Monday, February 28, 2011

His Kind of Diamond

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

In memory of Jane Russell

H.S.M. Coxeter's classic
Introduction to Geometry  (2nd ed.):

The image “http://www.log24.com/log/pix07/070523-Coxeter62.jpg” cannot be displayed, because it contains errors.

Note the resemblance of the central part to
a magical counterpart
the Ojo de Dios
of Mexico's Sierra Madre.

Related material page 55 of Polly and the Aunt ,
by Mary E. Blatchford.

Original Facebook

Filed under: General — m759 @ 12:00 PM

"What is your original face before you were born?" — Zen riddle

See also yesterday's sermon, the birth date of William Faulkner, and Of Time and the River.

Sunday, February 27, 2011

Oscar Sermon

Filed under: General — m759 @ 11:00 AM

From Leap Day 2004 — "Enter a Messenger."

Related material —


See also "Prince Caspian."

Saturday, February 26, 2011


Filed under: General — m759 @ 8:00 PM

A Meditation on Harvard, Pi, and Rhetoric

Recall that pi equals 3.14159… "Et cetera, et cetera, et cetera." —The King and I

IMAGE- Oscar contenders- NY Times photos of 'Social Network,' 'Black Swan,' and 'King's Speech'

Related material—

When the Man Comes Around

"It's hard for thee to kick against the pricks."

More Pricks Than Kicks

Happy birthday from Samuel Beckett to Johnny Cash.

The Pope’s Speech

Filed under: General — m759 @ 12:25 PM

Last night's post was about a talk last year at the annual student symposium of the ACCA (Associated Colleges of the Chicago Area), a group of largely Christian colleges.

The fact that the talk was by a student from Benedictine University suggests a review of the Urbi et Orbi  speech by Pope Benedict XVI on Christmas 2010.

“The Word became flesh”. The light of this truth is revealed to those who receive it in faith, for it is a mystery of love. Only those who are open to love are enveloped in the light of Christmas. So it was on that night in Bethlehem, and so it is today. The Incarnation of the Son of God is an event which occurred within history, while at the same time transcending history. In the night of the world a new light was kindled, one which lets itself be seen by the simple eyes of faith, by the meek and humble hearts of those who await the Saviour. If the truth were a mere mathematical formula, in some sense it would impose itself by its own power. But if Truth is Love, it calls for faith, for the “yes” of our hearts.

And what do our hearts, in effect, seek, if not a Truth which is also Love? Children seek it with their questions, so disarming and stimulating; young people seek it in their eagerness to discover the deepest meaning of their life; adults seek it in order to guide and sustain their commitments in the family and the workplace; the elderly seek it in order to grant completion to their earthly existence.

The above excerpt from the Pope's speech may be regarded as part of a continuing commentary on the following remark—

There is a pleasantly discursive treatment of Pontius Pilate's unanswered question "What is truth?" — H. S. M. Coxeter, 1987

Friday, February 25, 2011

Diamond Theorem Exposition

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

Victoria Blumen, Mathematics, Junior, Benedictine University
Tim Comar, Benedictine University
Secondary Source Research
Let D be a 4 by 4 block quilt shape, where each of the 16 square blocks is consists of [sic ] two triangles, one of which is colored red and the other of which is colored blue.  Let G: D -> D_g be a mapping of D that interchanges a pair of columns, rows, or quadrants of D.  The diamond theorem states that G(D) = D_g has either ordinary or color-interchange symmetry.  In this talk, we will prove the diamond theorem and explore symmetries of quilt patterns of the form G(D)."

Exercise Correct the above statement of the theorem.

Background— This is from a Google search result at about 10:55 PM ET Feb. 25, 2011—

File Format: Microsoft Word – 14 hours ago –
Let G: D -> D_g be a mapping of D that interchanges a pair of columns, rows, or quadrants of D. The diamond theorem states that G(D) = D_g has either

The document is from a list of mathematics abstracts for the annual student symposium of the ACCA (Associated Colleges of the Chicago Area) held on April 10, 2010.

Update of Feb. 26For a related remark quoted here  on the date of the student symposium, see Geometry for Generations.

Thursday, February 24, 2011

Now Lens (continued)

Filed under: General — m759 @ 10:48 AM

"…the farther back we manage to wiggle
 the more we need the loan of a lens…." —Finnegans Wake

For some background on the lens below, see the sermon on February 20th, 2011.

