Friday, May 31, 2013

A Very Strange Enchanted Girl

Filed under: General — Tags: — m759 @ 8:28 PM

"When it comes down to it,
I think we all just want
to love and be loved."

Ellen Page in Vanity Fair  online this afternoon

See also lyrics to a tune by Dvořák and eden ahbez.


Filed under: General — m759 @ 9:29 AM

A meditation on this morning's New York Times  obituaries:

IMAGE- NYT obits for Andrew Greeley and Mulgrew Miller, and an ad for Greater Fort Lauderdale

Happy birthday to jazz pianist Clint Eastwood.

Related material: Skylark in this journal and Return to Paradise.

Thursday, May 30, 2013

Two Characters

Filed under: General — m759 @ 12:00 PM

Yesterday, May 29, was JFK's birthday.
The above is a belated quotation for that occasion.

Click on the quotation for truth instead of rhetoric.

(Why the above Google Books description of the quotation's
source is in Danish, I do not know. A search for
Bohr + Chinese in this journal may be relevant, as may
also be Faust in Copenhagen.)

Tuesday, May 28, 2013


The hypercube  model of the 4-space over the 2-element Galois field GF(2):

IMAGE- A hyperspace model of the 4D vector space over GF(2)

The phrase Galois tesseract  may be used to denote a different model
of the above 4-space: the 4×4 square.

MacWilliams and Sloane discussed the Miracle Octad Generator
(MOG) of R. T. Curtis further on in their book (see below), but did not
seem to realize in 1977 that the 4×4 structures within the MOG are
based on the Galois-tesseract model of the 4-space over GF(2).

IMAGE- Octads within the Curtis MOG, which uses a 4x4-array model of the 4D vector space over GF(2)

The thirty-five 4×4 structures within the MOG:

IMAGE- The 35 square patterns within the Curtis MOG

Curtis himself first described these 35 square MOG patterns
combinatorially, (as his title indicated) rather than
algebraically or geometrically:

IMAGE- R. T. Curtis's combinatorial construction of 4x4 patterns within the Miracle Octad Generator

A later book co-authored by Sloane, first published in 1988,
did  recognize the 4×4 MOG patterns as based on the 4×4
Galois-tesseract model.

Between the 1977 and 1988 Sloane books came the diamond theorem.

Update of May 29, 2013:

The Galois tesseract appeared in an early form in the journal
Computer Graphics and Art , Vol. 2, No. 1, February 1977
(the year the above MacWilliams-Sloane book was first published):

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

Where Entertainment is God

Filed under: General — m759 @ 9:29 AM


A May 27, 2013, Washington Post  story by Ellen Nakashima:

Confidential report lists U.S. weapons system designs
compromised by Chinese cyberspies

Related entertainment:

From Ayn Sof  (January 7, 2011): 

"You're gonna need a bigger boat." — Roy Scheider in Jaws

"We're gonna need more holy water." — Season of the Witch


Liam Neeson (right) and Taylor Kitsch

Holy Water 

Sunday, May 26, 2013


Filed under: General — m759 @ 11:00 AM

A phrase in the news recently,

"la métaphysique de l'illimité ,"

suggests a search for related material.

Found: The discussion of the metaphysics of the limitless
in Chapter Two, "The Quest: Philebus ," of Plato and the Good:
Illuminating the Darkling Vision
, by Rosemary Desjardins.

See, too, the Log24 post Ayn Sof  of January 7, 2011,
and A Document in Madness :

* The title is from the 2011 film version of
   the 2001 novel The Dark Fields .

Thursday, May 23, 2013

Annals of Deception

Filed under: General — m759 @ 11:00 AM

These stories suggest a meditation by Kierkegaard
and some related remarks from July 2, 2009.

Wednesday, May 22, 2013


Filed under: General — m759 @ 9:48 AM

"The final ingredient of the design conception
was its most important and its most dangerous…."

The Cambridge Companion to Grand Opera

Starring Michael Douglas:

Related material: 

Happy Birthday, Mary Shelley (August 30, 2003)

Tuesday, May 21, 2013

For Whom the Bell

Filed under: General — m759 @ 11:22 PM

Disney image:

"But you cannot un-ring that bell." — Matt Damon

"Classy." — Emma Watson


Filed under: General — m759 @ 6:00 AM

from yesterday— Bling Ring and Church Logic.

Related narratives— Get Quotes (source of image below)

as well as Helprin's Doors and Trickster.

Monday, May 20, 2013

Church Logic

Filed under: General — m759 @ 6:30 PM

This post is continued from "Church Narrative," a Log24 post of November 17, 2010.

