Sunday, October 31, 2010

Diamond Theorem in Norway

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

IMAGE- The 2x2 case of the diamond theorem as illustrated by Josefine Lyche, Oct. 2010

Click on above image for artist's page.

Click here for exhibit page.

Click here for underlying geometry.

A Year Later

Filed under: General — m759 @ 8:00 PM

From this date last year—

Saturday, October 31, 2009

Happy Harvard Halloween

Filed under: Uncategorized — m759 @ 11:30 AM


Related material: This journal on the birthday of Kate Jackson ("Satan’s School for Girls") this year and in 2005.

For more literary depth, see Spider Girl references on March 1, 2005 and August 2, 2009, as well as Raiders of the Lost Well (Feb. 18, 2009). Related religious symbolism: Follow the Harvard links of October 28 ("serious" and then "de facto university motto. [1]").

"By these Festival-rites, from the Age that is past,
To the Age that is waiting before…"


Heaven’s Gate continues

Filed under: General — m759 @ 9:48 AM

In memory of Dutch author Harry Mulisch

The Discovery of Heaven


Mulisch died at his home in Amsterdam on the evening of October 30.

The Discovery of Heaven  was made into a film in 2001 by Jeroen Krabbé,
brother of Tim Krabbé. The latter is the author of the novel The Cave
(1997, first published in English in 2000 by Farrar, Straus and Giroux).

The Cave  is notable for a phrase, "a hole in time."

See also "starflight" in this journal.


Filed under: General — m759 @ 2:00 AM

Keanu vs. the Devil, continued

IMAGE- Still from 'Devil's Advocate' (also starring Charlize Theron)

Al Pacino and Keanu Reeves in Devil's Advocate

For Keanu —

IMAGE- 'Cambridge Tracts in Mathematics 168: The Cube'

(Click for some background.)

For Keanu's mentor —

                                  …    There is a Cave
Within the Mount of God, fast by his Throne,
Where light and darkness in perpetual round
Lodge and dislodge by turns, which makes through Heav'n
Grateful vicissitude, like Day and Night….

Paradise Lost , by John Milton


Click on figure for details.


Al Pacino in Devil's Advocate
as attorney John Milton

Saturday, October 30, 2010

The Fall

Filed under: General — m759 @ 2:09 PM

On the recent death of prominent Israeli biblical archaeologist Ehud Netzer—

Matti Friedman, AP story at Yahoo News — 

"Netzer was speaking with colleagues at the site on Sunday when a wooden safety railing broke and he fell several yards, suffering critical injuries, according to David Amit, a senior archaeologist at the Israel Antiquities Authority. He was rushed to a hospital but did not recover, and died Thursday."

Google Translate version of a ynet.co.il report in Hebrew  —

"On Monday, after a staff meeting Excavators Herodion, sat Professor Netzer on what is called a steel pipe … Theatre Royal cabin Herodium. Witnesses said that the mood was very cheerful – until suddenly broke a few screws and railing, archaeologist fell backwards on my back and hurt himself in the head. Then fell again, and hurt the neck vertebrae."

Hillel Fendel at IsraelNationalNews.com  —

"Prof. Netzer slipped and fell on Tuesday, sustaining severe injuries."

So, according to Jewish legend-in-the-making, this biblical fall may have occurred on Sunday, Monday, or Tuesday.  There seems to be agreement at least that the resulting death occurred on Thursday.

Keanu vs. the Devil

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

(Continued from Little Buddha  (1994), The Matrix  (1999), and Constantine  (2005))

This post was suggested by yesterday's post on Habermas and by his 1962 book The Structural Transformation of the Public Sphere  (English translation, 1989).

The "public sphere" of Habermas has come to pass; it is, of course, the World-Wide Web.

For October 30, the day leading up to Devil's Night, a more private sphere—though in a public setting— seems appropriate…


The Day the Earth Stood Still  (2008)

A Keanu Reeves scene related to this image—

"The low point of the movie’s persuasiveness is the single scene with Professor Barnhardt (John Cleese) — in the original an Einstein-like scientist who impresses Klaatu with his highly evolved thinking, here a caricature of professorial enlightenment. Helen decides to bring Klaatu to Professor Barnhardt when Klaatu professes his disappointment with earth’s leaders. 'Those aren’t our leaders!' she protests earnestly. 'Let me take you to one of our leaders!'"

A perhaps more persuasive scene, from today's New York Times

Prize in Hand, He Keeps His Eye on Teaching


Nobel winner Mario Vargas Llosa teaches
a seminar on Borges at Princeton

(Photo by James Leynse for The New York Times )

Friday, October 29, 2010

Kulturkampf at the Times

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



Some background:
Stanley Fish in the Times  on April 12, 2010.

See also this journal on that date

"Fact and fiction weave in and out of novels
 like a shell game." –R. B. Kitaj

Not just novels.

Church Logic

Filed under: General,Geometry — m759 @ 1:23 PM

"The law of excluded middle is the logical principle in
accordance with which every proposition is either true or
false. This principle is used, in particular, whenever a proof
is made by the method of reductio ad absurdum . And it is
this principle, also, which enables us to say that the denial of
the denial of a proposition is equivalent to the assertion of
the proposition."