Image-- The Asterisk of Evil

Finnegans Wake

“The quad gospellers may own the targum but any of the Zingari shoolerim
 may pick a peck of kindlings yet from the sack of auld hensyne.”

The above "Zingari shoolerim" passage was quoted here in Frame Tales (November 10th, 2008).

That post concerned the Heinrich Zimmer tale "The King and the Corpse." Some related material—


For Esmeralda

Filed under: General — m759 @ 12:00 AM

A sequel to Quadrat, Spring Style, and Jewel in the Crown


Click image for further details.

Wednesday, February 23, 2011

Jewel in the Crown

Filed under: General — m759 @ 2:00 PM


For seven — Two poems: Lord Shiva and somewhere i have never travelled

Incidentally… " 'Posh' is a word in Romany, the language of Gypsies, meaning 'half.' According to poet and etymologist John Ciardi, the word originally entered the argot of England's underworld in the 17th century in such compounds as 'posh-houri,' meaning 'half-pence,' and soon became a slang term for money in general. From there it was a short hop to meaning 'expensive' or 'fancy.' … the Gypsies… came originally from Northern India…." Word-Detective.com

Word detectives who are too clever by half may enjoy some context —


Spring Style*

Filed under: General — m759 @ 11:00 AM



From www.4to40.com/poems/

* Suggested by yesterday's post on a Martin Harris Centre production of "Posh,"
  by last night's remarks on horseness and Guild Awards, and
  by last year's  February Mysteries of Faith.

In Nomine Patris

Filed under: General — m759 @ 2:02 AM

In memory of Pete Postlethwaite, who played father figures in
"In the Name of the Father" and in "Inception."

He died on January 2, 2011.

"And I looked and behold: a pale horse" — Johnny Cash

This journal on the day of Postlethwaite's death—


For somewhat deeper discussions see "Blackburn+universals" in this journal.

"It is arguable that this is always the deepest, most profound problem of philosophy.”

– Simon Blackburn, Think  (Oxford, 1999)

Tuesday, February 22, 2011


Filed under: General — m759 @ 1:09 PM

Quotes from the new film "Unknown" —

  • "Welcome to Berlin."
  • "There is no Martin Harris."

Related fantasia —

Ad for PoshClick to enlarge



Filed under: General — m759 @ 12:00 PM

From May 11, 2010, an image—

Image-- The 4-dimensional space over the 2-element field

See also the same date in 2005 in light of


Filed under: General — m759 @ 12:12 AM



Related illustration —


Monday, February 21, 2011

For What It’s Worth

Filed under: General — m759 @ 11:32 PM

Christchurch Philosophy. See also today's news.

How Deep the Rabbit Hole Goes

Filed under: General — m759 @ 3:17 PM

The sequel to Another Manic Monday and The Abacus Conundrum


You'll glitter and gleam so
Make somebody dream so that
Some day he may buy you a ring, ringa-linga
I've heard that's where it leads…


Related material — Janet's Tea Party

The Abacus Conundrum*

From Das Glasperlenspiel  (Hermann Hesse, 1943) —

“Bastian Perrot… constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors. The wires corresponded to the lines of the musical staff, the beads to the time values of the notes, and so on. In this way he could represent with beads musical quotations or invented themes, could alter, transpose, and develop them, change them and set them in counterpoint to one another. In technical terms this was a mere plaything, but the pupils liked it.… …what later evolved out of that students’ sport and Perrot’s bead-strung wires bears to this day the name by which it became popularly known, the Glass Bead Game.”

