Sunday, November 12, 2017

Devil’s Music

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

From the groom in the previous post — Swedenborg Chapel

And from November 7 last year —

Monday, November 7, 2016

Subway Art for Times Square Church

Filed under: Uncategorized — m759 @ 9:11 PM 

Click images for related material.


"The Cardinal seemed a little preoccupied today."

Sunday, April 10, 2011


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

From tonight's online New York Times

John McCracken, Sculptor of Geometric Forms, Dies at 76

McCracken died in Manhattan on Friday, April 8.

From Christopher Knight in tonight's online LA Times

the works embody perceptual and philosophical conundrums. The colored planks stand on the floor like sculptures….

McCracken was bedeviled by Stanley Kubrick's famously obscure science-fiction epic, "2001: A Space Odyssey," with its iconic image of an ancient monolith floating in outer space. The 1968 blockbuster was released two years after the artist made his first plank.

"At the time, some people thought I had designed the monolith or that it had been derived from my work," he told art critic Frances Colpitt of the coincidence in a 1998 interview.

Two photos of McCracken's 1967 Black Plank  seem relevant—

November 28, 2010 (Click to enlarge)


December 28, 2010 (Click to enlarge)


Material that an artist might view as related, if only synchronistically—

Two posts in this journal on the dates the photos were taken—
The Embedding on November 28 and Dry Bones on December 28.

The photos are of an exhibition titled "There is nothing to see here" at the
National Gallery of Art, October 30, 2010-April 24, 2011 —

Click to enlarge.


For related nihilism from the National Gallery, see "Pictures of Nothing" in this journal.

Some less nihilistic illustrations—

The Meno  Embedding


A photo by one of the artists whose work is displayed above beside McCracken's—


"Accentuate the Positive."
 — Clint Eastwood

Saturday, March 18, 2017

News Search

Filed under: Uncategorized — Tags: — m759 @ 12:30 PM

See also, in this journal, "Before the Devil Knows You're Dead."

Saturday, April 5, 2014

A Princeton Half-Hour

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

"May you be in heaven a full half-hour
before the devil knows you're dead ."

Related material:
Yesterday's posts of 12 PM and 8 PM,
and the life of Philip Seymour Hoffman.

Monday, March 12, 2018

“Quantum Tesseract Theorem?”

Filed under: Uncategorized — Tags: — m759 @ 11:00 AM

Remarks related to a recent film and a not-so-recent film.

For some historical background, see Dirac and Geometry in this journal.

Also (as Thas mentions) after Saniga and Planat —

The Saniga-Planat paper was submitted on December 21, 2006.

Excerpts from this  journal on that date —

     "Open the pod bay doors, HAL."

Friday, February 2, 2018

For Plato’s Cave

Filed under: Uncategorized — Tags: , — m759 @ 12:06 PM

"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.'

Friday, January 19, 2018

The Pentagram Papers

Filed under: Uncategorized — Tags: — m759 @ 11:45 AM


Jodie Foster in  a Dec. 15, 2017, sketch  with Stephen Colbert —

"People invest in and take ownership of brands,
and they wonder why the brand didn’t
ask their permission to change."

— Michael Bierut of Pentagram Design
in  a Design Week  article  of Jan. 17, 2018


Filed under: Uncategorized — Tags: — m759 @ 4:04 AM

Wednesday, January 17, 2018

At Heaven’s Gate

Filed under: Uncategorized — Tags: — m759 @ 7:30 AM

(Continued from September 12, 2005)

The previous post contrasted the number-triple 11-7-8 below
with number triples 12-9-5 and 12-5-9.

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

A perhaps more logical counterpart of the triple 11-7-8, based
on opposite  locations of star-points or cube-edges, is
the triple 9-12-5. For a theological interpretation, see 9/12/05.

Tuesday, January 16, 2018

An Orison for Ha-Why

Filed under: Uncategorized — Tags: , — m759 @ 1:00 PM

'Cloud Atlas' book cover illustrating the film

Lines from characters played in the film by Tom Hanks and Halle Berry —

— Cloud Atlas , by David Mitchell (2004).

An orison of sorts from a post on Martin Scorsese's
birthday, Sunday, Nov. 18, 2007 —

BlackBerry with pictures from Log24

Displayed on the BlackBerry are parts
of Log24 posts from October 25, 2007,
and October 24, 2007.

Related pattern geometry 

From a Log24 search for Angleton + Brotherhood:
A photo of Angleton in a post from 12/9/5

The image “http://www.log24.com/log/pix05B/051209-Angleton.jpg” cannot be displayed, because it contains errors.

From a post of 11/7/8


A cryptic note for Dan Brown:

The above dates 11/7/8 and 12/9/5 correspond to the corner-labels
(read clockwise and counter-clockwise) of the two large triangles
in the Finkelstein Talisman

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

Above: More symbology for Tom Hanks from
this morning's post The Pentagram Papers.

The above symbology is perhaps better suited to Hanks in his
role as Forrest Gump than in his current role as Ben Bradlee.

The image “http://www.log24.com/log/pix05B/051211-gump.jpg” cannot be displayed, because it contains errors.

For Hanks as Dan Brown's Harvard symbologist 
Robert Langdon, see the interpretation 12/5/9, rather
than 12/9/5, of the above triangle/cube-corner label.

The Pentagram Papers

Filed under: Uncategorized — Tags: — m759 @ 9:16 AM

Other intersection-points-counting material —

The Finkelstein Talisman:

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

See also Hanks + Cube in this journal —

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube.

Tuesday, January 9, 2018

Koen Thas and Quantum Theory

Filed under: Uncategorized — Tags: — m759 @ 9:23 AM

'General Quantum Theory,' by Koen Thas, Dec. 13, 2017, preprint

This post supplies some background for earlier posts tagged
Quantum Tesseract Theorem.

Monday, January 8, 2018

Raiders of the Lost Theorem

Filed under: Uncategorized — Tags: — m759 @ 11:15 PM

The Quantum Tesseract Theorem 



Raiders —

A Wrinkle in Time
starring Storm Reid,
Reese Witherspoon,
Oprah Winfrey &
Mindy Kaling


Time Magazine  December 25, 2017 – January 1, 2018

Saturday, December 23, 2017

The Right Stuff

Filed under: Geometry — Tags: — m759 @ 1:12 PM

A figure related to the general connecting theorem  of Koen Thas —

Anticommuting Dirac matrices as spreads of projective lines

Ron Shaw on the 15 lines of the classical generalized quadrangle W(2), a general linear complex in PG(3,2)

See also posts tagged Dirac and Geometry in this  journal.

Those who prefer narrative to mathematics may, if they so fancy, call
the above Thas connecting theorem a "quantum tesseract theorem ."

The Patterning

Filed under: Uncategorized — Tags: — m759 @ 12:25 PM

See a Log24 search for "Patterning Windows."

Related material (Click for context) —


IT Girl (for Sweet Home Alabama)

Filed under: Uncategorized — Tags: — m759 @ 3:35 AM

Friday, December 22, 2017


Filed under: Geometry — Tags: — m759 @ 4:08 PM

Movie marquee on Camazotz, from the 2003 film of 'A Wrinkle in Time'

From a Log24 post of October 10, 2017

Koen Thas, 'Unextendible Mututally Unbiased Bases' (Sept. 2016)

Related material from May 25, 2016 —

Thursday, December 21, 2017


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

TIME magazine, issue of December 25th, 2017 —

" In 2003, Hand worked with Disney to produce a made-for-TV movie.
Thanks to budget constraints, among other issues, the adaptation
turned out bland and uninspiring. It disappointed audiences,
L’Engle and Hand. 'This is not the dream,' Hand recalls telling herself.
'I’m sure there were people at Disney that wished I would go away.' "

Not the dream?  It was, however, the nightmare, presenting very well
the encounter in Camazotz of Charles Wallace with the Tempter.