Alonzo Church, "On the Law of Excluded Middle,"
    Bulletin of the American Mathematical Society ,
    Vol. 34, No. 1 (Jan.–Feb. 1928), pp. 75–78

It seems reasonable to define a Euclidean  geometry as one describing what mathematicians now call a Euclidean  space.

    What sort of geometry
    is the following?


   Four points and six lines,
   with parallel lines indicated
   by being colored alike.

Consider the proposition "The finite geometry with four points and six lines is non-Euclidean."
Consider its negation. Absurd? Of course.

"Non-Euclidean," therefore, does not apply only  to geometries that violate Euclid's parallel postulate.

The problem here is not with geometry, but with writings about  geometry.

A pop-science website

"In the plainest terms, non-Euclidean geometry
 took something that was rather simple and straightforward
 (Euclidean geometry) and made it endlessly more difficult."

Had the Greeks investigated finite  geometry before Euclid came along, the reverse would be true.

Word Study

Filed under: General — m759 @ 2:02 AM

Commentary on Revelation 6:8—

And I looked, and behold a pale horse:
and his name that sat on him was Death,
and Hell followed with him.

Vincent's Word Studies

Pale (χλωρὸς)

Only in Revelation, except Mark 6:39. Properly, greenish-yellow, like young grass or unripe wheat. Homer applies it to honey, and Sophocles to the sand. Generally, pale, pallid. Used of a mist, of sea-water, of a pale or bilious complexion. Thucydides uses it of the appearance of persons stricken with the plague (ii., 49). In Homer it is used of the paleness of the face from fear, and so as directly descriptive of fear ("Iliad," x., 376; xv., 4). Of olive wood ("Odyssey," ix., 320, 379) of which the bark is gray. Gladstone says that in Homer it indicates rather the absence than the presence of definite color. In the New Testament, always rendered green, except here. See Mark 6:39; Revelation 8:7; Revelation 9:4.


Properly, Hades. The realm of the dead personified. See on Matthew 16:18.

Related material:

Death toll climbs to 394 in Indonesian tsunami

See also, in this journal, Pale Rider  and Hereafter.

Thursday, October 28, 2010

A Sort of Mirror

Filed under: General — m759 @ 5:01 PM

"Whence God is to be understood as a sort of mirror in which all things succeeding one another in the whole course of time have images shining back, a mirror indeed directly beholding itself and all the images existing in it."

Peter de Rivo, quoted in Wild Materialism , p. 102 (below)

"The stakes were high…. …the status, indeed, the ownership, of logic, a term common to the Faculties of Theology and Art, was in dispute…."

Wild Materialism: The Ethic of Terror and the Modern Republic , by Jacques Lezra, Fordham University Press, 2010, chapter on "The Logic of Sovereignty," page 102

See also Borges on the Aleph.

Wednesday, October 27, 2010


Filed under: General — m759 @ 2:29 PM

"The Faithful who gather at the mosque of Amr, in Cairo,
are acquainted with the fact that the entire universe
lies inside one of the stone pillars that ring its central court…"

"Un cofre de gran riqueza
Hallaron dentro un pilar,
Dentro del, nuevas banderas
Con figuras de espantar"

"No llores por mí, Argentina"

Language and Form

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

In memory of S. Neil Fujita, who died last Saturday—


Fujita did the cover art for this edition.

Another book by Langer with a striking cover (artist unknown)—


Note that the background may be constructed from
any of four distinct motifs. For another approach to these
motifs in a philosophical context, see June 8, 2010.

"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 discursive . 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. Langer, Philosophy in a New Key


Filed under: General — m759 @ 12:00 AM

A mathematical review—

IMAGE- Rota's review of 'Sphere Packings, Lattices and Groups'-- in a word, 'best'

      — Gian-Carlo Rota

A science fiction—

Tenser, said the tensor

      — Alfred Bester

Monday, October 25, 2010

The Embedding*

Filed under: General,Geometry — m759 @ 4:04 PM

A New York Times  "The Stone" post from yesterday (5:15 PM, by John Allen Paulos) was titled—

Stories vs. Statistics

Related Google searches—

"How to lie with statistics"— about 148,000 results

"How to lie with stories"— 2 results

What does this tell us?

Consider also Paulos's phrase "imbedding the God character."  A less controversial topic might be (with the spelling I prefer) "embedding the miraculous." For an example, see this journal's "Mathematics and Narrative" entry on 5/15 (a date suggested, coincidentally, by the time of Paulos's post)—

Image-- 'Then a miracle occurs' cartoon
Cartoon by S.Harris

Image-- Google search on 'miracle octad'-- top 3 results


* Not directly  related to the novel The Embedding  discussed at Tenser, said the Tensor  on April 23, 2006 ("Quasimodo Sunday"). An academic discussion of that novel furnishes an example of narrative as more than mere entertainment. See Timothy J. Reiss, "How can 'New' Meaning Be Thought? Fictions of Science, Science Fictions," Canadian Review of Comparative Literature , Vol. 12, No. 1, March 1985, pp. 88-126. Consider also on this, Picasso's birthday, his saying that "Art is a lie that makes us realize truth…."