From “Mimsy Were the Borogoves” (Lewis Padgett, 1943)—

…”Paradine looked up. He frowned, staring. What in—
…”Is that an abacus?” he asked. “Let’s see it, please.”
…Somewhat unwillingly Scott brought the gadget across to his father’s chair. Paradine blinked. The “abacus,” unfolded, was more than a foot square, composed of thin,  rigid wires that interlocked here and there. On the wires the colored beads were strung. They could be slid back and forth, and from one support to another, even at the points of jointure. But— a pierced bead couldn’t cross interlocking  wires—
…So, apparently, they weren’t pierced. Paradine looked closer. Each small sphere had a deep groove running around it, so that it could be revolved and slid along the wire at the same time. Paradine tried to pull one free. It clung as though magnetically. Iron? It looked more like plastic.
…The framework itself— Paradine wasn’t a mathematician. But the angles formed by the wires were vaguely shocking, in their ridiculous lack of Euclidean logic. They were a maze. Perhaps that’s what the gadget was— a puzzle.
…”Where’d you get this?”
…”Uncle Harry gave it to me,” Scott said on the spur of the moment. “Last Sunday, when he came over.” Uncle Harry was out of town, a circumstance Scott well knew. At the age of seven, a boy soon learns that the vagaries of adults follow a certain definite pattern, and that they are fussy about the donors of gifts. Moreover, Uncle Harry would not return for several weeks; the expiration of that period was unimaginable to Scott, or, at least, the fact that his lie would ultimately be discovered meant less to him than the advantages of being allowed to keep the toy.
…Paradine found himself growing slightly confused as he attempted to manipulate the beads. The angles were vaguely illogical. It was like a puzzle. This red bead, if slid along this  wire to that  junction, should reach there— but it didn’t. A maze, odd, but no doubt instructive. Paradine had a well-founded feeling that he’d have no patience with the thing himself.
…Scott did, however, retiring to a corner and sliding beads around with much fumbling and grunting. The beads did  sting, when Scott chose the wrong ones or tried to slide them in the wrong direction. At last he crowed exultantly.
…”I did it, dad!”
…””Eh? What? Let’s see.” The device looked exactly the same to Paradine, but Scott pointed and beamed.
…”I made it disappear.”
…”It’s still there.”
…”That blue bead. It’s gone now.”
…Paradine didn’t believe that, so he merely snorted. Scott puzzled over the framework again. He experimented. This time there were no shocks, even slight. The abacus had showed him the correct method. Now it was up to him to do it on his own. The bizarre angles of the wires seemed a little less confusing now, somehow.
…It was a most instructive toy—
…It worked, Scott thought, rather like the crystal cube.

* Title thanks to Saturday Night Live  (Dec. 4-5, 2010).

Another Manic Monday

Filed under: General — m759 @ 10:48 AM

"The curriculum begins with a game called Winding Around Positions.
There are twelve stations that could represent hours on a clock
or the Chinese years zodiac."

— The current (March 2011) Notices of the American Mathematical Society

Background — "Winding Games" (pdf, 1.43 MB)—


For the not-too-tightly wound —

“Always with a little humor.” – Dr. Yen Lo  (See The China Candidate and Humorism)

We are now at the Year of the Rabbit

(Click images for sources.)

http://www.log24.com/log/pix11/110221-DarkoRabbitSm.jpg IMAGE- Scene from a film based on the old SF story 'Mimsy Were the Borogoves'

Sunday, February 20, 2011

Sunday Dinner

Filed under: General — m759 @ 2:00 PM

Judith Shulevitz at The New York Times
on Sunday, July 18, 2010 —

"What would an organic Christian Sabbath look like today?
For James Carroll, an ex-priest and dissenting Catholic
in Boston (he is the author of Practicing Catholic ,
published in 2009), it would look like the Sunday dinners
of his childhood. These were big formal meals,
held at 2 p.m. every Sunday….

'If Jesus were to visit us, it would have been
the Sunday dinner he would have insisted on
being a part of, not the worship service at the church.'"

Possible Table Topics

Arts & Letters Daily (20 Feb 2011)

Sat Feb 19, 2011 23:00

Nobody likes a grammar scold, but it must be said:
Ambiguity has a death grip on our syntax.
The principles of effective speech are in tatters.
Verbal chaos reigns… more

How did the armies of Mordor cope with defeat?
A retelling of The Lord of the Rings
is more complicated and less sentimental
than the original… more

Is philosophy of science an obsolete
pseudo-discipline? Stephen Hawking thinks so.
But his work relies on the very sort of speculations
that philosophers invented… more

Some background for the discussion —

A book said to have received 15,480 reviews—


Brightness at Noon (continued)

Filed under: General — m759 @ 12:00 PM

IMAGE- 'There IS such a thing as a tesseract.'