From a trailer for the latest version —


From the 1962 book —

"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."

Song adapted from a 1960 musical —

"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"

Saturday, October 28, 2017

Lowell Brown at Vanity Fair

Filed under: Geometry — Tags: — m759 @ 8:18 PM

A sequel to the post  CP  is for Consolation Prize  (Sept. 3, 2016)

An image from Log24 on this date last year:

A recent comment on a discussion of CP symmetry

Just the Facts

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

The New Yorker  on the recent film "The Square"

"It’s an aesthetic that presents,
so to speak, just the facts, 
as if the facts themselves weren’t
deeply layered with living history
and crisscrossed with vectors
of divergent ideas and ideals."

— Richard Brody, Thursday, Oct. 26, 2017

For other images deeply layered  and crisscrossed ,
see Geometry of the I Ching.

Dating Harvard

Filed under: Uncategorized — Tags: — m759 @ 10:00 AM

See also this journal on today's date four years ago.

Sunday, August 13, 2017

Compare and Contrast

Filed under: Uncategorized — Tags: , — m759 @ 1:00 PM

From The Atlantic , September 2017 issue, online —
"How America Lost Its Mind," by former Harvard Lampoon  
writer Kurt Andersen

The Atlantic 's embedded Google ad for "Quantum Space Elements"
is, by the way, completely unrelated to similar-sounding work on 
models of space in finite geometry (cf. tsimtsum . . .

Friday, August 11, 2017

Symmetry’s Lifeboat

Filed under: Uncategorized — Tags: , — m759 @ 9:16 PM

A post suggested by the word tzimtzum  (see Wednesday)
or tsimtsum  (see this morning) —

Lifeboat from the Tsimtsum  in Life of Pi  —

Another sort of tsimtsum, contracting infinite space to a finite space —

IMAGE- Desargues's theorem in light of Galois geometry

Thursday, August 3, 2017

Glitter at the Dark Tower

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

"The centre of transformations that
Transform for transformation's self,

In a glitter that is a life, a gold
That is a being, a will, a fate."

— Wallace Stevens, "Human Arrangement"

From "The Dark Tower," a post of July 9, 2016 —

See also a search for Glitter in this journal.

Poetic Theology at the New York Times

Filed under: Uncategorized — Tags: — m759 @ 12:19 PM

Or:  Trinity Test Site

From the New York Times Book Review  of
next Sunday, August 6, 2017 —

"In a more conventional narrative sequence,
even a sequence of poems,
this interpenetration would acquire
sequence and evolution." [Link added.]

The concept under review is that of the Holy Trinity.

See also, in this  journal, Cube Trinity.

For a simpler Trinity model, see the three-point line  

Sunday, July 30, 2017

Sermon: MS R I

Filed under: Uncategorized — Tags: — m759 @ 9:57 AM

From Solomon's Cube

"Here MSRI, an acronym for Mathematical Sciences Research Institute,
is pronounced 'Misery.' See Stephen King [and] K.C. Cole . . . ."

From a manuscript by Mikhail Gromov cited yesterday in MSRI Program —

Quotes from a founder of geometric group theory

Sunday School:

Filed under: Uncategorized — Tags: — m759 @ 9:01 AM

Bullshit Studies  Continued

The remarks by Mikhail Gromov on neuroscience in his papers
cited in the previous post suggest some related remarks —

Saturday, July 29, 2017

MSRI Program

Filed under: Uncategorized — Tags: — m759 @ 8:29 PM

"The field of geometric group theory emerged from Gromov’s insight
that even mathematical objects such as groups, which are defined
completely in algebraic terms, can be profitably viewed as geometric
objects and studied with geometric techniques."

Mathematical Sciences Research Institute, 2016:

Geometric Group theory at MSRI (pronounced 'Misery')

See also some writings of Gromov from 2015-16:

For a simpler example than those discussed at MSRI
of both algebraic and geometric techniques applied to
the same group, see a post of May 19, 2017,
"From Algebra to Geometry." That post reviews
an earlier illustration —

For greater depth, see "Eightfold Cube" in this journal.

Science News

Filed under: Uncategorized — Tags: , — m759 @ 10:29 AM

Continued from the post Aesthetic Distance of July 28, 2017.

Friday, July 28, 2017

Aesthetic Distance

Filed under: Uncategorized — Tags: , — m759 @ 11:23 AM

In memory of a Disney "imagineer" who reportedly died yesterday.

From the opening scene  of a 2017 film, "Gifted":

Frank calls his niece Mary to breakfast on the morning she is 
to enter first grade. She is dressed, for the first time, for school —

- Hey! Come on. Let's move!
- No!
- Let me see.
- No.
- Come on, I made you special breakfast.
- You can't cook.
- Hey, Mary, open up. 
(She opens her door and walks out.)
- You look beautiful.
- I look like a Disney character.
  Where's the special?
- What?
- You said you made me special breakfast.

Read more: http://www.springfieldspringfield.co.uk/

Cube symmetry subgroup of order 8 from 'Geometry and Symmetry,' Paul B. Yale, 1968, p.21

Monday, June 26, 2017

Four Dots

Filed under: Uncategorized — Tags: , , — m759 @ 9:57 AM

Analogies — "A : B  ::  C : D"  may be read  "A is to B  as  C is to D."

Gian-Carlo Rota on Heidegger…

"… The universal as  is given various names in Heidegger's writings….

The discovery of the universal as  is Heidegger's contribution to philosophy….

The universal 'as' is the surgence of sense in Man, the shepherd of Being.

The disclosure of the primordial as  is the end of a search that began with Plato….
This search comes to its conclusion with Heidegger."

— "Three Senses of 'A is B' in Heideggger," Ch. 17 in Indiscrete Thoughts

See also Four Dots in this journal. 

Some context:  McLuhan + Analogy.

Wednesday, May 31, 2017

The Pinterest Directive …

Filed under: Uncategorized — Tags: — m759 @ 2:12 AM


Tuesday, May 30, 2017

Diamond Bits

Filed under: Uncategorized — Tags: — m759 @ 1:21 PM

Or:  Putting the Pinter in Pinterest

From "A Poem for Pinter"

Log24 on Oct. 13, 2005

The Guardian on Harold Pinter, winner of this year's Nobel Prize for Literature:

"Earlier this year, he announced his decision to retire from playwriting in favour of poetry,"

Michael Muskal in today's Los Angeles Times:

"Pinter, 75, is known for his sparse and thin style as well as his etched characters whose crystal patter cuts through the mood like diamond drill bits."

Robert Stone, A Flag for Sunrise  (See Jan. 25):

"'That old Jew gave me this here.'  Egan looked at the diamond….  'It's worth a whole lot of money– you can tell that just by looking– but it means something, I think.  It's got a meaning, like.'

'Let's see,' Egan said, 'what would it mean?'  He took hold of Pablo's hand cupping the stone and held his own hand under it.  '"The jewel is in the lotus," perhaps that's what it means.  The eternal in the temporal….'"

See as well an image in a link target from today's noon post

The Pinterest Directive

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

Click image for some background.

Monday, May 29, 2017

Ordinary Evening in a Paper Town

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

Click the above search for a larger version.