Saturday, October 23, 2010

Paranormal Jackass

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

From MTV.com this afternoon

The follow-up to last year's runaway horror hit, "Paranormal Activity 2," kicked off its first weekend in theaters with a major haul. The creepy tale… pulled in $20.1 million on Friday.

Trailing behind "Paranormal" is last week's box-office busting debut "Jackass 3D. " The prank-fest, which landed about $50 million its first weekend in theaters, slipped to the second-place slot….

The Clint Eastwood-helmed ensemble drama "Hereafter" landed in fourth place. Exploring the lives of three people who are dealing with death and the afterlife in several ways, including the story of a psychic played by Matt Damon, the screen legend's latest turn in the director's chair made approximately $4.1 million on Friday.

Related material—

IMAGE-- Matt Damon stands where a door opens in 'Hereafter'

Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

The Paranormal Trickster Blog

George P. Hansen on Martin Gardner and the paranormal.

Friday, October 22, 2010

But Seriously…

Filed under: General — Tags: — m759 @ 3:19 PM

Happy Birthday, Jean Simmons …  Jan. 31, 2008

Elmer Gantry … Hollywood's view of the Foursquare Church

Resurrection … An August 2003 post inspired by KHYI, then broadcasting from Plano, Texas

For what it's worth, some free advice for Matt Damon…


IMAGE- NY Times market news and ad for 'Hereafter,' Oct. 22, 2010


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

Google News this afternoon—


Related material:

  1. Celebration of Mind (Oct. 20)
  2. Problem Picture (Oct. 21)
  3. Hereafter (Oct. 22)
  4. The Gypsy in The French Mathematician



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



Click here for soundtrack.

Thursday, October 21, 2010

St. Ursula’s Day

Filed under: General,Geometry — Tags: — m759 @ 4:07 PM

Mathematics and Narrative continued

A search for Ursula in this journal yields a story…

“The main character is a slave woman who discovers new patterns in the mosaics.”

Other such stories: Plato’s Meno  and Changing Woman

Changing Woman:

“Kaleidoscope turning…

Juliette Binoche in 'Blue'  The 24 2x2 Cullinane Kaleidoscope animated images

Shifting pattern within
unalterable structure…”

— Roger Zelazny, Eye of Cat  

Philosophical postscript—

“That Lévi-Strauss should have been able to transmute the romantic passion of Tristes Tropiques  into the hypermodern intellectualism of La Pensée Sauvage  is surely a startling achievement. But there remain the questions one cannot help but ask. Is this transmutation science or alchemy? Is the ‘very simple transformation’ which produced a general theory out of a personal disappointment real or a sleight of hand? Is it a genuine demolition of the walls which seem to separate mind from mind by showing that the walls are surface structures only, or is it an elaborately disguised evasion necessitated by a failure to breach them when they were directly encountered? Is Lévi-Strauss writing, as he seems to be claiming in the confident pages of La Pensée Sauvage,  a prolegomenon to all future anthropology? Or is he, like some uprooted neolithic intelligence cast away on a reservation, shuffling the debris of old traditions in a vain attempt to revivify a primitive faith whose moral beauty is still apparent but from which both relevance and credibility have long since departed?”

— Clifford Geertz, conclusion of “The Cerebral Savage: On the Work of Claude Lévi-Strauss


Filed under: General — Tags: — m759 @ 3:57 AM

The NY Times recently discussed "Longing for the Lines That Had Us at Hello"

and  “We land in Albuquerque at 4 a.m. That’s strictly a 9 o’clock town.”

And so…


Click to enlarge.

"How much story do you want?" — George Balanchine

Problem Picture

Filed under: General — Tags: , — m759 @ 3:24 AM


The above image was suggested by yesterday's
Celebration of Mind and by Plan 9 From Outer Space
in yesterday's New York Times  and in this journal.

Wednesday, October 20, 2010

Celebration of Mind

Filed under: General,Geometry — Tags: — m759 @ 8:00 PM

"Why the Celebration?"

"Martin Gardner passed away on May 22, 2010."

IMAGE-- Imaginary movie poster- 'The Galois Connection'- from stoneship.org

Imaginary movie poster from stoneship.org

Context— The Gardner Tribute.

Tuesday, October 19, 2010

Savage Logic continued…

Filed under: General,Geometry — m759 @ 9:36 AM



"This is an account of the discrete groups generated by reflections…."

Regular Polytopes , by H.S.M. Coxeter (unabridged and corrected 1973 Dover reprint of the 1963 Macmillan second edition)

"In this article, we begin a theory linking hyperplane arrangements and invariant forms for reflection groups over arbitrary fields…. Let V  be an n-dimensional vector space over a field F, and let G ≤ Gln (F) be a finite group…. An element of finite order in Gl(V ) is a reflection if its fixed point space in V  is a hyperplane, called the reflecting hyperplane. There are two types of reflections: the diagonalizable reflections in Gl(V ) have a single nonidentity eigenvalue which is a root of unity; the nondiagonalizable reflections in Gl(V ) are called transvections and have determinant 1 (note that they can only occur if the characteristic of F is positive)…. A reflection group is a finite group G  generated by reflections."