Filed under: General,Geometry — m759 @ 10:30 AM

From Galleri MGM in Oslo —


Josefine Lyche
Theme and Variations
26. February – 28. March 2009
Opening reception 26. February 19.00 – 21.00

"Why do we remember the past, but not the future?"
Stephen Hawking, A Brief History of Time, Ch. 9, "The Arrow of Time"

"If you want a vision of the future, imagine a boot stamping on a human face – forever."
George Orwell

Galleri MGM is pleased to present the second solo exhibition by Josefine Lyche (b.1973).

Lyche presents a body of work consisting of sculptures and a wall painting, as well as a series of new paperwork, all using geometrical abstractions and light as a medium. Her work dissolves boundaries between fiction and documentation, depicting how fantasies and dreams collide with and yet help determine the shape of reality.

Theme and variations is a term most commonly used in the music genre as a musical form in which the fundamental musical idea, or theme, is repeated in altered form or accompanied in a different manner.

The exhibition explores geometric shapes and solids and revisits work of artists like Robert Morris and Ellsworth Kelly, giving it a disco treatment of glitter, neon and gloss. The mathematical, science-fiction and new age references incorporated in the works comments on the ambivalent foretelling of utopian hope and dystopian vision of a near, yet unknown future.

The transmission between past and future is shown in the sculpture "The Omega Point" a portal that leads in or out of time and space. …

A connection to today's earlier post, Sunday SchoolThe Oslo Version, from Friday, May 21, 2010.

Lyche's "Omega Point" portal, together with her last name, suggested three posts from the following Saturday morning— which later proved to be the date of Martin Gardner's death—

Art Space, Through the Lyche Gate and The Lyche Gate Asterisk.

For some further religious remarks, see November 9th, 2010— A Theory of Pure Design.

Sunday School

Filed under: General,Geometry — Tags: — m759 @ 9:29 AM

Annals of Finite Geometry:
A Quarter-Century of the Relativity Problem


(Click to enlarge.)

Saturday, February 19, 2011

Brightness at Noon (continued)

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

From Epiphany Revisited


A star figure and the Galois quaternion.

The square root of the former is the latter.

… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

Rubén Darío

Paradigms Lost

Filed under: General — Tags: — m759 @ 11:32 AM

IMAGE- 'Harvard Thinks Big 2' event on Thursday, Feb. 17, 2011

Harvard Science Review (Winter 1997) on Thomas Kuhn's
The Structure of Scientific Revolutions

"…his language often portrays paradigms as cults
 and the battle between paradigms as quasi-religious wars."

Related material: This journal's "Paradigms" on February 17th
and the following notes—

The Harvard Style, Epiphany 2010, and Epiphany 2011.

Friday, February 18, 2011

Diary of a Comedian

Filed under: General — m759 @ 10:10 AM

From this journal yesterday—

American Spectator – Ben Stein's Diary: Watch …

A vertiginous occlusion  opened at my feet…

From The New York Times  today—

"Isn’t it true that every great comedian operates on the edge of an abyss?"

Thursday, February 17, 2011


Filed under: General,Geometry — Tags: — m759 @ 4:16 PM

"These passages suggest that the Form is a character or set of characters
common to a number of things, i.e. the feature in reality which corresponds
to a general word. But Plato also uses language which suggests not only
that the forms exist separately (χωριστά ) from all the particulars, but also
that each form is a peculiarly accurate or good particular of its own kind,
i.e. the standard particular of the kind in question or the model (παράδειγμα )
[i.e. paradigm ] to which other particulars approximate….

… Both in the Republic  and in the Sophist  there is a strong suggestion
that correct thinking is following out the connexions between Forms.
The model is mathematical thinking, e.g. the proof given in the Meno
that the square on the diagonal is double the original square in area."

— William and Martha Kneale, The Development of Logic,
Oxford University Press paperback, 1985

Plato's paradigm in the Meno


Changed paradigm in the diamond theorem (2×2 case) —


Aspects of the paradigm change* —

Monochrome figures to
colored figures

Areas to

Continuous transformations to
non-continuous transformations

Euclidean geometry to
finite geometry

Euclidean quantities to
finite fields

Some pedagogues may find handling all of these
conceptual changes simultaneously somewhat difficult.