Thursday, May 25, 2017

Presidential Address of November 19, 1976

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

Deep Problems in the Faculty Lounge

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

The Story of Six Continues

Filed under: Uncategorized — Tags: — m759 @ 6:00 AM

A post of March 22, 2017, was titled "The Story of Six."

Related material from that date —

"I meant… a larger map." — Number Six in "The Prisoner"

Thursday, May 18, 2017

Bit Plot

Filed under: Uncategorized — Tags: — m759 @ 1:40 AM

From a May 15 review of a new book by Douglas Coupland, author of
the 1991 book Generation X: Tales for an Accelerated Culture .

"Minimalists are actually extreme hoarders:
 they hoard space." — Douglas Coupland

The title of Coupland's new book suggests a review of Schmeikal 
in this  journal

Coupland's above remark on hoarders suggests a look at
a wealthy California collector whom, were he not wealthy,
some might call a hoarder.

“I buy things because they strike an emotional bell,
they appeal to my curiosity, to the thrill of discovery
of the extraordinary in the ordinary,” Mr. Cotsen told
The Denver Post in 1998. “They appeal to my sense
of humor, and to my search for the beauty in simplicity.”

He added, “I decided I had a collection when there was
no more space to put anything.”

By the time he died at 88 on May 8 in Beverly Hills, Calif.,
Mr. Cotsen (pronounced COAT-zen) had donated about
half of the material in his collections to institutions like the
Asian Art Museum in San Francisco, Princeton University
and the Museum of International Folk Art in Santa Fe, N.M.

Richard Sandomir in the online New York Times , May 17

Cotsen reportedly died at 88 on May 8. 

See also this  journal on that date —

Monday, May 8, 2017

New Pinterest Board

Filed under: Uncategorized — m759 @ 9:29 PM 


Wednesday, April 26, 2017

A Tale Unfolded

Filed under: Uncategorized — Tags: , — m759 @ 2:00 AM

A sketch, adapted tonight from Girl Scouts of Palo Alto

From the April 14 noon post High Concept

From the April 14 3 AM post Hudson and Finite Geometry

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

From the April 24 evening post The Trials of Device

Pentagon with pentagram    

Note that Hudson's 1905 "unfolding" of even and odd puts even on top of
the square array, but my own 2013 unfolding above puts even at its left.

Wednesday, April 5, 2017

Dem Bones

Filed under: Uncategorized — Tags: , — m759 @ 12:15 PM

A note at the end of an article on architecture historian
Christopher Gray in the current online New Yorker  —

This article appears in other versions
of the April 10, 2017, issue, with
the headline “Dem Bones.”

"Defeated, you will rise to your feet as is said of Dry Bones .
These bones will rise again." — Agnes Martin, 1973

Accounting for Taste —

Faye Dunaway and Warren Beatty at the Oscars:

Ben Affleck, star of "The Accountant," at the Oscars:

See also Prisoner + Bones in this  journal.

Tuesday, April 4, 2017

Plan 9 Continues

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

"Plan 9 deals with the resurrection of the dead."

— Bill Murray in "Ed Wood"

For The Church of Plan 9

(The plan , as well as the elevation ,
of the above structure is a 3×3 grid.)

Making Science Come Alive

Filed under: Uncategorized — Tags: — m759 @ 8:42 PM

From a post on March 13, 2017

Shafarevich was not the only one with a legacy . . .

See also posts in this  journal
now tagged The Gray Legacy.

Wednesday, March 22, 2017

The Story of Six

Filed under: Uncategorized — Tags: , — m759 @ 8:01 PM

On a psychotherapist who died at 86 on Monday —

"He studied mathematics and statistics at the Courant Institute,
a part of New York University — he would later write   a
mathematical fable, Numberland  (1987)."

The New York Times  online this evening


From Publishers Weekly

This wry parable by a psychotherapist contains one basic message: though death is inevitable, each moment in life is to be cherished. In the orderly but sterile kingdom of Numberland, digits live together harmoniously under a rigid president called The Professor. Their stable society is held intact by the firm conviction that they are immortal: When has a number ever died? This placid universe is plunged into chaos when the inquisitive hero SIX crosses over into the human world and converses with a young mathematician. This supposedly impossible transition convinces the ruling hierarchy that if SIX can talk to a mortal, then the rest of the numbers are, after all, mortal. The digits conclude that any effort or achievement is pointless in the face of inevitable death, and the cipher society breaks down completely. The solution? Banish SIX to the farthest corners of kingdom. Weinberg (The Heart of Psychotherapy ) uses his fable to gently satirize the military, academics, politicians and, above all, psychiatrists. But his tale is basically inspirational; a triumphant SIX miraculously returns from exile and quells the turmoil by showing his fellow digits that knowledge of one's mortality should enrich all other experiences and that death ultimately provides a frame for the magnificent picture that is life. 

Copyright 1987 Reed Business Information, Inc.

See also The Prisoner in this journal.

Monday, March 13, 2017

Pragmatism at the Church of the Transformers*

Filed under: Uncategorized — Tags: — m759 @ 9:17 PM

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

Click the Auto Body image for some backstory.

* For the church, see Transformers in this journal.

Gray Space

Filed under: Uncategorized — Tags: — m759 @ 8:35 PM

Image in Log24 from the date of the architecture writer's death —

See also the post Gray Space of Palm Sunday, 2014.

Wednesday, November 23, 2016


Filed under: Uncategorized — Tags: , — m759 @ 12:31 PM

From the American Mathematical Society (AMS) webpage today —

From the current AMS Notices

Related material from a post of Aug. 6, 2014


(Here "five point sets" should be "five-point sets.")

From Gotay and Isenberg, “The Symplectization of Science,”
Gazette des Mathématiciens  54, 59-79 (1992):

“… what is the origin of the unusual name ‘symplectic’? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure ‘line complex group’ the ‘symplectic group.’
the adjective ‘symplectic’ means ‘plaited together’ or ‘woven.’
This is wonderfully apt….”

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

The above symplectic  structure* now appears in the figure
illustrating the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).

* The phrase as used here is a deliberate 
abuse of language .  For the real definition of 
“symplectic structure,” see (for instance) 
“Symplectic Geometry,” by Ana Cannas da Silva
(article written for Handbook of Differential
, Vol 2.) To establish that the above
figure is indeed symplectic , see the post 
Zero System of July 31, 2014.

Friday, October 28, 2016

Diamond-Theorem Application

Filed under: Uncategorized — Tags: — m759 @ 1:06 PM


"Protection of digital content from being tapped by intruders is a crucial task in the present generation of Internet world. In this paper, we proposed an implementation of new visual secret sharing scheme for gray level images using diamond theorem correlation. A secret image has broken into 4 × 4 non overlapped blocks and patterns of diamond theorem are applied sequentially to ensure the secure image transmission. Separate diamond patterns are utilized to share the blocks of both odd and even sectors. Finally, the numerical results show that a novel secret shares are generated by using diamond theorem correlations. Histogram representations demonstrate the novelty of the proposed visual secret sharing scheme."

— "New visual secret sharing scheme for gray-level images using diamond theorem correlation pattern structure," by  V. Harish, N. Rajesh Kumar, and N. R. Raajan.

Published in: 2016 International Conference on Circuit, Power and Computing Technologies (ICCPCT).
Date of Conference: 18-19 March 2016. Publisher: IEEE.
Date Added to IEEE Xplore: 04 August 2016

Excerpts —

Related material — Posts tagged Diamond Theorem Correlation.