— Julia Hartmann and Anne V. Shepler, "Reflection Groups and Differential Forms," Mathematical Research Letters , Vol. 14, No. 6 (Nov. 2007), pp. 955-971

"… the class of reflections is larger in some sense over an arbitrary field than over a characteristic zero field. The reflections in Gl(V ) not only include diagonalizable reflections (with a single nonidentity eigenvalue), but also transvections, reflections with determinant 1 which can not be diagonalized. The transvections in Gl(V ) prevent one from developing a theory of reflection groups mirroring that for Coxeter groups or complex reflection groups."

— Julia Hartmann and Anne V. Shepler, "Jacobians of Reflection Groups," Transactions of the American Mathematical Society , Vol. 360, No. 1 (2008), pp. 123-133 (Pdf available at CiteSeer.)

See also A Simple Reflection Group of Order 168 and this morning's Savage Logic.

Savage Logic…

Filed under: General,Geometry — Tags: — m759 @ 2:22 AM

and the New York Lottery

IMAGE-- NY Lottery Oct. 18, 2010-- Midday 069, Evening 359

A search in this journal for yesterday's evening number in the New York Lottery, 359, leads to…

The Cerebral Savage: 
On the Work of Claude Lévi-Strauss

by Clifford Geertz

Shown below is 359, the final page of Chapter 13 in
The Interpretation of Cultures: Selected Essays by Clifford Geertz,
New York, 1973: Basic Books, pp. 345-359 —


This page number 359 also appears in this journal in an excerpt from Dan Brown's novel Angels & Demons

See this journal's entries for March 1-15, 2009, especially…

Sunday, March 15, 2009  5:24 PM

Philosophy and Poetry:

The Origin of Change

A note on the figure
from this morning's sermon:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined

On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."

-- Wallace Stevens,
  "Notes Toward a Supreme Fiction,"
   Canto IV of "It Must Change"

Sunday, March 15, 2009  11:00 AM

Ides of March Sermon:

Angels, Demons,

"On Monday morning, 9 March, after visiting the Mayor of Rome and the Municipal Council on the Capitoline Hill, the Holy Father spoke to the Romans who gathered in the square outside the Senatorial Palace…

'… a verse by Ovid, the great Latin poet, springs to mind. In one of his elegies he encouraged the Romans of his time with these words:

"Perfer et obdura: multo graviora tulisti."

 "Hold out and persist:
  you have got through
  far more difficult situations."

 (Tristia, Liber  V, Elegia  XI, verse 7).'"

This journal
on 9 March:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

Note the color-interchange
of each symbol
under 180-degree rotation.

Related material:
The Illuminati Diamond:

IMAGE- Illuminati Diamond, pp. 359-360 in 'Angels & Demons,' Simon & Schuster Pocket Books 2005, 448 pages, ISBN 0743412397

The symmetry of the yin-yang symbol, of the diamond-theorem symbol, and of Brown's Illuminati Diamond is also apparent in yesterday's midday New York lottery number (see above).

"Savage logic works like a kaleidoscope…." — Clifford Geertz on Lévi-Strauss

Monday, October 18, 2010

For St. Luke’s Day —

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

The Turning

"To everything, turn, turn, turn…

Quaternion Rotations in a Finite Geometry

… there is a season, turn, turn, turn…"

For less turning and more seasons, see a search in this journal for

fullness + multitude + "cold mountain."

Sunday, October 17, 2010

An Intricate Reflection

Filed under: General — m759 @ 2:00 AM

"Humanity's fascination with numbers is ancient and complex. Our present relationship with numbers reveals both a highly developed tool and a highly developed user, working together to measure, create, and predict both ourselves and the world around us. But like every symbiotic couple, the tool we would like to believe is separate from us (and thus objective) is actually an intricate reflection of our thoughts, interests, and capabilities."

The Secret Lives of Numbers, by New Radio and Performing Arts

(recommended on the Frivolous Linkages page at Daniel Gilbert's Harvard website)

Other linkages:

New York Lottery on October 16: Midday 706, Evening 684.

Related material — 7/06, 2007, and post no. 684 in this journal.

The above "Secret Lives of Numbers" quotation was suggested by Gilbert's "Magic by Numbers" op-ed piece in today's New York Times


"Ay que bonito es volar…"

Saturday, October 16, 2010

Quaternion Day

Filed under: General — m759 @ 12:00 PM

Brightness at Noon continued

i2 = j2 = k2 = ijk = -1

— Sir William Rowan Hamilton, Oct. 16, 1843

See also this journal on 1/09, 2010.

The Mandelbrot Numbers

Filed under: General — m759 @ 11:36 AM

Benoît Mandelbrot died on Oct. 14.

