Saturday, April 30, 2016

A Lucifer for Walpurgisnacht

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

A politician as 'Lucifer in the flesh'

A more impressive Lucifer —

The late theoretical physicist John Archibald Wheeler,
author of the phrase "it from bit."

Related material —

"The Thing and I" (April 17, 2016) and an essay by
Julian Barbour, "Bit from It."

Bit by Bit

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

In memory of Claude Shannon, who would have turned 100 today.

See "The Matthias Defense" and citations of that page in this journal.

Friday, April 29, 2016

At the Still Point …

Filed under: General — m759 @ 10:00 PM


"OK Baby, let's go dancing."
— Amy Adams in "American Hustle"

Click image below for some backstory.

Happy birthday to Uma Thurman.

Blackboard Jungle…

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

Continues .

An older and wiser James Spader —

"Never underestimate the power of glitter."

Glitter by Josefine Lyche, as of diamond dust

Thursday, April 28, 2016

Kubrick’s Rube

Filed under: General — m759 @ 11:16 AM

(Continued from 9:23 PM ET yesterday)

For the rube himself, see the previous post.

Or a Martian?

Filed under: General — m759 @ 10:00 AM

See also Cruz and the Coeur d'Alene Manifesto

Wednesday, April 27, 2016


Filed under: General — m759 @ 10:16 PM

For those who prefer "Hamilton" to Hamilton

"You've got the look
You've got the hook
You sho' nuf do be cookin' in my book
Your face is jammin' …."

Happy birthday.

Kubrick’s Rube

Filed under: General — m759 @ 9:23 PM

In memory of a culture jammer *—

* "Mr. Lyons … made a living partly by buying,
reconditioning and selling used cars." —
— Ben Ratliff in The New York Times  this evening.

See also the previous post and, from Feb. 14 in
this  journal, the phrase "more global than local."

Local and Global

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

Three notes on local symmetries
that induce global symmetries

From July 1, 2011

Interplay of local symmetry with global symmetry

From November 5, 1981

Local symmetry groups induce global symmetry groups

From December 24, 1981

Local symmetry groups induce global symmetry groups

Tuesday, April 26, 2016

A Sense of Identity

Filed under: General,Geometry — m759 @ 9:01 PM

Peter Schjeldahl on Wallace Stevens in the current New Yorker

"Stevens was born in 1879 in Reading, Pennsylvania,
the second of five children. His father, from humble
beginnings, was a successful lawyer, his mother a
former schoolteacher. Each night, she read a chapter
of the Bible to the children, who attended schools
attached to both Presbyterian and Lutheran churches,
where the music left an indelible impression on Stevens.
Both sides of the family were Pennsylvania Dutch,
an identity that meant little to him when he was young
but a great deal later on, perhaps to shore up a precarious
sense of identity."

See also this  journal on Christmas Day, 2010


It's a start. For more advanced remarks from the same date, see Mere Geometry.


Filed under: General,Geometry — m759 @ 8:31 PM

"… I would drop the keystone into my arch …."

— Charles Sanders Peirce, "On Phenomenology"

" 'But which is the stone that supports the bridge?' Kublai Khan asks."

— Italo Calvino, Invisible Cities, as quoted by B. Elan Dresher.

(B. Elan Dresher. Nordlyd  41.2 (2014): 165-181,
special issue on Features edited by Martin Krämer,
Sandra Ronai and Peter Svenonius. University of Tromsø –
The Arctic University of Norway.

Peter Svenonius and Martin Krämer, introduction to the
Nordlyd  double issue on Features —

"Interacting with these questions about the 'geometric' 
relations among features is the algebraic structure
of the features."

For another such interaction, see the previous post.

This  post may be viewed as a commentary on a remark in Wikipedia

"All of these ideas speak to the crux of Plato's Problem…."

See also The Diamond Theorem at Tromsø and Mere Geometry.

Monday, April 25, 2016

Seven Seals

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

 An old version of the Wikipedia article "Group theory"
(pictured in the previous post) —

"More poetically "

From Hermann Weyl's 1952 classic Symmetry

"Galois' ideas, which for several decades remained
a book with seven seals  but later exerted a more
and more profound influence upon the whole
development of mathematics, are contained in
a farewell letter written to a friend on the eve of
his death, which he met in a silly duel at the age of
twenty-one. This letter, if judged by the novelty and
profundity of ideas it contains, is perhaps the most
substantial piece of writing in the whole literature
of mankind."

The seven seals from the previous post, with some context —

These models of projective points are drawn from the underlying
structure described (in the 4×4 case) as part of the proof of the
Cullinane diamond theorem .

Peirce’s Accounts of the Universe

Filed under: General,Geometry — Tags: , — m759 @ 8:19 PM

Compare and contrast Peirce's seven systems of metaphysics with
the seven projective points in a post of March 1, 2010 —

Wikipedia article 'Group theory' with Rubik Cube and quote from Nathan Carter-- 'What is symmetry?'

From my commentary on Carter's question —

Labelings of the eightfold cube

Sunday, April 24, 2016

Prima Materia as Cubes

Filed under: General — m759 @ 4:04 AM

Saturday, April 23, 2016

What Mad Pursuit

Filed under: General — m759 @ 9:00 AM

Quine, Pursuit of Truth , Harvard
University Press, 1990,  epigraphs:


For another quote from Sherwin-Williams,
see the April 21 post  Purple Requiem.