* "Paradigm shift " is a phrase that, as John Baez has rightly pointed out,
should be used with caution. The related phrase here was suggested by Plato's
term παράδειγμα  above, along with the commentators' specific reference to
the Meno  figure that serves as a model. (For "model" in a different sense,
see Burkard Polster.) But note that Baez's own beloved category theory
has been called a paradigm shift.

Les Mots

Filed under: General — m759 @ 11:07 AM

The White Album – Google Books Result

Joan Didion – 1990 – Fiction – 222 pages
a slippage, a certain vertiginous occlusion  of the imagined and the real, and this slippage was particularly acute the last time I arrived in Honolulu,

American Spectator – Ben Stein's Diary: Watch …

A vertiginous occlusion  opened at my feet… …He had so much time to spend with me it was hard to believe… …The food was ghastly, simply horrible,

"— and such small portions!"

Figure in the Carpet

Filed under: General — Tags: , — m759 @ 2:02 AM

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

– Steppenwolf lyrics

"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 Nabokov at Harvard in today's Crimson
and the Russian boxes of Henry James.

The Form, the Pattern

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

"…  Only by the form, the pattern,     
Can words or music reach
The stillness…."

— T. S. Eliot,
Four Quartets

For further details, see Time Fold.

Wednesday, February 16, 2011

Time Frames

Filed under: General — m759 @ 8:00 PM

From this evening's online New York Times

Flock Around ‘The Clock’


“The Clock,” a video work by Christian Marclay, uses thousands of film and television clips of timepieces to create, minute by minute, a 24-hour montage that unfolds in real time.

Benjamin Norman for The New York Times

“The Clock,” a video work by Christian Marclay, uses thousands of film and television clips of timepieces to create, minute by minute, a 24-hour montage that unfolds in real time.

“The Clock,” a 24-hour video work by Christian Marclay, draws crowds at the Paula Cooper Gallery in Chelsea.

Critic’s Notebook

The Musical Rhythms in Images Out of Time


Time is a kind of music, music is a kind of time, and Christian Marclay seems to understand this implicitly.

See also Don DeLillo's Point Omega , a novel published on Groundhog Day, 2010.


Filed under: General — m759 @ 2:02 PM

From the previous post, Stations of the Clock

"A reference station is selected… and one student
 sits at that station throughout the game."


Finnegans Wake

Book II

Episode 2

James Joyce

As we there are where are we are we there   UNDE ET UBI.

Stations of the Clock

Filed under: General — m759 @ 11:07 AM

Notices of the American Mathematical Society , March 2011

An Example

As a final example, here is a brief outline of curriculum
material based on certain games for the topic
of modular arithmetic….

The curriculum begins with a game called Winding
Around Positions. There are twelve stations
that could represent hours on a clock or the Chinese
years zodiac. A reference station is selected
(in general, selections are made by the class with
some input from the teacher), and one student
sits at that station throughout the game.

Related material—


See also Crucified on the Wheel of Time.

Tuesday, February 15, 2011

Glad Rags

Filed under: General — Tags: , — m759 @ 9:24 PM

For Fashion Week 2011—



The “Hi, Boys” Look



The Grammaton-Cleric Look

Annals of Symbolism

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

A phrase from last night's post— "God's empty chair."

For related material from this journal, see The Empty Chair.

A related scene from mathematics education (the theme of the new March 2011 AMS Notices )—

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

"Plato acknowledges how khora  challenges our normal categories
 of rational understanding. He suggests that we might best approach it
 through a kind of dream  consciousness."

  –Richard Kearney, quoted here Sunday afternoon

"You make me feel like I'm living a teenage dream."

Song at Sunday night's Grammy awards

"Put your glad rags on and join me, hon…"

Road House

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

A 1948 classic

Again, this couldn't happen again.
This is that "once in a lifetime,"
this is the thrill divine.

The great 1949 days (according to Jack Kerouac)—

IMAGE-- Scene from 'Blackboard Jungle,' 1955

On the Road

Shearing began to play his chords; they rolled out of the piano in great rich showers, you'd think the man wouldn't have time to line them up. They rolled and rolled like the sea. Folks yelled for him to "Go!" Dean was sweating; the sweat poured down his collar. "There he is! That's him! Old God! Old God Shearing! Yes! Yes! Yes!" And Shearing was conscious of the madman behind him, he could hear every one of Dean's gasps and imprecations, he could sense it though he couldn't see. "That's right!" Dean said. "Yes!" Shearing smiled; he rocked. Shearing rose from the piano, dripping with sweat; these were his great 1949 days before he became cool and commercial. When he was gone Dean pointed to the empty piano seat. "God's empty chair," he said.