In memory of Ray Manzarek, remarks from a different weblog on that same date:

IMAGE-Quote Investigator post from Nov. 17, 2010- '... and in between are the Doors'

Bling Ring

Filed under: General — m759 @ 7:59 AM

Click images for details.

Seth and Stefon, eat your hearts out.

Related material: Diamond Girl and the following ad
for Eliza Doolittle Day:

Sunday, May 19, 2013


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

Best vs. Bester

The previous post ended with a reference mentioning Rosenhain.

For a recent application of Rosenhain's work, see
Desargues via Rosenhain (April 1, 2013).

From the next day, April 2, 2013:

"The proof of Desargues' theorem of projective geometry
comes as close as a proof can to the Zen ideal.
It can be summarized in two words: 'I see!' "

– Gian-Carlo Rota in Indiscrete Thoughts (1997)

Also in that book, originally from a review in Advances in Mathematics ,
Vol. 84, Number 1, Nov. 1990, p. 136:
IMAGE- Rota's review of 'Sphere Packings, Lattices and Groups'-- in a word, 'best'

See, too, in the Conway-Sloane book, the Galois tesseract  
and, in this journal, Geometry for Jews and The Deceivers , by Bester.

Priority Claim

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

From an arXiv preprint submitted July 18, 2011,
and last revised on March 11, 2013 (version 4):

"By our construction, this vector space is the dual
of our hypercube F24 built on I \ O9. The vector space
structure of the latter, to our knowledge, is first
mentioned by Curtis
in [Cur89]. Hence altogether
our proposition 2.3.4 gives a novel geometric
meaning in terms of Kummer geometry to the known
vector space structure on I \ O9."

[Cur89] reference:
 R. T. Curtis, "Further elementary techniques using
the miracle octad generator," Proc. Edinburgh
Math. Soc. 
32 (1989), 345-353 (received on
July 20, 1987).

— Anne Taormina and Katrin Wendland,
    "The overarching finite symmetry group of Kummer
      surfaces in the Mathieu group 24 ,"
     arXiv.org > hep-th > arXiv:1107.3834

"First mentioned by Curtis…."

No. I claim that to the best of my knowledge, the 
vector space structure was first mentioned by me,
Steven H. Cullinane, in an AMS abstract submitted
in October 1978, some nine years before the
Curtis article.

Update of the above paragraph on July 6, 2013—

No. The vector space structure was described by
(for instance) Peter J. Cameron in a 1976
Cambridge University Press book —
Parallelisms of Complete Designs .
See the proof of Theorem 3A.13 on pages 59 and 60.

The vector space structure as it occurs in a 4×4 array
of the sort that appears in the Curtis Miracle Octad
Generator may first have been pointed out by me,
Steven H. Cullinane,
 in an AMS abstract submitted in
October 1978, some nine years before the Curtis article.

See Notes on Finite Geometry for some background.

See in particular The Galois Tesseract.

For the relationship of the 1978 abstract to Kummer
geometry, see Rosenhain and Göpel Tetrads in PG(3,2).

Saturday, May 18, 2013

Midnight in Bakhtin

Filed under: General — m759 @ 8:00 AM

A followup to last midnight's Black Hole Revisited .

See also Victor Turner on liminality, together with Paul Goodman
on public squares, in a post of May 8, 2007

Related material: Midnight in Dostoevsky (St. Andrew's Day, 2009).

Black Hole Revisited

Filed under: General — m759 @ 12:00 AM

Backstory: The two previous Log24 posts
Raiders of the Lost Aleph (May 14) and
The Crying of Bucharest (May 15).

The following sequence of images was suggested by
Peter Woit's May 16 post "One Ring to Rule Them All."

Also from Devil's Night 2008:

From the May 16 Nobel Symposium talk discussed in
Woit's "One Ring to Rule Them All":

Related material:

All Souls' Day at the Still Point (Nov. 2, 2003) and

Frodo and the Oxford Murders (Oct. 13, 2011).

Wednesday, May 15, 2013

The Crying of Bucharest

Filed under: General — m759 @ 11:02 PM

From a reported interview with Terry Gilliam:

Question: "You said in an interview that The Zero Theorem
was very influenced by Bucharest. In what way?"

Some related material from Log24:

IMAGE- 'Bright Star,' from March 30, 2013

See also a Google search from this evening—

— and the beginning of the Zero Theorem  screenplay —

A rim of swirling light appears, circling helplessly into a
gigantic BLACK HOLE. It spirals inward…

Tuesday, May 14, 2013

Raiders of the Lost Aleph

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

See Coxeter + Aleph in this journal.