Filed under: General — m759 @ 7:59 AM

"I could a tale unfold "

Friday, April 22, 2016


Filed under: General — m759 @ 12:26 PM

The prominent display of an ad for Elixir Vitae in
today's 11:02 AM post suggests a review of that concept.

See also Raiders of the Lost Crucible in this journal.

In Memoriam

Filed under: General — m759 @ 11:30 AM

Guy Hamilton, director of "Diamonds are Forever" 
and "Goldfinger," reportedly died at 93 on Wednesday, 
April 20, 2016. In his memory, here is a link to the
posts of All Souls' Day, 2015.

Vanity Fair Continues

Filed under: General — m759 @ 11:02 AM

Detail of illustration by Frederick Alfred Rhead of Vanity Fair,
page 96 in the John Bunyan classic Pilgrim's Progress 
(New York, The Century Co., 1912)

Yesterday's posts Legend and Purple Requiem suggest a review
of John Bunyan.  A search for "Vanity Fair" + "Temple of Art" yields

The above Vanity Fair  article was linked to here previously.

Thursday, April 21, 2016

Purple Requiem

Filed under: General — m759 @ 9:07 PM

Excerpt, Ch. 11 of 'The Stars My Destination,' by Alfred Bester

See as well "The Stars My Destination" in this journal.


Filed under: General — m759 @ 2:00 PM

See also White Mischief (Feb. 23, 2016).

The Alchemist’s Chessboard

Filed under: General,Geometry — m759 @ 12:25 PM

Material related to the previous post and to Alfred Bester's
1981 followup to The Stars My Destination  titled The Deceivers

The Lapis Philosophorum :

"The lapis  was thought of as a unity and therefore often stands for the prima materia  in general."
— Aion , by C. G. Jung

"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe."
— The Stars My Destination , by Alfred Bester

And from Bester's The Deceivers :

Meta  Physics

"'… Think of a match.  You've got a chemical head of potash, antimony, and stuff, full of energy waiting to be released.  Friction does it.  But when Meta  excites and releases energy, it's like a stick of dynamite compared to a match.  It's the chess legend for real.'

'I don't know it.'

'Oh, the story goes that a philosopher invented chess for the amusement of an Indian rajah.  The king was so delighted that he told the inventor to name his reward and he'd get it, no matter what.  The philosopher asked that one grain of rice be placed on the first square of the chessboard, two on the second, four on the third, and so on to the sixty-fourth.'

'That doesn't sound like much.'"

Related material :

Geometry of the I Ching

Wednesday, April 20, 2016

Symmetric Generation of a Simple Group

The reference in the previous post to the work of Guitart and
The Road to Universal Logic  suggests a fiction involving
the symmetric generation of the simple group of order 168.

See The Diamond Archetype and a fictional account of the road to Hell 

'PyrE' in Bester's 'The Stars My Destination'

The cover illustration below has been adapted to
replace the flames of PyrE with the eightfold cube.

IMAGE- 'The Stars My Destination' (with cover slightly changed)

For related symmetric generation of a much larger group, see Solomon’s Cube.

Detour …

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

on the Road to Universal Logic

Deck the Halls.

Tuesday, April 19, 2016

It’s 10 PM …

Filed under: General — m759 @ 10:00 PM

From a Washington Post  book review this evening —

"… some people find an almost spiritual, liminal state
called the Bright…."

And some people may see as an illustration of that fictional state 
this scene from a video

For more on the word "liminal," see October 20, 2015.
For a tale related to the above image, see Floating Dragon .

The Folding

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


A recent post about the eightfold cube  suggests a review of two
April 8, 2015, posts on what Northrop Frye called the ogdoad :

As noted on April 8, each 2×4 "brick" in the 1974 Miracle Octad Generator
of R. T. Curtis may be constructed by folding  a 1×8 array from Turyn's
1967 construction of the Golay code.

Folding a 2×4 Curtis array yet again  yields the 2x2x2 eightfold cube .

Those who prefer an entertainment  approach to concepts of space
may enjoy a video (embedded yesterday in a story on theverge.com) —
"Ghost in the Shell: Identity in Space." 

Monday, April 18, 2016

Talented but Modest

Filed under: General — m759 @ 10:20 PM

  "When Death tells a story"
Cover of The Book Thief


Filed under: General — m759 @ 9:01 PM

"Finnegan's waterlogged epiphany" 

— Phrase by John Lancaster in a Washington Post  review of an
autobiography by William Finnegan, a book that today won a Pulitzer Prize.

The review is dated August 7, 2015. This  journal on that date

The Philosopher’s Apprentice…

Filed under: General — m759 @ 3:21 PM

is a novel by James Morrow reviewed in The New York Times
on March 23, 2008:

"Morrow’s inventiveness is beguiling, as are his delight
in Western philosophy and his concern for the sorry state
of the world. Yet there’s also something comic-bookish
about his novel…."

Siddhartha Deb

"Something comic-bookish" 
in memory of Albert Einstein,
who reportedly died on this date
in 1955 —

A Problem

Filed under: General — m759 @ 12:00 PM

(Continued, in memory of the late meteorologist William Gray,
from August 10, 2010, and from April 16, 2016.)

For some backstory, see Huàn, the Flood and Impact Award.

"… Mathematics may be art, but to the general public
it is a black art, more akin to magic and mystery."