Friday, September 2, 2016


Filed under: Uncategorized — Tags: — m759 @ 7:22 PM

"Now a little trivial heuresis is in order."

The late Waclaw Szymanski on p. 279 of
"Decompositions of operator-valued functions 
in Hilbert spaces
" (Studia Mathematica  50.3
(1974): 265-280.)

See "A Talisman for Finkelstein," from midnight
on the reported date of Szymanski's death.  That post
refers to "the correspondence in the previous post
between Figures A and B" as does this  post

Raiders of the Lost Birthday

Filed under: Uncategorized — Tags: — m759 @ 10:00 AM

Some images from the posts of last July 13
(Harrison Ford's birthday) may serve as funeral
ornaments for the late Prof. David Lavery.

IMAGE- Massimo Vignelli, his wife Lella, and cube

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

See as well posts on "Silent Snow" and "Starlight Like Intuition."

Friday, August 19, 2016

Princeton University Press in 1947

Filed under: Uncategorized — Tags: , — m759 @ 11:17 AM

From a review, in the context of Hollywood, of a Princeton
University Press book on William Blake from 1947 —

Wednesday, August 10, 2016

Analogies Test

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

Obituary for Wilford Stanton Miller, author in 1926
of the Miller Analogies Test  —  

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."

A line for W. S. Miller, taken from "Annie Hall" —

"You know nothing of my work."

Sunday, August 7, 2016

A Talisman for Finkelstein

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

The late physicist David Ritz Finkelstein on the magic square
in Dürer's "Melencolia I" —

"As a child I wondered why such a square was called magic.
The Occult Philosophy  [of Agrippa] answers this question
at least. They were used as magical talismans."

The correspondence  in the previous post between
Figures A and B may serve as a devotional talisman
in memory of Finkelstein, a physicist who, in the sort of
magical thinking enjoyed by traditional Catholics, might
still be lingering in Purgatory.

See also this journal on the date of Finkelstein's death —

Saturday, August 6, 2016

Mystic Correspondence:

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

The Cube and the Hexagram

The above illustration, by the late Harvey D. Heinz,
shows a magic cube* and a corresponding magic 
hexagram, or Star of David, with the six cube faces 
mapped to the six hexagram lines and the twelve  
cube edges mapped to the twelve hexagram points.
The eight cube vertices correspond to eight triangles
in the hexagram (six small and two large). 

Exercise:  Is this noteworthy mapping** of faces to lines, 
edges to points, and vertices to triangles an isolated 
phenomenon, or can it be viewed in a larger context?

* See the discussion at magic-squares.net of
   "perimeter-magic cubes"

** Apparently derived from the Cube + Hexagon figure
    discussed here in various earlier posts. See also
    "Diamonds and Whirls," a note from 1984.

Thursday, July 14, 2016

Symmetries and Correspondences

Filed under: Uncategorized — Tags: — m759 @ 7:30 PM

The title is that of a large-scale British research project
in mathematics. On a more modest scale

"Hanks + Cube" in this journal —

Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

Block That Metaphor

Wednesday, July 13, 2016

Block That Metaphor

Filed under: Uncategorized — Tags: , — m759 @ 8:38 PM

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points (The 6 cube faces are mapped to the 6 hexagram lines.)

Happy dies natalis  to the late Frida Kahlo.

Thursday, July 7, 2016

About Nothing

Filed under: Uncategorized — Tags: — m759 @ 9:16 PM

"For the listener, who listens in the snow, 
And, nothing himself, beholds 
Nothing that is not there and the nothing that is."

Wallace Stevens

See as well A Riddle for Davos.

The Curious Case of the Concrete Universal

Filed under: Uncategorized — Tags: , — m759 @ 3:35 AM


Erica Goode in the online New York Times  tonight

"Irving Gottesman, a pioneer in the field of behavioral genetics
whose work on the role of heredity in schizophrenia helped
transform the way people thought about the origins of serious
mental illness, died on June 29 at his home in Edina, Minn., a
suburb of Minneapolis. He was 85.

His wife, Carol, said he died while taking an afternoon nap.
Although Dr. Gottesman had some health problems, she said,
his death was unexpected, and several of his colleagues said
they received emails from him earlier that day."

A note from noon (EDT) on that day, June 29, for the Church of Synchronology

A detail from the page mentioned in the June 29 post above —

A passage related to the word "soul" discussed by Sullivan —

See as well a related biblical passage, better known at the time of Royce (ca. 1892)
than today, that would probably mean nothing to the late Dr. Gottesman.

Thursday, June 2, 2016

Bullshit Studies

Filed under: Uncategorized — Tags: — m759 @ 11:30 AM


"The allusion to 'the most precious square of sense' shows
Shakespeare doing an almost scholastic demonstration of
the need for a ratio and interplay among the senses as
the very constitution of rationality."

— Marshall McLuhan, The Gutenberg Galaxy ,
University of Toronto Press, 1962, page 13

"What Shakespeare refers to in Lear  as the 'precious
square of sense' probably has reference to the traditional
'square of opposition' in logic and to that four-part analogy
of proportionality which is the interplay of sense and reason."     

— McLuhan, ibid. , page 241

This is of course nonsense, and, in view of McLuhan's pose
as a defender of the Catholic faith, damned  nonsense.

Epigraph by McLuhan —

"The Gutenberg Galaxy  develops a mosaic or field
approach to its problems."

I prefer a different "mosaic or field" related to the movable
blocks  of Fröbel, not the movable type  of Gutenberg.

Sunday, May 29, 2016

The Ideogram Principle …

Filed under: Uncategorized — 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.

Wednesday, March 2, 2016

A Defense of Meaning

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

"In certain moods the horror of a word is the meaning it defends against all comers; so metaphor is the device by which one undermines that defense. In Stevens’ 'Someone Puts a Pineapple Together,' the someone contemplates 'A wholly artificial nature, in which / The profusion of metaphor has been increased.' If you put a pineapple together and see metaphors becoming more profuse, you release yourself from psychological determinations, you become a performative gesture and are happy to find yourself in that state. But then a scruple may assert itself:

He must say nothing of the fruit that is
Not true, nor think it, less. He must defy
The metaphor that murders metaphor.

Presumably a bad metaphor murders a good one: bad in the sense of telling lies, ignoring the truths that can’t honorably be ignored."

— Denis Donoghue, "The Motive for Metaphor,"
     The Hudson Review , Winter 2013 issue

A Geometric Glitter

Filed under: Uncategorized — Tags: — m759 @ 11:10 AM

"In the planes that tilt hard revelations on
The eye, a geometric glitter, tiltings …."

— Wallace Stevens, "Someone Puts a Pineapple Together" (1947)

Tuesday, March 1, 2016

Art and Geometry

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

See "Behind the Glitter" (a recent magazine article
on Oslo artist Josefine Lyche), and the much more
informative web page Contact (from Noplace, Oslo).

From the latter —

"Semiotics is a game of ascribing meaning, or content, to mere surface."

Friday, February 26, 2016


Filed under: Uncategorized — Tags: — m759 @ 4:00 PM


"The study of social memory allows scholars to
understand how different memories form within
a collective group, thus exploring the societal
and ideological elements of disparate groups
that form the over-arching memory of Melkisedeq."

The Melkisedeq Memoirs , by Cale Staley,
2015 master's thesis at the University of Iowa

Elements of groups that I prefer —

"Right through hell
 there is a path…."
 — Malcolm Lowry,
Under the Volcano

Literacy Test

Filed under: Uncategorized — Tags: , — m759 @ 3:13 PM

Being Interpreted:

9 + 4 = 13.