NY Lottery Thursday, Oct. 14, 2010-- Midday 109, Evening 060

— New York Lottery on Thursday, Oct. 14, 2010

Related material on 109: See 1/09, 2009.
Related material on 060: See Hexagram 60 of the I Ching  and…

IMAGE-- Matt Damon stands where a door opens in 'Hereafter'

Margaret Atwood on Lewis Hyde's Trickster Makes This World: Mischief, Myth, and Art

"Trickster is among other things the gatekeeper who opens the door into the next world; those who mistake him for a psychopath never even know such a door exists." (159)

What is "the next world"? It might be the Underworld….

The pleasures of fabulation, the charming and playful lie– this line of thought leads Hyde to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning "to join," "to fit," and "to make." (254)  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart.

Friday, October 15, 2010

Mathematics and Narrative, continued

Filed under: General — Tags: — m759 @ 6:29 AM

The Story of N


Roberta Smith in the New York Times  of July 7, 2006

Art Review

Endgame Art? It's Borrow, Sample and Multiply in an Exhibition at Bard College

"… The show has an endgame, end-time mood, as if we are looking at the end of the end of the end of Pop, hyperrealism and appropriation art. The techniques of replication and copying have become so meticulous that they are beside the point. This is truly magic realism: the kind you can't see, that has to be explained. It is also a time when artists cultivate hybridism and multiplicity and disdain stylistic coherence, in keeping with the fashionable interest in collectivity, lack of ego, the fluidity of individual identity. But too often these avoidance tactics eliminate the thread of a personal sensibility or focus.

I would call all these strategies fear of form, which can be parsed as fear of materials, of working with the hands in an overt way and of originality. Most of all originality. Can we just say it? This far from Andy Warhol and Duchamp, the dismissal of originality is perhaps the oldest ploy in the postmodern playbook. To call yourself an artist at all is by definition to announce a faith, however unacknowledged, in some form of originality, first for yourself, second, perhaps, for the rest of us.

Fear of form above all means fear of compression— of an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible. With a few exceptions, forms of collage and assemblage dominate this show: the putting together (or simply putting side by side) of existing images and objects prevails. The consistency of this technique in two and three dimensions should have been a red flag for the curators. Collage has driven much art since the late 1970's. Lately, and especially in this exhibition, it often seems to have become so distended and pulled apart that its components have become virtually autonomous and unrelated, which brings us back to square one. This is most obvious in the large installations of graphic works whose individual parts gain impact and meaning from juxtaposition but are in fact considered distinct artworks."

Margaret Atwood on art and the trickster

"The pleasures of fabulation, the charming and playful lie— this line of thought leads Hyde* to the last link in his subtitle, the connection of the trickster to art. Hyde reminds us that the wall between the artist and that American favourite son, the con-artist, can be a thin one indeed; that craft and crafty rub shoulders; and that the words artifice, artifact, articulation  and art  all come from the same ancient root, a word meaning 'to join,' 'to fit,' and 'to make.'  If it’s a seamless whole you want, pray to Apollo, who sets the limits within which such a work can exist.  Tricksters, however, stand where the door swings open on its hinges and the horizon expands: they operate where things are joined together, and thus can also come apart."

* Lewis Hyde, Trickster Makes This World: Mischief, Myth, and Art,  Farrar Straus & Giroux, January 1998

Smith mentions "an artistic focus that condenses experiences, ideas and feelings into something whole, committed and visually comprehensible."

Atwood mentions "a seamless whole."

For some related remarks, see "A Study in Art Education" and the central figure pictured above. (There "N" can stand for "number," "nine," or "narrative.")

Thursday, October 14, 2010

Diamond Theory and Magic Squares

Filed under: General,Geometry — Tags: , — m759 @ 6:19 PM

"A world of made
is not a world of born— pity poor flesh
and trees, poor stars and stones, but never this
fine specimen of hypermagical

— e. e. cummings, 1944

For one such specimen, see The Matrix of Abraham
a 5×5 square that is hypermagical… indeed, diabolical.

Related material on the algebra and geometry underlying some smaller structures
that have also, unfortunately, become associated with the word "magic"—

  1. Finite Geometry of the Square and Cube
  2. Clifford Pickover on a 4×4 square
  3. Christopher J. Henrich on the geometry of 4×4 magic squares
    (without any mention of  [1] above or related work dating back to 1976)

" … listen: there's a hell
of a good universe next door; let's go"

— e. e. cummings

Happy birthday, e. e.


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

This journal on October 12 (the traditional Columbus day)—

"The text is a two-way mirror
that allows me to look into
the life and times of the reader."
The French Mathematician
   (Galois), by Tom Petsinis

It is not clear how this is supposed to work.

However, there is synchronicity and the New York Lottery—

October 12, 2010—

Midday 765, Evening 365 —

Life  and Times.


APRIL 25, 2008

From Log24 on April 21, the date of Mark Twain’s death–

Psychoshop,  by Alfred Bester and Roger Zelazny:

His manner was all charm and grace; pure cafe society….

He purred a chuckle. “My place. If you want to come, I’ll show you.”

“Love to. The Luogo Nero? The Black Place?”