Epigraph to "The Aleph," a 1945 story by Borges:

"O God! I could be bounded in a nutshell,
and count myself a King of infinite space…"
– Hamlet, II, 2

Snakes on a Plane

Filed under: General,Geometry — m759 @ 7:27 AM


The order-3 affine plane:

Detail from the video in the previous post:

For other permutations of points in the
order-3 affine plane—

See Quaternions in an Affine Galois Plane
and Group Actions, 1984-2009.

See, too, the Mathematics and Narrative post 
from April 28, 2013, and last night's
For Indiana Spielberg.


Filed under: General,Geometry — m759 @ 7:00 AM

(Continued from December 30, 2012)

IMAGE- Valéry on ornament in 'Method of Leonardo,' with Valéry's serpent-and-key emblem

"And let us finally, then, observe the
parallel progress of the formations of thought
across the species of psychical onomatopoeia
of the primitives, and elementary symmetries
and contrasts, to the ideas of substances,
to metaphors, the faltering beginnings of logic,
formalisms, entities, metaphysical existences."

— Paul Valéry, Introduction to the Method of
    Leonardo da Vinci

But first, a word from our sponsor

Brought to you by two uploads, each from Sept. 11, 2012—

Symmetry and Hierarchy and the above VINCI Genius commercial.

Monday, May 13, 2013

Joyce Brothers

Filed under: General — m759 @ 11:30 PM

Shem and Shaun present NewsArse!

Part I:  Camp Germania

Part II:  NewsArse

For Indiana Spielberg…

Filed under: General — m759 @ 10:23 PM

From Uncle Walt.

IMAGE- Actor playing Walt Disney in NY Times piece titled 'A Dream Is a Wish Your Id Makes'

IMAGE- A 3x3 array of snakes, top center of NY Times online front page

Game Show

Filed under: General — m759 @ 10:00 PM

For the late Bob Stewart:

"She was a panelist on many game shows, including
'What’s My Line?' and 'The Hollywood Squares.'"

Translation Studies Continued:

See Cameron's Kernel and

Image-- The Three-Point Line: A Finite Projective Space
 (Click image for some background.)

A Fitting Symmetry

Filed under: General — m759 @ 9:00 PM

For a pundit of pugilism:  Plan 9 continues.

"She was a panelist on many game shows, including
'What’s My Line?' and 'The Hollywood Squares.'*
These appearances had a fitting symmetry:
It was as a game-show contestant that Dr. Brothers
had received her first television exposure."

— Margalit Fox in this evening's online New York Times

* A language game for Hofstadter: click on "Seeing As"
   in today's noon post.

Hofstadter Meets Heidegger

Filed under: General — m759 @ 12:00 PM

"On Seeing A's and Seeing As" — Hofstadter

"Man redet dann vom Kern der Dinge." — Heidegger


Filed under: General — m759 @ 5:16 AM

"So we moved, and they, in a formal pattern"

Four Quartets

See also yesterday's "Multi-Levels to Keep All Happy"
and past posts that mention Multispeech.

Sunday, May 12, 2013


Filed under: General,Geometry — Tags: — m759 @ 7:12 PM

Western Washington University in Bellingham maintains a
website to benefit secondary-school math: MathNEXUS.

The MathNEXUS "website of the week" on April 14, 2013,
was the Diamond 16 Puzzle and its related webpages.

Click on the above image for the April 14 webpage.

Language Game

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

The above images are from a prequel (March 29, 2013)
to 'Nauts  (March 26, 2006.)

See also Spider Mother,  Gamer Post,  and Spider Tale.

Saturday, May 11, 2013

Invariant Core

Filed under: General — m759 @ 11:00 PM

The title is from today's noon post, Core.

It also appears, quoted from Popovič, in Susan Bassnett's
Translation Studies  (third edition, Routledge, 2002)—

"It is an established fact in Translation Studies that if a dozen
translators tackle the same poem, they will produce a dozen
different versions. And yet somewhere in those dozen versions there
will be what Popovič calls the ‘invariant core’ of the original poem.
This invariant core, he claims, is represented by stable, basic and
constant semantic elements in the text, whose existence can be
proved by experimental semantic condensation. Transformations, or
variants, are those changes which do not modify the core of meaning
but influence the expressive form. In short, the invariant can be
defined as that which exists in common between all existing
translations of a single work. So the invariant is part of a dynamic
relationship and should not be confused with speculative arguments
about the ‘nature’, the ‘spirit’ or ‘soul’ of the text; the ‘indefinable
quality’ that translators are rarely supposed to be able to capture."