Line at Infinity .

Thursday, February 25, 2016

Mixed Emojis

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

For the New York Post 's Kyle Smith

Wednesday, February 24, 2016


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

For related episodes, see previous posts tagged "The Fit."

Sunday, February 21, 2016

Phone Logic

Filed under: Uncategorized — Tags: — m759 @ 9:23 PM

" 'This is a new category (of device) we’re talking about,'
said Andy Nuttall, HP’s director of mobility strategy.
HP introduced the device Sunday ahead of this week’s
Mobile World Congress trade show in Barcelona, Spain."

— Matt Day in The Seattle Times  today

See also the previous post and the recent film "The Intern."

"Buckle up!" — Harlan Kane

The Masonic Mandorla

Filed under: Uncategorized — Tags: — m759 @ 7:45 PM

A post for Tom Hanks and Dan Brown

Fictional Harvard professor of symbology Robert Langdon, as portrayed by Tom Hanks

Yahoo! President and CEO Marissa Mayer delivers a keynote
during the Yahoo Mobile Developers Conference on February 18,
2016, at Nob Hill Masonic Center in San Francisco, California.
Credit: Stephen Lam

Saturday, February 13, 2016

The Path

Filed under: Uncategorized — Tags: — m759 @ 5:45 PM

(The title is a reference to the previous post.)

"Pope Reminds Us The Devil Is Real"
Catholic Online , Oct. 14, 2013

Related material:

The reported death of Justice Scalia

and posts on Scalia in this  journal.

Friday, February 12, 2016

The Game

Filed under: Uncategorized — Tags: — m759 @ 8:14 PM

"Right through hell
 there is a path…."
 — Malcolm Lowry,
Under the Volcano

Monday, January 25, 2016

A Hateful Eight

Filed under: Uncategorized — Tags: , — m759 @ 8:00 AM

In memory of physicist David Ritz Finkelstein,
who reportedly died yesterday —

"His sense of irony and precision was appreciated" ….



An illustration of the song "Stuck in the Middle with You"
(from the Tarantino film "Reservoir Dogs") was posted by
an academic at Christmas 2015 —

See also, in this  journal,
The Jewel in the Lotus Meets the Kernel in the Nutshell 
(December 16, 2015).

Sunday, January 24, 2016

Long Line

Filed under: Uncategorized — Tags: — m759 @ 6:00 PM

"The ideal of a complete mathematical theory of beauty
lies on the same long line of distinguished fantasies of
mathematical wisdom as the number mysticism of
Pythagoras and Plato, the Ars Magna  of Ramon Llull
(whom Agrippa studied) and Giordano Bruno
(who studied Llull and Agrippa), the vision of Mathesis
  that Descartes and Leibniz shared, and the
Ars Combinatoria  of Leibniz. Dürer does not deny the
existence of absolute beauty but despairs of knowing it."

The late David Ritz Finkelstein in 2007.
     He reportedly died today.

Sunday, December 13, 2015

Another Opening, Another Show

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

Ben Brantley in tonight's online review of a show that
reportedly opened off-Broadway on Dec. 10, 2015 —

" 'Mattress' has its charms, but they do wear thin. "

See also The New York Times  on Martin Gardner Nov. 30:

A companion image from this  journal
on the "Mattress" opening date —

Images of time and eternity in a 1x4x9 black monolith

Vonnegut Asterisk

The Monster as Big as the Ritz

Filed under: Uncategorized — Tags: , — m759 @ 11:30 AM

"The colorful story of this undertaking begins with a bang."

— Martin Gardner on the death of Évariste Galois

Monday, November 16, 2015

Good Question.

Filed under: Uncategorized — Tags: — m759 @ 4:00 PM


Uploaded on Sep 17, 2009

Who'll love the devil?
Who'll sing his song?
Who will love the devil and his song?

"The pictures are understood to have been taken
just a few minutes before three gunmen burst into
the venue at 9.40pm (8.40pm GMT) as the
Californian rock band were launching into one of
their favourites, Kiss The Devil."

Read more: DailyMail.com.

Friday, November 13, 2015

A Connection between the 16 Dirac Matrices and the Large Mathieu Group

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

Note that the six anticommuting sets of Dirac matrices listed by Arfken
correspond exactly to the six spreads in the above complex of 15 projective
lines of PG(3,2) fixed under a symplectic polarity (the diamond theorem
). As I noted in 1986, this correlation underlies the Miracle
Octad Generator of R. T. Curtis, hence also the large Mathieu group.


Arfken, George B., Mathematical Methods for Physicists , Third Edition,
Academic Press, 1985, pages 213-214

Cullinane, Steven H., Notes on Groups and Geometry, 1978-1986

Related material:

The 6-set in my 1986 note above also appears in a 1996 paper on
the sixteen Dirac matrices by David M. Goodmanson —

Background reading:

Ron Shaw on finite geometry, Clifford algebras, and Dirac groups 
(undated compilation of publications from roughly 1994-1995)—

Friday, October 23, 2015

Retro or Not?

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

Happy birthday to the late Michael Crichton (Harvard '64).

See also Diamond Theory Roulette —

Part of the ReCode Project (http://recodeproject.com).
Based on "Diamond Theory" by Steven H. Cullinane,
originally published in "Computer Graphics and Art" 
Vol. 2 No. 1, February 1977.
Copyright (c) 2013 Radames Ajna 
— OSI/MIT license (http://recodeproject/license).

Related remarks on Plato for Harvard's
Graduate School of Design

See also posts from the above publication date, March 31,
2006, among posts now tagged "The Church in Philadelphia."

Thursday, October 15, 2015

Contrapuntal Interweaving

Filed under: Uncategorized — Tags: — m759 @ 2:01 AM

The title is a phrase from R. D. Laing's book The Politics of Experience .
(Published in the psychedelic year 1967. The later "contrapuntal interweaving"
below is of a less psychedelic nature.)

An illustration of the "interweaving' part of the title —
The "deep structure" of the diamond theorem:

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

The word "symplectic" from the end of last Sunday's (Oct. 11) sermon
describes the "interwoven" nature of the above illustration.

An illustration of the "contrapuntal" part of the title (click to enlarge):


Saturday, September 26, 2015

Symbols, Local and Global

Filed under: Uncategorized — Tags: — m759 @ 10:19 PM


Photo by Jimmy Emerson, DVM


Photo by Brendan Smialowski today

Msgr. Mark Miles, the Pope's translator, at
Independence Hall in Philadelphia today.

What, if anything, the Church means by the symbol
he holds is not clear, but presumably its meaning,
if there is one, is more global than local.

Wednesday, September 16, 2015

The World as Myth

Filed under: Uncategorized — m759 @ 10:48 PM

Three approaches to The World as Myth

From Heinlein's 1985 The Cat Who Walks Through Walls

The World as Myth is a subtle concept. It has sometimes been called multiperson solipsism, despite the internal illogic of that phrase. Yet illogic may be necessary, as the concept denies logic. For many centuries religion held sway as the explanation of the universe- or multiverse. The details of revealed religions differed wildly but were essentially the same: Somewhere up in the sky-or down in the earth-or in a volcano-any inaccessible place- there was an old man in a nightshirt who knew everything and was all powerful and created everything and rewarded and punished and could be bribed.

      "Sometimes this Almighty was female but not often because human males are usually bigger, stronger, and more belligerent; God was created in Pop's image.