— Sir Michael Atiyah, "The Art of Mathematics"
     in the AMS Notices , January 2010, quoted in
     Log24 on April 4, 2016.

Related material:  Gray Space and

Sunday, April 17, 2016

The Thing and I

Filed under: General,Geometry — Tags: — m759 @ 2:01 PM

The New York Times  philosophy column yesterday —

The Times's philosophy column "The Stone" is named after the legendary
"philosophers' stone." The column's name, and the title of its essay yesterday
"Is that even a thing?" suggest a review of the eightfold cube  as "The object
most closely resembling a 'philosophers' stone' that I know of" (Page 51 of
the current issue of a Norwegian art quarterly, KUNSTforum.as).

The eightfold cube —

Definition of Epiphany

From James Joyce’s Stephen Hero , first published posthumously in 1944. The excerpt below is from a version edited by John J. Slocum and Herbert Cahoon (New York: New Directions Press, 1959).

Three Times:

… By an epiphany he meant a sudden spiritual manifestation, whether in the vulgarity of speech or of gesture or in a memorable phase of the mind itself. He believed that it was for the man of letters to record these epiphanies with extreme care, seeing that they themselves are the most delicate and evanescent of moments. He told Cranly that the clock of the Ballast Office was capable of an epiphany. Cranly questioned the inscrutable dial of the Ballast Office with his no less inscrutable countenance:

— Yes, said Stephen. I will pass it time after time, allude to it, refer to it, catch a glimpse of it. It is only an item in the catalogue of Dublin’s street furniture. Then all at once I see it and I know at once what it is: epiphany.

— What?

— Imagine my glimpses at that clock as the gropings of a spiritual eye which seeks to adjust its vision to an exact focus. The moment the focus is reached the object is epiphanised. It is just in this epiphany that I find the third, the supreme quality of beauty.

— Yes? said Cranly absently.

— No esthetic theory, pursued Stephen relentlessly, is of any value which investigates with the aid of the lantern of tradition. What we symbolise in black the Chinaman may symbolise in yellow: each has his own tradition. Greek beauty laughs at Coptic beauty and the American Indian derides them both. It is almost impossible to reconcile all tradition whereas it is by no means impossible to find the justification of every form of beauty which has ever been adored on the earth by an examination into the mechanism of esthetic apprehension whether it be dressed in red, white, yellow or black. We have no reason for thinking that the Chinaman has a different system of digestion from that which we have though our diets are quite dissimilar. The apprehensive faculty must be scrutinised in action.

— Yes …

— You know what Aquinas says: The three things requisite for beauty are, integrity, a wholeness, symmetry and radiance. Some day I will expand that sentence into a treatise. Consider the performance of your own mind when confronted with any object, hypothetically beautiful. Your mind to apprehend that object divides the entire universe into two parts, the object, and the void which is not the object. To apprehend it you must lift it away from everything else: and then you perceive that it is one integral thing, that is a  thing. You recognise its integrity. Isn’t that so?

— And then?

— That is the first quality of beauty: it is declared in a simple sudden synthesis of the faculty which apprehends. What then? Analysis then. The mind considers the object in whole and in part, in relation to itself and to other objects, examines the balance of its parts, contemplates the form of the object, traverses every cranny of the structure. So the mind receives the impression of the symmetry of the object. The mind recognises that the object is in the strict sense of the word, a thing , a definitely constituted entity. You see?

— Let us turn back, said Cranly.

They had reached the corner of Grafton St and as the footpath was overcrowded they turned back northwards. Cranly had an inclination to watch the antics of a drunkard who had been ejected from a bar in Suffolk St but Stephen took his arm summarily and led him away.

— Now for the third quality. For a long time I couldn’t make out what Aquinas meant. He uses a figurative word (a very unusual thing for him) but I have solved it. Claritas is quidditas . After the analysis which discovers the second quality the mind makes the only logically possible synthesis and discovers the third quality. This is the moment which I call epiphany. First we recognise that the object is one  integral thing, then we recognise that it is an organised composite structure, a thing  in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that  thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany.

Having finished his argument Stephen walked on in silence. He felt Cranly’s hostility and he accused himself of having cheapened the eternal images of beauty. For the first time, too, he felt slightly awkward in his friend’s company and to restore a mood of flippant familiarity he glanced up at the clock of the Ballast Office and smiled:

— It has not epiphanised yet, he said.

Saturday, April 16, 2016

Wind Over Water

Filed under: General — m759 @ 10:45 PM

Google News this evening —

See also Feng Shui  in this journal.

Dorm Room in Purgatory

Filed under: General — m759 @ 9:45 PM

Dorm Room Feng Shui: 'YOU ARE HERE'

Happy birthday to Pope Emeritus Benedict XVI.

Matinee (continued)

Filed under: General — m759 @ 2:15 PM

Today is Kelli O'Hara's last Saturday matinee in "The King and I."

A show that some may prefer —

Related to the plot of Dante's film

"…it would be quite a long walk
for him if he had to walk straight across."

The image “http://www.log24.com/log/pix07A/070831-Ant1.gif” cannot be displayed, because it contains errors.

Swiftly Mrs. Who brought her hands… together.

"Now, you see," Mrs. Whatsit said,
"he would be  there, without that long trip.
That is how we travel."