“That’s what the locals call it. It’s really Buoco Nero, the Black Hole.”

“Like the Black Hole of Calcutta?”

“No. Black Hole as in astronomy. Corpse of a dead star, but also channel between this universe and its next-door neighbor.”

The Pennsylvania Lottery
yesterday, April 24, 2008:

Mid-day 923, Evening 765….

and hence Log24, 9/23 (2007), and page 765 of From Here to Eternity  (Delta paperback, 1998):

He stayed that way for eight days, never what you could really call drunk, but certainly never anywhere near sober, and always with a bottle of Georgette’s expensive scotch in one hand and a glass in the other. He did not talk at all except to say “Yes” or “No,” mostly “No,” when confronted with a direct question, and he never ate anything when they were there. It was like living in the same house with a dead person.


See "Seasons of Love" from the musical "Rent."

See also Mark 15:38— "And the veil of the temple…"

Wednesday, October 13, 2010

Jungian Four-Group

Filed under: General — m759 @ 11:07 AM


For some background, see "four-group" in this journal.

Tuesday, October 12, 2010

King Solomon’s Mind

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

"Always keep a diamond in your mind."

Tom Waits/Kathleen Brennan song performed by Solomon Burke at the Paradiso in Amsterdam

The Galois Quaternion

The Galois Quaternion

"The text is a two-way mirror
that allows me to look into
the life and times of the reader.
Who knows, someday i  may rise
to a text that will compel me
to push through to the other side."

The French Mathematician
   (Galois), by Tom Petsinis



Monday, October 11, 2010


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

… Don't you know that when you play
at this level there's no ordinary venue?

— Lyrics from Chess

Why don't you come with me little girl
On a magic carpet ride?

— Steppenwolf lyrics in Star Trek: First Contact

I like to fold my magic carpet, after use,
in such a way as to superimpose
one part of the pattern upon another.

Vladimir Nabokov in Speak, Memory

See also recent Log24 posts.

The Starflight Problem

Filed under: General — m759 @ 10:31 AM

"Nabokov's problem, in its simple prettiness and purity, suggests he has just invented starflight himself."

Tim Krabbé, Open Chess Diary, Entry 9— July 1, 1999

Related— New York Lottery on October 10, 2010—

Midday 137,
Evening 701.

Some context for the Halloween season—

137: Jung, Pauli, and the Pursuit of a Scientific Obsession

Skeleton Crew  by Stephen King

http://www.log24.com/log/pix10B/101011-137JungPauli-sm.jpg   http://www.log24.com/log/pix10B/101011-SkeletonCrew.jpg

See also Saturday evening's post in this journal, Jaunt 701.

Sunday, October 10, 2010


Filed under: General — m759 @ 11:59 AM

For Solomon Burke


Filed under: General — m759 @ 11:00 AM

Brynner + Welles


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

Pythagoreans might regard today as the Day of the Tetraktys.

Some relevant epigraphs—

"Contrary to John Keats's First and Second Laws of Aesthetics ('Beauty is truth, truth beauty') truth and beauty are poles apart. Keats's ode itself, while denying this by precept, bears it out by example. Truth occupies the alethic pole of the intellectual sphere and beauty the aesthetic pole. Each is admirable in its way. The alethic pole exerts the main pull on science, in the broad sense: Wissenschaft,  comprising mathematics, history, and all the hard and soft sciences in between. The aesthetic pole is the focus of belles lettres,  music, art for art's sake."

— W. V. Quine in Quiddities

Weisheit und Wissenschaft: Studien zu Pythagoras, Philolaos und Platon

Original title of Burkert's Lore and Science in Ancient Pytthagoreanism

"What song the Sirens sang…" — Sir Thomas Browne


  1. Stanford Encyclopedia of Philosophy  on the Pythagorean acusmatici  and mathematici
  2. Burkert on the same topic
  3. Father Robert Sokolowski's foreword to Rota's Indiscrete Thoughts

Saturday, October 9, 2010

Jaunt 701

Filed under: General — m759 @ 9:57 PM

Pennsylvania Lottery today

Image-- PA lottery Oct. 9, 2010-- Midday 701, Evening 987

Context: See the past few days' posts and search for

"Death itself would start working backwards."

Some Like It in the Pot

Filed under: General — m759 @ 11:59 AM

Seven is Heaven, Eight is a Gate, Nine is a Vine

"And the serpent's eyes shine…."

Requiem for a Screenwriter

Filed under: General — m759 @ 2:02 AM

For William Norton:

Part 1— Everybody Comes to Rick's.

Part 2— Here Comes Everybody.

Friday, October 8, 2010

Starting Out in the Evening

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

… and Finishing Up at Noon

This post was suggested by last evening’s post on mathematics and narrative
and by Michiko Kakutani on Vargas Llosa in this morning’s New York Times.


Above: Frank Langella in
Starting Out in the Evening

Right: Johnny Depp in
The Ninth Gate


“One must proceed cautiously, for this road— of truth and falsehood in the realm of fiction— is riddled with traps and any enticing oasis is usually a mirage.”