Monday, February 14, 2011

Simplify (continued)

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

"Plato acknowledges how khora  challenges our normal categories
 of rational understanding. He suggests that we might best approach it
 through a kind of dream  consciousness."
  —Richard Kearney, quoted here yesterday afternoon

"You make me feel like I'm living a teenage dream."
 — Song at last night's Grammy awards

Image-- Richard Kiley with record collection in 'Blackboard Jungle,' 1955

Richard Kiley in "Blackboard Jungle" (1955)
Note the directive on the blackboard.

Quoted here last year on this date

Alexandre Borovik's Mathematics Under the Microscope  (American Mathematical Society, 2010)—

"Once I mentioned to Gelfand that I read his Functions and Graphs ; in response, he rather sceptically asked me what I had learned from the book. He was delighted to hear my answer: 'The general principle of always looking at the simplest possible example.'….

So, let us look at the principle in more detail:

Always test a mathematical theory on the simplest possible example…

This is a banality, of course. Everyone knows it; therefore, almost no one follows it."

Related material— Geometry Simplified and A Simple Reflection Group of Order 168.

"Great indeed is the riddle of the universe.
 Beautiful indeed is the source of truth."

– Shing-Tung Yau, Chairman,
Department of Mathematics, Harvard University

"Always keep a diamond in your mind."

King Solomon at the Paradiso

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

Image from stoneship.org

Sunday, February 13, 2011

Where Entertainment is God (continued)

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

"… the clocks were striking thirteen…"

"Entertainment continued," a Log24 post last year on this date, suggests…

A reading from Richard Kearney's Strangers, Gods and Monsters  (Routledge, 2003)—

IMAGE- Richard Kearney on 'khora' in 'Strangers, Gods and Monsters'

Neither earth nor air nor fire nor water… perhaps a Fifth Element  ?

Friday, February 11, 2011


Filed under: General — m759 @ 1:00 PM

And I'd  like to thank the heroine of Finale

Image-- Josefine Lyche as Diamond Girl, representing the soul's triumph over evil

*  The title refers to a 2009 sculpture by Lyche


   For a related shape, see today's noon post.

Brightness at Noon (continued)

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

From The Seventh Symbol

The image “http://www.log24.com/theory/images/GF64-63cycleA495.gif” cannot be displayed, because it contains errors.

"First of all, I'd like to thank the Academy…"

Wednesday, February 9, 2011

An Abstract Window

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

The sliding window in blue below


Click for the web page shown.

is an example of a more general concept.

Such a sliding window,* if one-dimensional of length n , can be applied to a sequence of 0's and 1's to yield a sequence of n-dimensional vectors. For example— an "m-sequence" (where the "m" stands for "maximum length") of length 63 can be scanned by a length-6 sliding window to yield all possible 6-dimensional binary vectors except (0,0,0,0,0,0).

For details, see A Galois Field


The image is from Bert Jagers at his page on the Galois field GF(64) that he links to as "A Field of Honor."

For a discussion of the m-sequence shown in circular form above, see Jagers's  "Pseudo-Random Sequences from GF(64)." Here is a noncircular version of the length-63 m-sequence described by Jagers (with length scale below)—


This m-sequence may be viewed as a condensed version of 63 of the 64 I Ching  hexagrams. (See related material in this journal.)

For a more literary approach to the window concept, see The Seventh Symbol (scroll down after clicking).

* Moving windows also appear (in a different way) In image processing, as convolution kernels .

An Abstract Power

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

Two characters named “Black” and “White” debate religion and the afterlife in the Cormac McCarthy play “The Sunset Limited.”

The play opened in Chicago in a Steppenwolf Theatre production on May 18, 2006.

A New York Times  theater review from All Hallows’ Eve, 2006—

“…there is an abstract power in the mysteriousness of Mr. McCarthy’s
vision’s allowing for a multitude of interpretations.” –Jason Zinoman

The current New Yorker  (Feb.14) has a note
by Lillian Ross on the same play— “Two-Man Show: O Death


Some purely visual black-and-white variations that are less dramatic, but have their own “abstract power”—

A book cover pictured here last November to contrast with
“the sound and fury of the rarified Manhattan art world”—


and a web page with multiple interpretations of the book cover’s pattern—


A synchronicity— The first version of “Symmetry Framed” was done
on May 18, 2006— the day “The Sunset Limited” opened.