The image “http://www.log24.com/log/pix07A/070831-Ant2.gif” cannot be displayed, because it contains errors.

– A Wrinkle in Time , Chapter 5, "The Tesseract"

Review for Kelli O’Hara’s Birthday

Filed under: General — m759 @ 1:31 PM

In memory of a Toledo Presbyterian who reportedly
died at 96 on April 11, 2016 — Log24 on that day.

A post reproduced here on April 11

See also some lyrics from the following day:

"Try the grey stuff, it's delicious
Don't believe me? Ask the dishes"

— Disney's "Beauty and the Beast"


Filed under: General — m759 @ 12:00 PM

A search in Log24 for Wallace Stevens's phrase
"the A B C of Being" suggests a related search, for
"Happy Birthday, Wallace Stevens." That search
in turn suggests a search for "Maori."

“Literature begins with geography.”

— Attributed to Robert Frost

Thursday, April 14, 2016

One Funeral at a Time

Filed under: General,Geometry — Tags: — m759 @ 1:37 PM

On this date in 2005, mathematician Saunders Mac Lane died at 95.

Related material —

Max Planck quotations:

Mac Lane on Boolean algebra:

Mac Lane’s summary chart (note the absence of Galois geometry ):

I disagree with Mac Lane’s assertion that “the finite models of
Boolean algebra are dull.”  See Boole vs. Galois in this journal.

Banach Revisited

Filed under: General — m759 @ 12:00 PM

A  1960  analogy by Max Black

"Those who see a model as a mere crutch
are like those who consider metaphor
a mere decoration or ornament."

This suggests a search for "Analogies between Analogies" —

“A mathematician is a person who can find analogies
between theorems; a better mathematician is one who
can see analogies between proofs and the best
mathematician can notice analogies between theories.
One can imagine that the ultimate mathematician is one
who can see analogies between analogies.”

— Stefan Banach, according to MacTutor.

Strange Awards

Filed under: General,Geometry — Tags: , — m759 @ 10:38 AM

From a review of a play by the late Anne Meara* —

"Meara, known primarily as an actress/comedian
(half of the team of Stiller & Meara, and mother of
Ben Stiller), is also an accomplished writer for the
stage; her After Play  was much acclaimed….
This new, more ambitious piece starts off with a sly
send-up of awards dinners as the late benefactor of
a wealthy foundation–the comically pixilated scientist
Herschel Strange (Jerry Stiller)–is seen on videotape.
This tape sets a light tone that is hilariously
heightened when John Shea, as Arthur Garden,
accepts the award given in Strange's name." 

Compare and contrast —

A circular I Ching

I of course prefer the Galois I Ching .

* See the May 25, 2015, post The Secret Life of the Public Mind.

Garden Paths

Filed under: General — m759 @ 10:16 AM

Anne Jackson's obituary in yesterday's online New York Times
mentioned her appearance in "Down the Garden Paths,"
a play by Anne Meara

Some may prefer to  picture Jackson and her late husband,
Eli Wallach, on a garden path pictured here in a post of 
January 17, 2003, "The Walk to Paradise Garden."

Wednesday, April 13, 2016

“Jackson has identified the seventh symbol!”

Filed under: General — m759 @ 9:48 PM

For the above title, see today's 1 PM post Black List.


Filed under: General — m759 @ 2:22 PM

Click for a related film.

Black List

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

A search for "Max Black" in this journal yields some images
from a post of August 30, 2006 . . .

A circular I Ching

The image “http://www.log24.com/log/pix06A/060830-SeventhSymbol.jpg” cannot be displayed, because it contains errors.

"Jackson has identified the seventh symbol."
— Stargate

The "Jackson" above is played by the young James Spader,
who in an older version currently stars in "The Blacklist."

"… the memorable models of science are 'speculative instruments,'
to borrow I. A. Richards' happy title. They, too, bring about a wedding
of disparate subjects, by a distinctive operation of transfer of the
implications  of relatively well-organized cognitive fields. And as with
other weddings, their outcomes are unpredictable."

Max Black in Models and Metaphors , Cornell U. Press, 1962

A Motive for Metaphor

Filed under: General — m759 @ 12:00 PM

From 'Models and Metaphors' by Max Black, Cornell U. Press 1962

Tuesday, April 12, 2016

Requiem for a Leprechaun

Filed under: General — m759 @ 11:02 PM

Slow Art

Filed under: General,Geometry — Tags: — m759 @ 10:45 PM


The American Mathematical Society today got around to
publishing an obituary for Solomon Marcus, a Bucharest
mathematician who died on St. Patrick's Day, March 17.

See as well this  journal on March 22.

Black Trinity

Filed under: General — m759 @ 8:12 PM

In memory of a producerBlack Trinity.

See also a phrase from an image* in today's earlier post
For Non -Charlatans:

"Let us make a small example. . . ."

* Page 149 of "Groups and Symmetries," by F. Oggier
& A. M. Bruckstein. "These notes were designed to fit
the syllabus of the course 'Groups and Symmetries',
taught at Nanyang Technological University in autumn
2012, and 2013."

Lyrics for a Cartoon Graveyard

Filed under: General — m759 @ 2:01 PM

"Try the grey stuff, it's delicious
Don't believe me? Ask the dishes"

— Disney's "Beauty and the Beast"

Related material —

Friday, April 1, 2016

Blackboard Jungle Continues

Filed under: Uncategorized — m759 @ 12:00 AM

See also the previous post and the usual suspects.