— “Is Fiction the Art of Lying?”* by Mario Vargas Llosa, New York Times  essay of October 7, 1984

My own adventures in that realm— as reader, not author— may illustrate Llosa’s remark.

A nearby stack of paperbacks I haven’t touched for some months (in order from bottom to top)—

  1. Pale Rider by Alan Dean Foster
  2. Franny and Zooey by J. D. Salinger
  3. The Hobbit by J. R. R. Tolkien
  4. Le Petit Prince by Antoine de Saint Exupéry
  5. Literary Reflections by James A. Michener
  6. The Ninth Configuration by William Peter Blatty
  7. A Streetcar Named Desire by Tennessee Williams
  8. Nine Stories by J. D. Salinger
  9. A Midsummer Night’s Dream by William Shakespeare
  10. The Tempest by William Shakespeare
  11. Being There by Jerzy Kosinski
  12. What Dreams May Come by Richard Matheson
  13. Zen and the Art of Motorcycle Maintenance by Robert M. Pirsig
  14. A Gathering of Spies by John Altman
  15. Selected Poems by Robinson Jeffers
  16. Hook— Tinkerbell’s Challenge by Tristar Pictures
  17. Rising Sun by Michael Crichton
  18. Changewar by Fritz Leiber
  19. The Painted Word by Tom Wolfe
  20. The Hustler by Walter Tevis
  21. The Natural by Bernard Malamud
  22. Truly Tasteless Jokes by Blanche Knott
  23. The Man Who Was Thursday by G. K. Chesterton
  24. Under the Volcano by Malcolm Lowry

What moral Vargas Llosa might draw from the above stack I do not know.

Generally, I prefer the sorts of books in a different nearby stack. See Sisteen, from May 25. That post the fanciful reader may view as related to number 16 in the above list. The reader may also relate numbers 24 and 22 above (an odd couple) to By Chance, from Thursday, July 22.

* The Web version’s title has a misprint— “living” instead of “lying.”

Thursday, October 7, 2010

Geometry and the Evening Star

Filed under: General,Geometry — m759 @ 7:20 PM

An ancient symbol of Venus, the Evening Star—


For some background, see Anti-Christmas (June 25), 2008 and The Devil and Wallace Stevens.

A purely mathematical version of the same figure—


Wednesday, October 6, 2010

Critic’s Picks

Filed under: General — m759 @ 7:20 PM
Tonight On TCM [ET]       
8:00 PM     
Citizen Kane       
10:15 PM     
Seventh Seal, The       

The Rising…

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

Notes on Mathematics and Narrative, continued

"the Citizen Kane of horror films"
Sarah Lawless quoting other reviews
in Saga of the Wicker Man,
cited here on September 7

"Frivolous as a willow on a tombstone"
— Robert Stone on "our secret culture" in A Flag for Sunrise


"world's wildfire, leave but ash"
— Gerard Manley Hopkins, S.J.,
quoted here on October 4

Happy birthday, Britt.

Claves Regni Caelorum continued…

Filed under: General — m759 @ 1:30 AM

The Praised and the Damned


Albeck died on September 29, the Feast of St. Michael and All Angels.

Tuesday, October 5, 2010


Filed under: General,Geometry — m759 @ 5:24 PM

From the American Mathematical Society today—

Richard Kane (1944-2010)
Tuesday October 5th 2010

Kane, a professor at the University of Western Ontario, died October 1 at the age of 66. He received his PhD from the University of Waterloo in 1973 under the direction of Peter Hoffman. Kane authored approximately 30 research papers and the texts The Homology of Hopf Spaces and Reflection Groups and Invariant Theory. He served as president and vice-president of the Canadian Mathematical Society and was the recipient of the Society's first David Borwein Distinguished Career Award in 2004 and its Distinguished Service Award in 2006. Kane was a member of the AMS since 1991. Read more about his life in an online obituary.


Richard Michael Kane

I added a link to a review of Kane's book on reflection groups to the Wikipedia article on that topic on August 20, 2005.

The Ending That Fell Off a Truck

Filed under: General — Tags: — m759 @ 2:19 PM

"…the ending arrives as if dropped from a passing truck."
    — Stephen Hunter, Washington Post  review of the 2007 film
   "The Invasion" (starring Nicole Kidman)



"The Invasion"



Leiber's Big Time


Related material— "The reviews are in!"— Wall Street Journal  today

See also this  journal on October First, the date of the above death.

"We've lost the plot!" — "Slipstream"

"Big time." — Dick Cheney

Monday, October 4, 2010

The Search for Wisdom

Filed under: General — m759 @ 10:25 PM

"Even before Thales fell into the well, and the ancient Greeks laid the foundation
for Western philosophy, humans were engaged in the search for wisdom…."

Introducing "The Stone," NY Times, May 16, 2010, quoted here this morning

Some have Wisdom thrust upon them.
Context— Happy Birthday Reba, 2009, and "I'll Follow a Star."


Filed under: General — m759 @ 3:09 PM

For the Feast of St. Francis of Assisi—



The above scene  was suggested by Robert Langdon's
Harvard course on Symbology —

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

Stone Junction

Filed under: General — m759 @ 6:29 AM

Continued from May 18, 2010.