      "The Almighty-God idea came under attack because it explained nothing; it simply pushed all explanations one stage farther away. In the nineteenth century atheistic positivism started displacing the Almighty-God notion in that minority of the population that bathed regularly.

      "Atheism had a limited run, as it, too, explains nothing, being merely Godism turned upside down. Logical positivism was based on the physical science of the nineteenth century which, physicists of that century honestly believed, fully explained the universe as a piece of clockwork.

      "The physicists of the twentieth century made short work of that idea. Quantum mechanics and Schrodringer's cat tossed out the clockwork world of 1890 and replaced it with a fog of probability in which anything could happen. Of course the intellectual class did not notice this for many decades, as an intellectual is a highly educated man who can't do arithmetic with his shoes on, and is proud of his lack. Nevertheless, with the death of positivism, Godism and Creationism came back stronger than ever.

      "In the late twentieth century -correct me when I' m wrong, Hilda-Hilda and her family were driven off Earth by a devil, one they dubbed 'the Beast.' They fled in a vehicle you have met, Gay Deceiver, and in their search for safety they visited many dimensions, many universesand Hilda made the greatest philosophical discovery of all time."

      "I'll bet you say that to all the girls!"

      "Quiet, dear. They visited, among more mundane places, the Land of Oz-"

      I sat up with a jerk. Not too much sleep last night and Dr. Harshaw's lecture was sleep-inducing. "Did you say 'Oz'?"

      "I tell you three times. Oz, Oz, Oz. They did indeed visit the fairyland dreamed up by L. Frank Baum. And the Wonderland invented by the Reverend Mr. Dodgson to please Alice. And other places known only to fiction. Hilda discovered what none of us had noticed before because we were inside it: The World is Myth. We create it ourselves-and we change it ourselves. A truly strong myth maker, such as Homer, such as Baum, such as the creator of Tarzan, creates substantial and lasting worlds whereas the fiddlin', unimaginative liars and fabulists shape nothing new and their tedious dreams are forgotten. ….

Friday, November 6, 2009

Where Entertainment is God (continued)

Filed under: Uncategorized — m759 @ 1:06 AM 

Click to enlarge.

Ad, with army base shooter in video, for 'The Men Who Stare at Goats'

Colorado Springs Gazette
movie reviewer Brandon Fibbs yesterday:

“Much of this is genuinely amusing.
So why then am I not laughing?”

NY Times on the Fort Hood shootings that took place in the afternoon of Nov. 5, 2009

Tuesday, July 7, 2015

Haiku for DeLillo*

Filed under: Uncategorized — Tags: — m759 @ 4:23 PM

A music video that opens with remarks by Lawrence Ferlinghetti
at the Last Waltz concert (Thanksgiving Day, Nov. 25, 1976):

"Our Father, whose art's in heaven…" —

For other religious remarks from the above upload date,
Sept. 9, 2011, see Holy Field GF(3).

Click the above "ripple" image for a Grateful Dead haiku
quoted here on Sunday, July 5, 2015.

For another meditation from the second upload date above,
March 19, 2012, see some thoughts on the word "field."

IMAGE- Japanese character for 'field'

* For the title, see an excerpt from Point Omega .

Saturday, July 4, 2015


Filed under: Uncategorized — Tags: , — m759 @ 10:00 AM

Some context for yesterday's post on a symplectic polarity —

This 1986 note may or may not have inspired some remarks 
of Wolf Barth in his foreword to the 1990 reissue of Hudson's
1905 Kummer's Quartic Surface .

See also the diamond-theorem correlation.  

Wednesday, May 27, 2015

The Coffee Detective

Filed under: Uncategorized — Tags: , — m759 @ 7:01 AM

See also this morning's earlier posts.


Filed under: Uncategorized — Tags: , — m759 @ 6:06 AM

"J.A.R.V.I.S. (Stands for Just A Rather Very Intelligent System),
also stylized as JARVIS, or Jarvis, is a highly advanced
computerized A.I. developed by Tony Stark, and was voiced
by actor Paul Bettany, to manage almost everything, especially
matters related to technology, in Tony's life."

Happy birthday, Mr. Bettany.

View from the intersection of U.S. Routes 6 and 62.


Filed under: Uncategorized — Tags: , — m759 @ 5:12 AM

For Madonna —


Filed under: Uncategorized — Tags: , — m759 @ 4:45 AM

"Looking for what was, where it used to be" —Wallace Stevens

A section of Route 6 at the former location of an A&P store —

"Wake up and smell the coffee" —

Tuesday, May 26, 2015

Colorful Tales

Filed under: Uncategorized — Tags: , — m759 @ 9:50 PM

See also the Log24 post from May 18,
the date of Eric Caidin's reported death,
as well as Hexagram 50 and May 14, 2014—
Death in Mathmagic Land.

Tuesday, March 10, 2015

The Big Screw

Filed under: Uncategorized — 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: Uncategorized — 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"—

Wednesday, February 25, 2015

Words and Images

Filed under: Uncategorized — Tags: — m759 @ 5:30 PM

The words:  "symplectic polarity"—

The images:

The Natural Symplectic Polarity in PG(3,2)

Symmetry Invariance in a Diamond Ring

The Diamond-Theorem Correlation

Picturing the Smallest Projective 3-Space

Quilt Block Designs

Saturday, February 21, 2015

High and Low Concepts

Filed under: Uncategorized — Tags: — m759 @ 4:30 PM

Steven Pressfield on April 25, 2012:

What exactly is High Concept?

Let’s start with its opposite, low concept.
Low concept stories are personal,
idiosyncratic, ambiguous, often European. 
“Well, it’s a sensitive fable about a Swedish
sardine fisherman whose wife and daughter
find themselves conflicted over … ”


Fans of Oslo artist Josefine Lyche know she has
valiantly struggled to find a high-concept approach
to the diamond theorem. Any such approach must,
unfortunately, reckon with the following low
(i.e., not easily summarized) concept —

The Diamond Theorem Correlation:

From left to right





For some backstory, see ProjPoints.gif and "Symplectic Polarity" in this journal.

Thursday, December 4, 2014

The Pony Argument

Filed under: Uncategorized — Tags: — m759 @ 7:00 PM

The title was suggested by this morning's post "Follow This."

From a previous incarnation of my home website, m759.com —
The second of the site's three pages mentions authors
Alfred Bester and Zenna Henderson :

"Bester and Henderson are particularly good at
fictional accounts of telepathy. The noted Harvard
philosopher W. V. Quine doubts such a thing exists,
but I prefer the 'There must be a pony' argument."

Related material: The date Nov. 27, 2014, in a web search today 

 in The Washington Post 

and in this  journal

Followup for Josefine

Filed under: Uncategorized — Tags: — m759 @ 11:11 AM

The title refers to the previous post, "Follow This."

Dialogue from "Night at the Museum 3"—

"He's not in charge, we're just following him."
"That's what being in charge means ." 

See also Smoke and Mirrors and Angels & Demons.

From Lie Groups for Holy Week :

Stellan Skarsgaard as the head of Vatican Security —

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

Follow This

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

The "Phony Pony" images below by Josefine Lyche
may or may not have been created in response to the link
on "magic" in the previous post to Katy Perry's "Dark Horse" video.

Wednesday, December 3, 2014

Pyramid Dance

Filed under: Uncategorized — Tags: , — m759 @ 10:00 AM

Oslo artist Josefine Lyche has a new Instagram post,
this time on pyramids (the monumental kind).