Happy birthday to Saoirse Ronan.

For Non-Charlatans

Filed under: General — m759 @ 12:45 PM

The previous post, Charlatans 101, was on a book whose author
is associated rather closely with an Alabama institution called
"Samford University" (not to be confused with Stanford University).

A photo from Samford

Related material for non-charlatans, not  from Samford —

See as well A Wrinkle in Terms in this journal.

Charlatans 101

Filed under: General — m759 @ 12:00 PM

Thanks to Chris Matthews, who last night recommended
the book quoted below —

“I dislike the charlatan class, even if it is they who pay me,”
he said as we drove to my house. “To whom do you refer?”
I asked. He tapped his cigarette out of the cracked window
and looked at me with a sardonic smile: “The sort who
subscribe to Vanity Fair .”

— Taunton, Larry Alex (2016-04-12).
The Faith of Christopher Hitchens: The Restless Soul
of the World's Most Notorious Atheist  
(p. 115).
Thomas Nelson. Kindle Edition. 

See also Orson Welles in this journal.

The Remnick Remark

Filed under: General — m759 @ 12:12 AM

A remark by New Yorker  editor David Remnick
at Princeton on June 3, 2013 —

"Finally, speaking of fabric design. . . ."

Monday, April 11, 2016

Social Network

Filed under: General — Tags: , — m759 @ 11:48 PM

The new New Yorker  online this evening —

" 'If we look at the word "eulogy," it comes from
the ancient Greek word eulogia , and eulogia 
simply means "praise." ' The desire to be present
at one’s own funeral is nothing new. In an era of
near-constant mutual affirmation—pause here to
check the number of likes on your most recent selfie—
why let a little thing like death stand in the way? "

Like Decorations in a Cartoon Graveyard

Filed under: General,Geometry — Tags: , — m759 @ 10:48 PM

From Sunday evening's In Memoriam post —

The "from Princeton" remark in the previous post came  from
Princeton, but originated with a retired professor in Rochester,
NY, one Joseph Neisendorfer.

Another remark by Neisendorfer, from his weblog —

Those familiar with the chapter on Galois in the
Eric Temple Bell classic Men of Mathematics  
will know that the words quoted above by
Neisendorfer are definitely not  those of Albert Einstein.

Princeton Style

Filed under: General — Tags: , — m759 @ 6:00 PM

The previous post contained a remark from Princeton
on the January 1, 2016, death of a mathematician.

"There's a certain Princeton style that focuses on
precision, centrality and simplicity."

See also

For a different sort of style, see Death on New Year's Day.

Gospel of the Nobodies

Filed under: General — Tags: , — m759 @ 2:56 PM

"Principles before personalities" — AA saying


From an April 8 Princeton obituary of a mathematician —

" Moore embodied a 'Princeton style' that made him
a challenging and influential presence in the careers
of his students, said Joseph Neisendorfer, a professor
of mathematics at the University of Rochester who
received his Ph.D. in mathematics from Princeton in
1972. Because of Moore's style, his students would
write theses that 'almost without exception' were
significant advances in mathematics, Neisendorfer said.

'There's a certain Princeton style that focuses on
precision, centrality and simplicity. He was a superb
mathematician and he exercised a lot of influence
by imparting his style to his students,' Neisendorfer said.
'He epitomized the Princeton style.' "


Gospel of the Nobodies 

Combinatorial Spider

Filed under: General,Geometry — Tags: , — m759 @ 1:16 PM

“Chaos is order yet undeciphered.”

— The novel The Double , by José Saramago,
on which the film "Enemy" was based

Some background for the 2012 Douglas Glover
"Attack of the Copula Spiders" book
mentioned in Sunday's Synchronicity Check

  • "A vision of Toronto as Hell" — Douglas Glover in the
    March 25, 2011, post Combinatorial Delight
  • For Louise Bourgeois — a post from the date of Galois's death—


  • For Toronto — Scene from a film that premiered there
    on Sept. 8, 2013:

Sunday, April 10, 2016

In Memoriam

Filed under: General — Tags: — m759 @ 8:48 PM

A great cartoonist died on Friday.

Related religious art — Ogdoads and Miracle Cartoon.

Bodies for Crosses

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

The saying of poet Mary Karr that
"there is a body  on the cross in my church,"
together with the crosses of the previous post
suggests a synchronicity check of the
date  discussed in that post —

“Be serious, because
The stone may have contempt
For too-familiar hands”

— Adrienne Rich in “The Diamond Cutters” (1955)

Blackboard Jungle , 1955 —

IMAGE- Richard Kiley in 'Blackboard Jungle,' with grids and broken records

Space crosses, simple and not-so-simple

Synchronicity Check

Filed under: General — Tags: — m759 @ 2:29 PM

The book quoted in the previous post, Attack of the Copula Spiders,
was reportedly published on March 27, 2012.

For the Church of Synchronology

The above icon may be viewed as a simplified version
of the image described in the April 8 post Space Cross.

Reality Check

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

"But now, as a kind of reality check,
let’s look at James Joyce’s 'The Dead.' "

Attack of the Copula Spiders

And at day five  of April 2016 —

(Today is day ten .  See the previous post.)

Five’ll Getcha Ten*

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

"Driving the car is Beat Personified Johnny Five. . . ."