Previous logo for the New York Times  feature "The Stone"—


Today's new logo, appearing retroactively



http://www.log24.com/log/pix10A/100518-TheStoneNYT.jpg   http://www.log24.com/log/pix10B/101004-NYT-thestone75.gif

From the October 3 "The Stone," Hegel on Wall Street

The “Phenomenology” is a philosophical portrait gallery that presents depictions, one after another, of different, fundamental ways in which individuals and societies have understood themselves.  Each self-understanding has two parts: an account of how a particular kind of self understands itself and, then, an account of the world that the self considers its natural counterpart.  Hegel narrates how each formation of self and world collapses because of a mismatch between self-conception and how that self conceives of the larger world.  Hegel thinks we can see how history has been driven by misshapen forms of life in which the self-understanding of agents and the worldly practices they participate in fail to correspond.  With great drama, he claims that his narrative is a “highway of despair.”

J.M. Bernstein of the New School for Social Research

A two-part self-understanding that is not  from Hegel—

1. An account of how a particular kind of self understands itself:

            … world’s wildfire, leave but ash:
                In a flash, at a trumpet crash,
I am all at once what Christ is, ' since he was what I am, and
This Jack, joke, poor potsherd, ' patch, matchwood, immortal diamond,
                Is immortal diamond.

2. An account of the world that the self considers its natural counterpart:

CLOUD-PUFFBALL, torn tufts, tossed pillows ' flaunt forth, then chevy on an air-
built thoroughfare: heaven-roysterers, in gay-gangs ' they throng; they glitter in marches.
Down roughcast, down dazzling whitewash, ' wherever an elm arches,
Shivelights and shadowtackle in long ' lashes lace, lance, and pair.
Delightfully the bright wind boisterous ' ropes, wrestles, beats earth bare
Of yestertempest’s creases; in pool and rut peel parches
Squandering ooze to squeezed ' dough, crust, dust; stanches, starches
Squadroned masks and manmarks ' treadmire toil there
Footfretted in it. Million-fuelèd, ' nature’s bonfire burns on.

Sunday, October 3, 2010

Search for the Basic Picture

Filed under: General,Geometry — Tags: — m759 @ 5:01 PM

(Click to enlarge.)


The above is the result of a (fruitless) image search today for a current version of Giovanni Sambin's "Basic Picture: A Structure for Topology."

That search was suggested by the title of today's New York Times  op-ed essay "Found in Translation" and an occurrence of that phrase in this journal on January 5, 2007.

Further information on one of the images above—


A search in this journal on the publication date of Giaquinto's Visual Thinking in Mathematics  yields the following—

Thursday July 5, 2007

m759 @ 7:11 PM

In defense of Plato’s realism

(vs. sophists’ nominalism– see recent entries.)

Plato cited geometry, notably in the Meno , in defense of his realism.
Consideration of the Meno 's diamond figure leads to the following:

The Eightfold Cube and its Inner Structure

For the Meno 's diamond figure in Giaquinto, see a review—


— Review by Jeremy Avigad (preprint)

Finite geometry supplies a rather different context for Plato's  "basic picture."

In that context, the Klein four-group often cited by art theorist Rosalind Krauss appears as a group of translations in the mathematical sense. (See Kernel of Eternity and Sacerdotal Jargon at Harvard.)

The Times  op-ed essay today notes that linguistic  translation "… is not merely a job assigned to a translator expert in a foreign language, but a long, complex and even profound series of transformations that involve the writer and reader as well."

The list of four-group transformations in the mathematical  sense is neither long nor complex, but is apparently profound enough to enjoy the close attention of thinkers like Krauss.

Saturday, October 2, 2010

Doctor of Maimonides

Filed under: General — m759 @ 7:48 PM



Filed under: General — m759 @ 5:24 AM

“Logos and logic, crystal hypothesis,
Incipit and a form to speak the word
And every latent double in the word….”

Notes Toward a Supreme Fiction

(Quoted here four years ago on October 2, 2006.)

Friday, October 1, 2010

Simply Spoken

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

“There’s still time to catch Helen Mirren in ‘The Tempest’ at the New York Film Festival”

— Headline in the New York Daily News today


And after all, it’s my wall” — E.B. White, 1933

Volcano Dawn

Filed under: General — Tags: — m759 @ 6:24 AM

Estas son las mañanitas
Que cantaba el rey David

Who is she that looketh forth as the morning,
fair as the moon, clear as the sun, and terrible as an army with banners?


Good question.

A clue:

From The Hunchback of Notre Dame :

Un cofre de gran riqueza
Hallaron dentro un pilar,
Dentro del, nuevas banderas
Con figuras de espantar.

A coffer of great richness
In a pillar’s heart they found,
Within it lay new banners,
With figures to astound.

Those who prefer more commercial banners may consult this morning’s New York Times.


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

Ay que bonito es volar
a las dos de la mañana

—  La Bruja

Diego Rivera and Frida Kahlo

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