My response —

Wikipedia's definition of a tetrahedron as a
"triangle-based pyramid"

and remarks from a Log24 post of August 14, 2013 :

Norway dance (as interpreted by an American)

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

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

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

See also some of Burkard Polster's triangle-based pyramids
and a 1983 triangle-based pyramid in a paper that Polster cites —

(Click image below to enlarge.)

Some other illustrations that are particularly relevant
for Lyche, an enthusiast of magic :

From On Art and Magic (May 5, 2011) —





The Fano plane block design



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


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

Tuesday, November 18, 2014

For the Green Mountain Girls

Filed under: Uncategorized — Tags: — m759 @ 9:13 AM

Tom Wolfe in The Painted Word  (1975):

"It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde  understood, they
were not only theories but … hot news,
straight from the studios, from the scene."

"Parable of American Painting," 1954 — From The Tradition of the New by Harold Rosenberg

"In this essay Rosenberg set out to explain what he believed to be definitively American about Abstract Expressionism. He did so by drawing on the American Revolutionary War for his metaphors, likening the new Americans to the coonskin trappers whose knowledge of their terrain enabled them to pick off the British soldiers (Redcoats), who followed the dictates of their military training. The professionally- trained soldiers were defeated because, as Rosenberg states, 'They were such extreme European professionals … they did not even see  the American trees.' 'Redcoatism' was, Rosenberg argued, a symptom of the old European world's stubborn rejection of the new. It did at one time also '[dominate] the history of American art,' he wrote, but with the advent of Abstract Expressionism, times had changed. And just as the Coonskins were victorious because they stood apart from the professional military, so the new American art was triumphant because, as Rosenberg saw it, it marked a profound break with the traditions of European art."

— TheArtStory.org

Lectures at Bennington, 1971

For example:

Art adapted today from the Google search screen. Discuss.

The Abacus Conundrum…

Filed under: Uncategorized — Tags: — m759 @ 1:44 AM



Prequel from 1961 (click image for context):

Detail that may be interpreted as the Chinese
3×3 "Holy Field" and a Chinese temple bell—

"Ting-a-ling." — Kurt Vonnegut.

Our Most Important Product

Filed under: Uncategorized — Tags: — m759 @ 12:45 AM

Hexagram 35:

"Then came a 'Robot Psychologist,' known as a Psychological Matrix Rotator,
developed for the Department of Defense. It is still used to literally 'see' that
the right man gets the right Army job."

Ronald Reagan, 1961 GE Sales Meeting

"Always with a little humor." — Yen Lo

In memory of Dr. Irving Peress,
who reportedly died on Thursday,
November 13, 2014.

Thursday, November 13, 2014

Progressive Matrix

Filed under: Uncategorized — Tags: , — m759 @ 6:00 AM

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

Oct. 12-14, 2005:

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

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

Click to enlarge.

"My card."

Structurally related images —

A sample Raven's Progressive Matrices  test item
(such items share the 3×3 structure of the hash symbol above):

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

Structural background —

Friday, September 26, 2014


Filed under: Uncategorized — Tags: — m759 @ 11:30 AM

For T. S. Eliot’s birthday:

“Time present and time past
Are both perhaps present in time future,
And time future contained in time past.
If all time is eternally present
All time is unredeemable.
What might have been is an abstraction
Remaining a perpetual possibility
Only in a world of speculation.
What might have been and what has been
Point to one end, which is always present.”

— Opening passage of  Four Quartets

See also the previous post.

The X-Men Omen

Filed under: Uncategorized — Tags: — m759 @ 11:00 AM

Days of Future Past :

Saturday, September 6, 2014

But Seriously…

Filed under: Uncategorized — Tags: — m759 @ 10:55 AM

The previous post, Infinite Jest, suggests
a midrash on “–1/12” (i.e., minus one-twelfth):


Infinite Jest

Filed under: Uncategorized — Tags: , — m759 @ 9:18 AM

“1 + 2 + 3 + … = –1/12.”

Keith Devlin, Sept. 2, 2014

Robin Williams at Bunker Hill Community College

Robin Williams and the Stages of Math

i)   shock & denial
ii)  anger
iii) bargaining
iv) depression
v)  acceptance

And then

vi)  checking
vii) Joan Rivers:

Mathematics and Art: Totentanz from Seventh Seal

Sunday, August 24, 2014

Symplectic Structure…

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

In the Miracle Octad Generator (MOG):

The above details from a one-page note of April 26, 1986, refer to the
Miracle Octad Generator of R. T. Curtis, as it was published in 1976:


From R. T. Curtis (1976). A new combinatorial approach to M24,
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42. doi:10.1017/S0305004100052075.

The 1986 note assumed that the reader would be able to supply, from the
MOG itself, the missing top row of each heavy brick.

Note that the interchange of the two squares in the top row of each
heavy brick induces the diamond-theorem correlation.

Note also that the 20 pictured 3-subsets of a 6-set in the 1986 note
occur as paired complements  in two pictures, each showing 10 of the

This pair of pictures corresponds to the 20 Rosenhain tetrads  among
the 35 lines of PG(3,2), while the picture showing the 2-subsets
corresponds to the 15 Göpel tetrads  among the 35 lines.

See Rosenhain and Göpel tetrads in PG(3,2). Some further background:

Wednesday, August 13, 2014

Symplectic Structure continued

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

Some background for the part of the 2002 paper by Dolgachev and Keum
quoted here on January 17, 2014 —

Related material in this journal (click image for posts) —

Monday, August 11, 2014


Filed under: Uncategorized — Tags: , — m759 @ 4:00 PM

(Continued from August 9, 2014.)



"Visual forms— lines, colors, proportions, etc.— are just as capable of
articulation , i.e. of complex combination, as words. But the laws that govern
this sort of articulation are altogether different from the laws of syntax that
govern language. The most radical difference is that visual forms are not
. They do not present their constituents successively, but
simultaneously, so the relations determining a visual structure are grasped
in one act of vision."

– Susanne K. LangerPhilosophy in a New Key

For examples, see The Diamond-Theorem Correlation
in Rosenhain and Göpel Tetrads in PG(3,2).

This is a symplectic  correlation,* constructed using the following
visual structure:

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

* Defined in (for instance) Paul B. Yale, Geometry and Symmetry ,
Holden-Day, 1968, sections 6.9 and 6.10.

Wednesday, August 6, 2014

Symplectic Structure*

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

From Gotay and Isenberg, "The Symplectization of Science,"
Gazette des Mathématiciens  54, 59-79 (1992):

"… what is the origin of the unusual name 'symplectic'? ….
Its mathematical usage is due to Hermann Weyl who,
in an effort to avoid a certain semantic confusion, renamed
the then obscure 'line complex group' the 'symplectic group.'
the adjective 'symplectic' means 'plaited together' or 'woven.'
This is wonderfully apt…."

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

The above symplectic  structure** now appears in the figure
illustrating the diamond-theorem correlation in the webpage
Rosenhain and Göpel Tetrads in PG(3,2).

Some related passages from the literature:


* The title is a deliberate abuse of language .
For the real definition of "symplectic structure," see (for instance)
"Symplectic Geometry," by Ana Cannas da Silva (article written for
Handbook of Differential Geometry, vol 2.) To establish that the
above figure is indeed symplectic , see the post Zero System of
July 31, 2014.

** See Steven H. Cullinane, Inscapes III, 1986

Friday, August 1, 2014

The Diamond-Theorem Correlation

Filed under: Uncategorized — Tags: , — m759 @ 2:00 AM

Click image for a larger, clearer version.