What Does the Protagonist Want?  website

* See Getcha in this journal.

The Quick and the Dead

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

I watched the 2015 film "Mojave" this morning. Some related remarks:

"Mojave" screenwriter William Monahan won an Oscar for "The Departed."

The opening of a book by another Hollywood author, now departed —

The Latecomers

"Nicholas Concert, a minister without particular portfolio
or flock, and once, long ago, a priest of the Roman faith,
awoke in a troubled dawn. It was the new day sensed
rather than perceptible to him in the interior blackness of
the detached truck camper. It was cold. He was tempted
to huddle in his sleeping bag awhile longer, until the sun
would rise out of the Mojave, climb the ridge and fill the
isolated desert valley. He had not slept well. His night had
been frantic with apparitions, sounds, fragments of dialogue. 

It had been a long night, a terrible night, one that Concert
had thought would never end or, at its worst, that it had ended
and he had died during its passing and this was his eternal hell,
to be transfixed in this night forever, kept from his tomorrow as
Moses, flawed, had been kept from his. …"

E. M. Nathanson

Saturday, April 9, 2016


Filed under: General — Tags: — m759 @ 10:38 PM

See also Local and Global.

Where Everybody Knows Your Name

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

Expanding the Spielfeld (continued)

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

"Mr. Conrad was relentless and rigorous in expanding
the parameters of the fields in which he worked."

The New York Times  today

See also Spielfeld in this  journal, as well as Conrad Moonshine.

Raiders of the Lost Crucible

Filed under: General — Tags: — m759 @ 2:28 PM


Vanity Fair illustrated —

Detail of illustration by Frederick Alfred Rhead of Vanity Fair,
page 96 in the John Bunyan classic Pilgrim's Progress 
(New York, The Century Co., 1912)

See also

Space Invocation

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

Handbook of Combinatorics, 1995- 'Invoke your favorite characterization of AG(4,2)....'

   Consider the space AG(4,2) invoked . See last night's Space Cross.

Midnight in the Garden Continues

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

Scene from a 1997 film by Clint Eastwood:

Related remarks by Wallace Stevens —

Friday, April 8, 2016

Prominent Modernist Foreground

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

Click the above image for some context.

See also "accomplished in steps."

Space Cross

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

For George Orwell

Illustration from a book on mathematics —

This illustrates the Galois space  AG(4,2).

For some related spaces, see a note from 1984.

"There is  such a thing as a space cross."
— Saying adapted from a young-adult novel

The Spacey Version

Filed under: General — Tags: — m759 @ 1:27 PM

"Arthur's favorite scripture was Romans  8."

— Legacy.com on a death of March 28, 2016

 Cf.  Karl Barth on Romans . 

Ogdoads by Curtis

Filed under: General,Geometry — Tags: , — m759 @ 12:25 PM

As was previously noted here, the construction of the Miracle Octad Generator
of R. T. Curtis in 1974 involved his "folding" the 1×8 octads constructed in 1967
by Turyn into 2×4 form.

This resulted in a way of picturing a well-known correspondence (Conwell, 1910)
between partitions of an 8-set and lines of the projective 3-space PG(3,2).

For some background related to the "ogdoads" of the previous post, see
A Seventh Seal (Sept. 15, 2014).

Ogdoads: A Space Odyssey

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

"Like the Valentinian Ogdoad— a self-creating theogonic system
of eight Aeons in four begetting pairs— the projected eightfold work
had an esoteric, gnostic quality; much of Frye's formal interest lay in
the 'schematosis' and fearful symmetries of his own presentations." 

— From p. 61 of James C. Nohrnberg's "The Master of the Myth
of Literature: An Interpenetrative Ogdoad for Northrop Frye," 
Comparative Literature , Vol. 53 No. 1, pp. 58-82, Duke University
Press (quarterly, January 2001)

See also Two by Four  in this  journal.

Thursday, April 7, 2016

Nailing It

Filed under: General — m759 @ 9:57 PM

In memory of an author who
reportedly died Tuesday —

See also "Sausage Party" in this journal.

Symmetry Rag

Filed under: General — m759 @ 9:00 PM

The previous post is about two Princeton-related deaths
on March 12, 2016. See Log24 posts on that date.

Fun and Games at Princeton

Filed under: General — m759 @ 8:22 PM

Two deaths on March 12, 2016
(for the first-listed, see the previous post

Plan 9 Continues (Very Slowly)

Filed under: General — m759 @ 1:00 PM

From the American Mathematical Society today —

Verena Huber-Dyson (1923-2016) 
Thursday April 7th 2016

Huber-Dyson, who worked in group theory and logic, died March 12 at the age of 92. She was born to Swiss parents in Naples and grew up in Athens but moved with her family to Switzerland in 1940 because of the war. Huber-Dyson received her PhD from the University of Zurich in 1947 and moved to the U.S. in 1948 for a post-doctoral fellowship at the Institute for Advanced Study. She held positions at many universities around the world and taught courses on the foundation of mathematics as a philosophy professor at the University of Calgary from 1973 to 1988. Her son, George Dyson, said that her last words were, "This will all go smoothly. Let's get going." She was an AMS member since 1949. Read more about her life.      

See also Huber-Dyson in this  journal.


Filed under: General — m759 @ 12:00 PM

For related rotations, see 
"Turn your head around."

