiments, and proofs, but into the center, the mystery
and innermost heart of the world, into primal knowledge.
Every transition from major to minor in a sonata, every
transformation of a myth or a religious cult, every classical
or artistic formulation was, I realized in that flashing moment,
if seen with a truly meditative mind, nothing but a direct route
into the interior of the cosmic mystery, where in the alternation
between inhaling and exhaling, between heaven and earth,
between Yin and Yang, holiness is forever being created.”

A less poetic meditation on the above web page* —

“I saw that in the alternation between front and back,
between top and bottom, between left and right,
symmetry is forever being created.”

Update of Sept. 5, 2016 — See also a related remark
by Lévi-Strauss in 1955: “…three different readings
become possible: left to right, top to bottom, front
to back.”

* For the underlying mathematics, see a June 21, 1983, research note.

Monday, May 2, 2016


Filed under: General,Geometry — Tags: , — m759 @ 3:48 PM

The previous post, on subjective  and objective  quality,
suggests a review of Pirsig

     “And finally: Phaedrus, following a path
that to his knowledge had never been taken before
in the history of Western thought,
went straight between the horns of
the subjectivity-objectivity dilemma and said
Quality is neither a part of mind, nor is it a part of matter.
It is a third  entity which is independent of the two.
He was heard along the corridors
and up and down the stairs of Montana Hall
singing softly to himself, almost under his breath,
‘Holy, holy, holy…blessed Trinity.’ “

See also Guitart in this journal, noting esp. Zen and the Art.

Subjective Quality

Filed under: General,Geometry — m759 @ 6:01 AM

The previous post deals in part with a figure from the 1988 book
Sphere Packings, Lattices and Groups , by J. H. Conway and
N. J. A. Sloane.

Siobhan Roberts recently wrote a book about the first of these
authors, Conway.  I just discovered that last fall she also had an
article about the second author, Sloane, published:

"How to Build a Search Engine for Mathematics,"
Nautilus , Oct 22, 2015.

Meanwhile, in this  journal

Log24 on that same date, Oct. 22, 2015 —

Roberts's remarks on Conway and later on Sloane are perhaps
examples of subjective  quality, as opposed to the objective  quality
sought, if not found, by Alexander, and exemplified by the
above bijection discussed here  last October.

Sunday, May 1, 2016

Sunday Appetizer from 1984

Filed under: General,Geometry — Tags: — m759 @ 2:00 PM

Judith Shulevitz in The New York Times
on Sunday, July 18, 2010
(quoted here Aug. 15, 2010) —

“What would an organic Christian Sabbath look like today?”

The 2015 German edition of Beautiful Mathematics ,
a 2011 Mathematical Association of America (MAA) book,
was retitled Mathematische Appetithäppchen —
Mathematical Appetizers . The German edition mentions
the author's source, omitted in the original American edition,
for his section 5.17, "A Group of Operations" (in German,
5.17, "Eine Gruppe von Operationen") —  

Mathematische Appetithäppchen:
Faszinierende Bilder. Packende Formeln. Reizvolle Sätze

Autor: Erickson, Martin —

"Weitere Informationen zu diesem Themenkreis finden sich
unter http://​www.​encyclopediaofma​th.​org/​index.​php/​
und http://​finitegeometry.​org/​sc/​gen/​coord.​html ."

That source was a document that has been on the Web
since 2002. The document was submitted to the MAA
in 1984 but was rejected. The German edition omits the
document's title, and describes it as merely a source for
"further information on this subject area."

The title of the document, "Binary Coordinate Systems,"
is highly relevant to figure 11.16c on page 312 of a book
published four years after the document was written: the 
1988 first edition of Sphere Packings, Lattices and Groups
by J. H. Conway and N. J. A. Sloane —

A passage from the 1984 document —

In Other News…

Filed under: General — m759 @ 5:14 AM

A check of this morning's newsfeed suggests 
a search in this journal for America + Welcome
in memory of Daniel Berrigan.


Filed under: General — m759 @ 4:17 AM

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