"A writer hopes to leave behind a work no one forgets…."

Song sung on NBC's Smash  tonight

Fulsere vere candidi mihi soles….

— André Weil, The Apprenticeship of a Mathematician

nam unguentum dabo, quod meae puellae
donarunt Veneres Cupidinesque….

Catullus, quoted in Bassnett's Translation Studies


Vale puella, iam Catullus obdurat.


Promotional description of a new book:

“Like Gödel, Escher, Bach  before it, Surfaces and Essences  will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core— the incessant, unconscious quest for strong analogical links to past experiences— this book puts forth a radical and deeply surprising new vision of the act of thinking.”

“Like Gödel, Escher, Bach  before it….”

Or like Metamagical Themas .

Rubik core:

Swarthmore Cube Project, 2008

Non- Rubik cores:

Of the odd  nxnxn cube:

Of the even  nxnxn cube:

The image “http://www.log24.com/theory/images/cube2x2x2.gif” cannot be displayed, because it contains errors.

Related material: The Eightfold Cube and

“A core component in the construction
is a 3-dimensional vector space  over F.”

—  Page 29 of “A twist in the M24 moonshine story,”
by Anne Taormina and Katrin Wendland.
(Submitted to the arXiv on 13 Mar 2013.)

A Writers’ Day*

Filed under: General — m759 @ 10:00 AM

From Amazon.com:

Book Description
"Publication Date: April 23, 2013
James Blish called him the “finest conscious artist
science fiction ever produced.” Kurt Vonnegut based
the famous character Kilgore Trout on him. And
such luminaries as Harlan Ellison, Stephen King, and
Octavia Butler have hailed him as a mentor.
Theodore Sturgeon was both a popular favorite and
a writer’s writer…."

A writers' writer's writer:

"A writer's writer, Mrs. Le Guin 
brings reality itself to the proving ground."

Theodore Sturgeon

* Shakespeare's birthday, April 23

Friday, May 10, 2013

Cullinane diamond theorem

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

A page with the above title has been created at
the Encyclopedia of Mathematics.

How long it will stay there remains to be seen.

Thursday, May 9, 2013

Mathematics and Narrative (continued)

Filed under: General — m759 @ 7:00 PM

"Why history?
Well, the essence of history  is story ,
and a good story is an end in itself."

— Barry Mazur, "History of Mathematics  as a tool,"
    February 17, 2013

This  journal on February 17, 2013:

FROM Christoph Waltz

Filed under: Uncategorized — m759 @ 12:12 AM 

"Currently in post-production": The Zero Theorem.

For Christoph Waltz

Filed under: Uncategorized — m759 @ 12:00 AM 

Raiders of the Lost Tesseract  continues…

SOCRATES: Is he not better off in knowing his ignorance?
MENO: I think that he is.
SOCRATES: If we have made him doubt, and given him the 'torpedo's shock,' have we done him any harm?
MENO: I think not.

Torpedo… LOS!

IMAGE- Theodore Sturgeon, 1972 reviews of Del Rey's 'Pstalemate' and Le Guin's 'Lathe of Heaven'   

See also today's previous post.

An Education

Filed under: General — m759 @ 8:00 AM


Click a course description below for some related material.

IMAGE- Harvard students teach classes on Dante and China (Spring 2010).

See also Strike That Pose and Gone to China.

Wednesday, May 8, 2013


Filed under: General — Tags: — m759 @ 3:00 AM

From February 24, 2005:

The image “http://www.log24.com/log/pix05/050224-Symbols.gif” cannot be displayed, because it contains errors.

The above three-part image may be viewed as a tribute to
Jerusalem Day (today), to Saul Bass, or to Spider Jerusalem.

(See related posts and Damnation Morning.)

Tuesday, May 7, 2013

Outrageous Fantasy

Filed under: General — m759 @ 6:00 PM

Or:  Ready When You Are, C. B.

Dennis McLellan, Special to The Los Angeles Times , May 7, 2013:

Born in Los Angeles on June 29, 1920, Harryhausen was 13
when he saw "King Kong" during its run at Grauman's Chinese
Theater in Hollywood.

"I haven't been the same since," he is repeatedly quoted
as saying over the years.

"I came out of the theater awestruck," Harryhausen elaborated
in a 1999 interview with the Chicago Tribune. "It was such a
totally different, unusual film. The story line led you from the
mundane world into the most outrageous fantasy that's ever
been put on the screen."