Wednesday, April 6, 2016

Global Game

Filed under: General — m759 @ 9:06 PM

Seymour Lazar, Flamboyant Entertainment Lawyer, Dies at 88

The New York Times  this evening has an obituary for Seymour Lazar, 
"Seymour the Head in Supermoney George Goodman’s 1972 account
of the global financial game, written under the pen name Adam Smith."

From that obituary —

"It was in Cuernavaca that Mr. Goodman, quite skeptical of the Lazar lore
he had heard so much of, met the man behind the myth. 'Seymour was
real,' he wrote…."

As is the Hungarian algorithm.

Mr. Lazar reportedly died on March 30. This journal on that date

Unbroken Circles

Filed under: General — m759 @ 7:31 PM

"Will the circle be unbroken?" — Funeral hymn

"Like a forgotten dream" — Merle Haggard

Scene from 'Spellbound,' starring Ingrid Bergman and Gregory Peck

"Like Shakespeare, Ingrid Bergman was born and died
on the same date In her case, August 29."

Tennessean News

Filed under: General — m759 @ 2:00 PM


Filed under: General — m759 @ 12:00 PM

"Then-Secretary of State Hillary Rodham Clinton
checked her Blackberry inside a C-17 military plane
upon her departure from Malta bound for Tripoli, Libya,
in October 2011. (Kevin Lamarque/AP)"

Washington Post, 11:13 AM today

See as well

It was only in retrospect
 that the silliness became profound.

Blackboard Jungle Continues

Filed under: General — m759 @ 11:30 AM

All Saints’ Day Theatre

Filed under: General — m759 @ 2:01 AM

The Washington Post  pictures an event from
the evening of Sunday, November 1, 2015:

All Saints' Day —

See as well Ay Que Bonito .


Tuesday, April 5, 2016

Enda’s Game

Filed under: General — Tags: , — m759 @ 6:21 PM

An April 4 Boston Globe  story by Kevin Cullen
suggests a review of …

  • "The Dead," by James Joyce
  • "Clay," by James Joyce
  • Dreamcatcher , by Stephen King
  • Enda's Game, a post quoting Tolkien
    on telepathic communication

Spring Play

Filed under: General — Tags: , , — m759 @ 4:24 PM

The spring play this March at Princeton's McCarter Theatre Center
was Agatha Christie's "The Mousetrap."

In related news —

See as well, in this  journal, a post from the date pictured above,
that of the Disneyland Diamond Celebration on May 22, 2015 —

Donald Duck with pentagram

Stevens Illustrated

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

From a Stevens poem, "The Public Square" —

"A slash of angular blacks."

I Ching hexagram 14, box style

See also "Hexagram 14."

A Hard Card

Filed under: General — Tags: — m759 @ 3:25 PM

From the April 2 obituary of a counterculture figure —

"Ms. Crystal was born Jacqueline Diamond
on Dec. 21, 1947, in Manhattan and grew up
in Mamaroneck, N.Y. Her father, Jack, owned
J. Diamond Furs. Her mother, the former Rita
Dunn, was a fur model who, after marrying,
stayed home to raise her children."

— William Grimes in The New York Times

"Jack o' Diamonds is a hard card to play."

From Log24 on the reported date of Ms. Crystal's death —

On 'The Public Square,' from 'Edgar Allan Poe, Wallace Stevens, and the Poetics of American Privacy'- 'A slash of angular blacks...'

Blackboard Jungle Continues

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

Images from a post titled For Stephen King

IMAGE- Long division, yellow chalk, 12977 divided by 23

IMAGE- From a Lawrence Block mystery 'A Stab in the Dark'- 'There was a problem in long division worked out in yellow chalk on the blackboard' and 'You wanted a picture'-Lynn London

Related images —

"Pray for the grace of accuracy" — Robert Lowell

“Puzzle Cube of a Novel”

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

"To know the mind of the creator"

Or that of Orson Welles

Related material — Cube Coloring.

Monday, April 4, 2016

Language Game

Filed under: General — m759 @ 9:09 PM

The previous post was about the death of a figure
from the world of entertainment.

I prefer the work of a figure with the same last name
but from a different world —

"Spiel ist nicht Spielerei." — Friedrich Fröbel

The Bauersfeld Structure*

Filed under: General,Geometry — m759 @ 8:31 PM

"If you would be a poet, create works capable of
answering the challenge of apocalyptic times,
even if this meaning sounds apocalyptic."

Lawrence Ferlinghetti

"It's a trap!"

Ferlinghetti's friend Erik Bauersfeld,
     who reportedly died yesterday at 93

* See also, in this journal, Galois Cube and Deathtrap.

Noon for London

Filed under: General — m759 @ 12:00 PM

(A sequel to today's earlier posts Cube for Berlin and Midnight for Paris.)

See London in this journal.

That search yields

“The more intellectual, less physical,
the spell of contemplation
the more complex must be the object,
the more close and elaborate
must be the comparison
the mind has to keep making
between the whole and the parts,
the parts and the whole.”

— The Journals and Papers of Gerard Manley Hopkins , 
ed. by Humphry House (London: Oxford University Press, 1959),
as quoted by Philip A. Ballinger in The Poem as Sacrament 

(From the post The Inscape of 24, April 24, 2014. The 14 blocks in
the design S(3, 4, 8) of today's previous post are analogous to the 759
blocks in the design S(5, 8, 24).)