Another synchronicity relates the mathematics underlying
such patterns to the Halloween date of the above review.
See “To Announce a Faith,” from October 31, 2006.

Tuesday, February 8, 2011

Cold Mountain

Filed under: General — Tags: — m759 @ 12:48 AM

For Nicole (see Jan. 9).

"Ninth of January, Two Thousand… and Eleven." — Andrew Keeling


This, with the entry on Nicole from January ninth,
suggests the following dialogue from
"Escape to Witch Mountain" (1975)—

Where are the others? 
Other kids?

Neighbors, I mean.  
There are no neighbors.
Look out of the window. Go on...                   
Look as far as you can see.                   
Mr. Bolt owns everything in sight.   
Well, I could see the sky.

See also "establishment of the Talented" in this journal.

Monday, February 7, 2011

An Ordinary Evening

Filed under: General — m759 @ 11:32 PM

Happy birthday to G. H. Hardy and E. T. Bell.

"It was a perfectly ordinary night at Christ’s high table, except that Hardy was dining as a guest."


Reappearing All Over Again

Filed under: General — m759 @ 1:06 PM

A sequel to "A Reappearing Number," "Reappearing Continued," and "Classical Requiem"—

IMAGE- Page 168 of 'Moonshine Beyond the Monster,' on the number 24

A connection to the numerology of today's date, The Seventh— "Frame Tale." (Click, then scroll down.)

Sunday, February 6, 2011

Classical Requiem

Filed under: General — m759 @ 12:00 PM

Quotation from an obituary on page A24 of the New York edition of today's New York TImes

“Even Gods Must Die.”


Related material from Log24 on the day this classical singer of India died
and on the following day—

Monday, January 24, 2011

A Reappearing Number, continued

m759 @ 12:24 PM 

"In the work of Ramanujan, the number 24 appears repeatedly. This is an example of what mathematicians call magic numbers, which continually appear, where we least expect them, for reasons that no one understands."

– Michio Kaku, Hyperspace, Oxford U. Press, 1994, p. 173

See also "A Reappearing Number," this journal, July 4, 2010.

Tuesday, January 25, 2011

A song.

IMAGE- Detail of a photo by Richard Newton at flickr.com

Related material— a video of the song—
Ida Lupino in "Road House" (1948) singing "Again."

See also this journal's Twelfth Night posts. (Note particularly the 4/01 link.)

Saturday, February 5, 2011

Lament for Camelot

Filed under: General — m759 @ 7:20 PM

New York Times this afternoon



"Everybody's leavin' town…" — The King

Zen and the Art of Philosophy

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

Wallace Stevens Concordance

An Ordinary Evening in New Haven
line 540 (xxx.18): In which hundreds of eyes, in one mind, see at once.

The cover art of a 1976 monograph, "Diamond Theory," was described in this morning's post.

As Madeleine L'Engle noted in 1976, the cover art resembles the character Proginoskes in her novel A Wind in the Door.

A search today for Proginoskes yields a description by Brendan Kidwell


A link at Kidwell's site leads to a weblog by Jeff Atwood, a founder of Stack Overflow, a programmers' question-and-answer site.
(Stack Overflow is said to have inspired the similar site for mathematicians, Math Overflow.)

Yesterday Atwood discussed technical writing.

This suggests a look at Robert M. Pirsig on that subject in his 1974 philosophical novel Zen and the Art of Motorcycle Maintenance.

(See also a document on Pirsig's technical-writing background.)

Pirsig describes his novel as "a sort of Chautauqua."

This, together with the Stevens and Proginoskes quotes above, leads back to the Log24 Feb. 1 post The Search.

An image from that post (click to enlarge)—


Here the apparently fragmented nature of the set of
images imagined as rising above the podium of the
Hall of Philosophy at Chautauqua rather naturally
echoes Stevens's "hundreds of eyes" remark.

Cover Art

Filed under: General,Geometry — m759 @ 3:17 AM

Click to enlarge


This updates a webpage on the 4×4 Latin squares.