Midnight in Jerusalem

Filed under: General — m759 @ 5:00 PM

See Damascus Gate.

Strange Correspondences

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

For Jerusalem Day

Strange Correspondences :

"There are interesting correspondences between
Jewish Kabbala, Torah, and Talmud, and
Chinese Buddhism and Taoism…."

Tony Smith

See also Chinese Checkers in this journal.

Sunday, May 5, 2013

Night of Lunacy*

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

Structure vs. Character continued

   IMAGE- The 3x3 square


IMAGE- Chinese character for 'well' and I Ching Hexagram 48, 'The Well'


Related vocabulary:

Nick Tosches on the German word “Quell 

and Heidegger on Hölderlin.

* The title is from Heidegger.

Saturday, May 4, 2013

Master Class

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


From yesterday’s post “Structure“—

IMAGE- 'Where do you believe you're going?'- The Club Dumas

A meditation on today’s New York Times  obituaries:

Gone to China.”

Structure vs. Character

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

“… Reality is not a given whole. An understanding of this,
a respect for the contingent, is essential to imagination
as opposed to fantasy. Our sense of form, which is an
aspect of our desire for consolation, can be a danger to
our sense of reality as a rich receding background.
Against the consolations of form, the clean crystalline
work, the simplified fantasy-myth, we must pit the
destructive power of the now so unfashionable naturalistic
idea of character.

Real people are destructive of myth, contingency is
destructive of fantasy and opens the way for imagination.
Think of the Russians, those great masters of the contingent.
Too much contingency of course may turn art into journalism.
But since reality is incomplete, art must not be too much
afraid of incompleteness. Literature must always represent a
battle between real people and images; and what it requires
now is a much stronger and more complex conception of the

— Iris Murdoch, January 1961, “Against Dryness

See also the recent posts Structure and Character.

Friday, May 3, 2013


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

For the Church of St. Frank:

See Strange Correspondences and Eightfold Geometry.

Correspondences , by Steven H. Cullinane, August 6, 2011

The rest is the madness of art.”

Thursday, May 2, 2013


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

For the Church of St. Frank:

The phrase “Church of St. Frank” was coined in 1995 by
a Harvard professor sneering at literary critic Frank Kermode.
(See a related Log24 note from 1995.)

Now that Frank Kermode is gone, perhaps the phrase suits Frank Langella.


Above: Langella at Cannes with fellow actors from
Wall Street: Money Never Sleeps . He also starred in
the film version of Starting Out in the Evening  (quoted above).

Some related reflections on character:

Diamond Speech (this journal, July 3, 2012) and
Robert Diamond’s Next Life in today’s online New York Times .

Wednesday, May 1, 2013

The Crosswicks Curse

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


"There is  such a thing as a tesseract." —A novel from Crosswicks

Related material from a 1905 graduate of Princeton,
"The 3-Space PG(3,2) and Its Group," is now available
at Internet Archive (1 download thus far).

The 3-space paper is relevant because of the
connection of the group it describes to the
"super, overarching" group of the tesseract.

For Law Day

Filed under: General — m759 @ 12:00 PM

Harvard Gazette , March 4th, 2013:

"Winfrey will speak on May 30 during Commencement day’s
Afternoon Exercises, which serve as the annual meeting of
the Harvard Alumni Association. The exercises will take place
in the Tercentenary Theatre of Harvard Yard,
between Memorial Church and Widener Library."

On the 1977 Octavia Butler novel Mind of My Mind :

"The first chapter in a history that Butler has already taken up
at a much later stage in Patternmaster  (1976).
Mind of My Mind  begins with Doro, a ruthless mutant
as old as the pyramids who has spent the last 4,000 years
trying to breed a race in his own image. The culminating
experiment is his daughter Mary. But, to Doro's astonishment,
Mary's first instinct on attaining her full powers is to begin
building a mental community— a Pattern— out of the
wretched thousands of Doro's half-telepathic failures
and partial successes. Despite some ragged moments,
Butler is clearly on to a promising vein— something like
Zenna Henderson's 'People' stories without their
saccharine silliness. There's a lot of intrinsic energy in the
Pattern idea, and one wants to see where this erratic, gifted
storyteller will pick it up next."

Kirkus Reviews , Vol. XLV, No. 8 (1977), p. 453.

See this journal on Butler's dies natalis , the feast of St. Matthias, 2006.

Those who prefer Eastern approaches to religion may consult
Robert Thurman and his daughter Uma.

"Oprah, Uma. Uma, Oprah." — David Letterman

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