Cube for Berlin

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

Foreword by Sir Michael Atiyah —

“Poincaré said that science is no more a collection of facts
than a house is a collection of bricks. The facts have to be
ordered or structured, they have to fit a theory, a construct
(often mathematical) in the human mind. . . . 

 Mathematics may be art, but to the general public it is
a black art, more akin to magic and mystery. This presents
a constant challenge to the mathematical community: to
explain how art fits into our subject and what we mean by beauty.

In attempting to bridge this divide I have always found that
architecture is the best of the arts to compare with mathematics.
The analogy between the two subjects is not hard to describe
and enables abstract ideas to be exemplified by bricks and mortar,
in the spirit of the Poincaré quotation I used earlier.”

— Sir Michael Atiyah, “The Art of Mathematics”
in the AMS Notices , January 2010

Judy Bass, Los Angeles Times , March 12, 1989 —

“Like Rubik’s Cube, The Eight  demands to be pondered.”

As does a figure from 1984, Cullinane’s Cube —

The Eightfold Cube

For natural group actions on the Cullinane cube,
see “The Eightfold Cube” and
A Simple Reflection Group of Order 168.”

See also the recent post Cube Bricks 1984

An Approach to Symmetric Generation of the Simple Group of Order 168

Related remark from the literature —


Note that only the static structure is described by Felsner, not the
168 group actions discussed by Cullinane. For remarks on such
group actions in the literature, see “Cube Space, 1984-2003.”

(From Anatomy of a Cube, Sept. 18, 2011.)

Midnight for Paris

Filed under: General — m759 @ 12:00 AM

Illustration for Florence King's 1989 review of The Eight , a  novel 
by Katherine Neville that features prominently the date April 4.

Sunday, April 3, 2016

The Joker

Filed under: General — m759 @ 11:28 PM

A check on the source of the Wittgenstein quotations
in the previous post yields

   Sounds like Verhexung  to me. See also Plotnitsky in this journal.

Grammatical Joke

Filed under: General — m759 @ 11:07 PM

The previous post suggests a review of Wittgenstein's
Verhexung  remark in context.

Die Verhexung

Filed under: General — m759 @ 10:38 PM

Backstory:  Verhexung  and Ein Kampf .

Prequel: The Verhexung  quote above is from Wittgenstein's section 109 
in Philosophical Investigations . The search result shown links to a page
containing part of the preceding  Wittgenstein section —

For another look at "crystalline purity" and language, see the previous
two posts, Logic and Fruit Loom.

Wallace Stevens, “Country Words” —

“What is it that my feeling seeks?
I know from all the things it touched
And left beside and left behind.
It wants the diamond pivot bright.”

Fruit Loom

Filed under: General — m759 @ 10:10 PM

"This area is called Silicon Valley and it was not always
called Silicon Valley. When I grew up here from seven
years old on, it was called Santa Clara Valley and as far
as you could see it was fruit trees — one of the greatest
fruit-producing areas in the world."

— Steve Wozniak at mashable.com today

See also Just Desserts and The Looming.


Filed under: General — m759 @ 9:29 PM

See also Stone Logical Dimensions 

“Lord Arglay had a suspicion that the Stone
would be purely logical.  Yes, he thought,
but what, in that sense, were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

Ay Que Bonito Es Comer…

Filed under: General — m759 @ 2:00 PM

at The Restaurant Quarré in Berlin,
   with a view of the Brandenburg Gate:

Berlin restaurant with view of Brandenburg Gate

See also versions of the title more suited to 2 AM .

Just Desserts:

Filed under: General — Tags: — m759 @ 1:20 PM

Meditation  for a  Sunday Dinner

'The Power Of The Center: A Study of Composition in the Visual Arts,' by Rudolf Arnheim

Click images for related material.

The Cruelest Month

Filed under: General — m759 @ 12:40 PM

Continued from the April 1 posts
Apple Gate and Wonders of the Invisible World

Background music: "Like a rose under the April snow…." — Streisand

The Emergence of Harlan Kane  continues from yesterday —

Saturday, April 2, 2016

The Emergence of Harlan Kane

Filed under: General — m759 @ 9:48 AM

Publisher's description of a book about everything

"When the whole is greater than the sum of the parts—
indeed, so great that the sum far transcends the parts
and represents something utterly new and different—
we call that phenomenon emergence."

— Oxford University Press

Titles for Harlan Kane, from the date that
the above book's author reportedly died

Friday, April 1, 2016

Savagery 101

Filed under: General — m759 @ 9:30 PM

Continued from Easter Sunday 2016 —

A favicon for Princeton:

256×256 pixels, enlarged from 16×16

Related reporting from this evening's New York Times  —

Clicking the above favicon will yield the cited Federation webpage.

Wonders of the Invisible World

Filed under: General — m759 @ 7:59 PM

Related four-dimensional figure from 1976 —

See as well "Or Only Die."

Apple Gate

Filed under: General — m759 @ 2:04 PM

Latin Class

Filed under: General — m759 @ 12:26 PM

Opening of the film 'Child's Play,' with commentary

See also The Play's the Thing and Rivalry.

In His Own Time

Filed under: General — m759 @ 11:30 AM

See also Wall Power and Moonshine and Lion.

Blackboard Jungle Continues

Filed under: General — m759 @ 12:00 AM

See also the previous post and the usual suspects.

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