IMAGE- The symplectic correlation underlying Rosenhain and Göpel tetrads

Thursday, July 31, 2014

Zero System

Filed under: Uncategorized — Tags: , — m759 @ 6:11 PM

The title phrase (not to be confused with the film 'The Zero Theorem')
means, according to the Encyclopedia of Mathematics,
a null system , and

"A null system is also called null polarity,
a symplectic polarity or a symplectic correlation….
it is a polarity such that every point lies in its own
polar hyperplane."

See Reinhold Baer, "Null Systems in Projective Space,"
Bulletin of the American Mathematical Society, Vol. 51
(1945), pp. 903-906.

An example in PG(3,2), the projective 3-space over the
two-element Galois field GF(2):

IMAGE- The natural symplectic polarity in PG(3,2), illustrating a symplectic structure

See also the 10 AM ET post of Sunday, June 8, 2014, on this topic.

Thursday, June 26, 2014

The McLuhan Dimension

Filed under: Uncategorized — Tags: , — m759 @ 2:56 AM

"History is a deep and complicated puzzle—
especially when it involves more dimensions than time."

Introduction to a novella in Analog Science Fiction

IMAGE- Marshall McLuhan

IMAGE- Annenberg Hall at Harvard

IMAGE- Search for 'quilt geometry' yields a result from Annenberg Media.

"Annenberg Hall" at Harvard was originally part of a memorial for
Civil War dead. Formerly "Alumni Hall," it was renamed in 1996.

Sunday, June 8, 2014


Filed under: Uncategorized — Tags: , , — m759 @ 10:00 AM

Some background on the large Desargues configuration

The relevance of a geometric theorem is determined by what the theorem
tells us about space, and not by the eventual difficulty of the proof.”

— Gian-Carlo Rota discussing the theorem of Desargues

What space  tells us about the theorem :  

In the simplest case of a projective space  (as opposed to a plane ),
there are 15 points and 35 lines: 15 Göpel  lines and 20 Rosenhain  lines.*
The theorem of Desargues in this simplest case is essentially a symmetry
within the set of 20 Rosenhain lines. The symmetry, a reflection
about the main diagonal in the square model of this space, interchanges
10 horizontally oriented (row-based) lines with 10 corresponding
vertically oriented (column-based) lines.

Vide  Classical Geometry in Light of Galois Geometry.

* Update of June 9: For a more traditional nomenclature, see (for instance)
R. Shaw, 1995.  The “simplest case” link above was added to point out that
the two types of lines named are derived from a natural symplectic polarity 
in the space. The square model of the space, apparently first described in
notes written in October and December, 1978, makes this polarity clearly visible:

A coordinate-free approach to symplectic structure

Wednesday, May 21, 2014

Through the Vanishing Point*

Filed under: Uncategorized — Tags: , — m759 @ 9:48 AM

Marshall McLuhan in "Annie Hall" —

"You know nothing of my work."

Related material — 

"I need a photo opportunity
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard"

— Paul Simon

It was a dark and stormy night…


— Page 180, Logicomix

A photo opportunity for Whitehead
(from Romancing the Cube, April 20, 2011)—

IMAGE- Whitehead on Fano's construction of the 15-point projective Galois space over GF(2)

See also Absolute Ambition (Nov. 19, 2010).

* For the title, see Vanishing Point in this journal.

Sunday, February 2, 2014

Say It With Flowers

Filed under: Uncategorized — Tags: — m759 @ 6:30 PM

The title is a reference to the Jan. 4 post "Learning Guide."

Update of 7:59 PM ET Feb. 2 —

"… they entered the apartment together around 11:30 a.m."

— NY Times  today on the discovery of Hoffman's body.

Synchronicity:  Today's 11 AM (ET) Log24 post, as well as
a 2007 Hoffman film involving drugs, jewels, and a planned
​escape to Brazil —

"May you be in heaven a full half-hour
 before the devil knows you're dead ."

Friday, January 31, 2014

Diamond Star

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

From The Diamond and the Star ,  by John Warden*
(London, Shepheard-Walwyn Ltd.,  June 1, 2009) —

(The quotation is from Kipling's "The Conundrum of the Workshops.")

IMAGE- The Devil's question - 'It's pretty, but is it Art?'

Answer — Some would say "Yes."

Part I: From a search for "Diamond Star" in this journal —

The Diamond Star


Part II: From the Facebook photos of Oslo artist Josefine Lyche—

* Obituary link, added at 10:45 PM ET Jan. 31 after reading  a publisher's note 
  saying that "The author sadly died before the book was published."

  Perhaps sadly, perhaps not.

Friday, January 24, 2014

Prizes —

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

Israel and Nobel —

For the former, see the life of Shulamit Aloni,
who reportedly died today.

For the latter, see the life of Yasunari Kawabata,
who reportedly died in 1972.

Illustrations —

From post 1424, linked to last night

IMAGE- 'The Big Nothing' - Citywide Philadelphia art exhibits, 2004

and from 2004

Tuesday, November 12, 2013


Filed under: Uncategorized — Tags: , — m759 @ 6:45 AM

IMAGE- 'Devil Music' from 'Kaleidoscopes- Selected Writings of H.S.M. Coxeter'


20 pages of incidental music written at school
for G. K. Chesterton's play MAGIC

by D. Coxeter."

See also

Related material —  Chesterton + Magic in this journal.

Monday, November 11, 2013

The Mystic Hexastigm…

Filed under: Uncategorized — Tags: , — m759 @ 11:00 AM

Or: The Nutshell

What about Pascal?

For some background on Pascal's mathematics,
not his wager, see

Richmond, H. W., 
"On the Figure of Six Points in Space of Four Dimensions," 
Quarterly Journal of Pure and Applied Mathematics , 
Volume 31 (1900), pp. 125-160,
dated by Richmond March 30,1899

Richmond, H. W.,
"The Figure Formed from Six Points in Space of Four Dimensions,"
Mathematische Annalen , 
Volume 53 (1900), Issue 1-2, pp 161-176,
dated by Richmond February 1, 1899

See also Nocciolo  in this journal.

Recall as well that six points in space may,
if constrained to lie on a circle, be given
a religious interpretation.  Richmond's
six points are secular and more general.

Friday, November 1, 2013

Cameron’s Group Theory Notes

Filed under: Uncategorized — Tags: , — m759 @ 7:00 AM

In "Notes on Finite Group Theory"
by Peter J. Cameron (October 2013),
some parts are particularly related to the mathematics of
the 4×4 square (viewable in various ways as four quartets)—

  • Definition 1.3.1, Group actions, and example on partitions of a 4-set, p. 19.
  • Exercise 1.1, The group of Fano-plane symmetries, p. 35.
  • Exercise 2.17, The group of the empty set and the 15 two-subsets of a six-set, p. 66.
  • Section 3.1.2, The holomorph of a group, p. 70.
  • Exercise 3.7, The groups A8 and AGL(4,2), p. 78.

Cameron is the author of Parallelisms of Complete Designs ,
a book notable in part for its chapter epigraphs from T.S. Eliot's
Four Quartets . These epigraphs, if not the text proper, seem
appropriate for All Saints' Day.

But note also Log24 posts tagged Not Theology.

Monday, October 28, 2013

Harvard Anniversary

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

From the AP Today in History  page
for October 28, 2013 —

IMAGE- Harvard founded Oct. 28.

From this journal seven years ago:

The Practical Cogitator


Older Posts »

Powered by WordPress