Thursday, February 3, 2011

Brightness at Noon (continued)

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

"The predicate of bright origin"

— A phrase of Wallace Stevens from "An Ordinary Evening in New Haven" (1950)

Perhaps the predicate Stevens means is "bright."

If so, an apt illustration can be found on the cover of
the 1943 first edition of Hesse's Glasperlenspiel


See also Stevens's use of the phrase "heaven-haven" in "Notes" (1942),
the original plan of New Haven, and related scholia in this journal.


… Todo lo sé por el lucero puro
que brilla en la diadema de la Muerte.

– Rubén Darío

An academic work from 2003 discusses Stevens's "Notes" as
"a perfect geometric whole."

Note that "perfect" means "complete, finished, done."

Summa Mythologica, continued…

Filed under: General — Tags: , — m759 @ 10:30 AM

Yesterday's New York Lottery— Midday 392, Evening 946.

Catechism of the Catholic Church

392   Scripture speaks of a sin of these angels. This "fall" consists in the free choice of these created spirits, who radically and irrevocably rejected  God and his reign. We find a reflection of that rebellion in the tempter's words to our first parents: "You will be like God." The devil "has sinned from the beginning"; he is "a liar and the father of lies."

946   After confessing "the holy catholic Church," the Apostles' Creed adds "the communion of saints." In a certain sense this article is a further explanation of the preceding: "What is the Church if not the assembly of all the saints?" The communion of saints is the Church.

Some context related to last night's Rite of Change

Glasperlenspiel  Philosophy.

Those who prefer Dan Brown to Hermann Hesse may consult Fast Forward.

Wednesday, February 2, 2011

Rite of Change

Filed under: General — m759 @ 11:32 PM

An image suggested by the date July 19, 2010

the day that abstract painter Alan Uglow (see this morning's Origin) turned 69—


Some background — In the Details and Savage Logic.

Candlemas Requiem

Filed under: General — m759 @ 6:00 PM

Continuing the Hall of Philosophy series…

Et in Arcadia ego  and

A New Heaven Opening.


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

"the predicate* of bright origin"

— A phrase of Wallace Stevens quoted here yesterday

One origin, noted here on January 25

IMAGE- Detail of a photo by Richard Newton at flickr.com

This commemorated the death of noted discographer Brian Rust.
Rust appears in today's New York Times  obituary index—


Also in today's obituaries: artist Alan Uglow, who reportedly died on January 20.

A link ("Noland") from this journal on that date leads to… a geometric origin.

“At the still point,
there the dance is.”
— T. S. Eliot

What Stevens's "predicate" is, I do not know.
Eliot's predicate would seem to be "still."

Related material—  The dance from "Pulp Fiction"** illustrated here
on the Feast of St. Michael and All Angels last year.


* Some background for the Hall of Philosophy (yesterday's post)—
"Unity of the Proposition" at Wikipedia and at Oxford University Press.

** A flickr.com page gives examples. (The link is thanks to The Ghost Light).

Tuesday, February 1, 2011

The Search

Filed under: General — m759 @ 10:01 AM

An image suggested by last night's PBS hour "Chautauqua: An American Narrative"—


Click for larger versions of the image search and of the Hall of Philosophy.

Both the screenshot and the Chautauqua photo (by jbi46 at flickr.com) were taken on July 19th, 2010.

The screenshot appeared in the post "Pediments of Appearance" (which also included two much less complex images).

Some background —  A webpage on  Analytical Cubism and a related search in this journal.

From Wallace Stevens, who appears at top center in the image above—

An Ordinary Evening in New Haven, XXII

Professor Eucalyptus said, “The search
For reality is as momentous as
The search for god.” It is the philosopher’s search

For an interior made exterior
And the poet’s search for the same exterior made
Interior: breathless things broodingly abreath

With the Inhalations of original cold
And of original earliness. Yet the sense
Of cold and earliness is a daily sense,

Not the predicate of bright origin.
Creation is not renewed by images
Of lone wanderers. To re-create, to use

The cold and earliness and bright origin
Is to search. Likewise to say of the evening star,
The most ancient light in the most ancient sky,

That it is wholly an inner light, that it shines
From the sleepy bosom of the real, re-creates,
Searches a possible for its possibleness.

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