Friday, April 30, 2021

Box759 Logo

Filed under: General — Tags: — m759 @ 3:52 PM

Continuing Work on Box759:

Filed under: General — Tags: — m759 @ 6:02 AM

Wednesday, August 26, 2020

Plan 9 from Prescott Street*

Filed under: General — m759 @ 2:22 AM

Plan 9 deals with the resurrection of the dead.” 

IMAGE- Bill Murray explains Ed Wood's 'Plan 9 from Outer Space'

* See the previous post‘s link to the phrase
“Turn on, tune in, drop dead.”

Saturday, April 4, 2020

Plan 9 From Yale…

Filed under: General — Tags: — m759 @ 10:22 AM


Sunday, March 29, 2020

Plan 9 from Yale

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

“Play ‘Stella by Starlight’ for Lady Macbeth” — Bob Dylan

Thursday, August 29, 2019

Plan 9

Filed under: General — Tags: , — m759 @ 6:20 PM

Continuing the themes of the last three posts, which
are now also tagged News Women . . .

"publishDate":"04-07-2017 01:48"


Tuesday, July 9, 2019

Schoolgirl Space: 1984 Revisited

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

Cube Bricks 1984 —

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

From "Tomorrowland" (2015) —

From John Baez (2018) —

See also this morning's post Perception of Space 
and yesterday's Exploring Schoolgirl Space.

Sunday, June 16, 2019

Master Plan from Outer Space

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

IMAGE- The large Desargues configuration and Desargues's theorem in light of Galois geometry

Sunday, February 17, 2019

For the Schoolgirls of 1959

Filed under: General — Tags: — m759 @ 1:35 PM

The dies natalis  of St. Buddy Holly was Feb. 3, 1959.

This  year on Feb. 3, a geometric illustration of the well-known
schoolgirl problem was added to a brand-new Wikipedia article
on the finite geometry PG(3,2).

Tuesday, October 17, 2017

Plan 9 Continues

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

See also Holy Field in this journal.

Some related mathematics —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Analysis of the Lo Shu structure —

Structure of the 3×3 magic square:

4  9  2
3  5  7    decreased by 1 is
8  1  6

3  8  1
2  4  6
7  0  5

In base 3 —

10  22  01
02  11  20
21  00  12

As orthogonal Latin squares
(a well-known construction) —

1  2  0     0  2  1
0  1  2     2  1  0
2  0  1     1  0  2 .

— Steven H. Cullinane,
October 17, 2017

Wednesday, September 13, 2017

Summer of 1984

The previous two posts dealt, rather indirectly, with
the notion of "cube bricks" (Cullinane, 1984) —

Group actions on partitions —

Cube Bricks 1984 —

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

Another mathematical remark from 1984 —

For further details, see Triangles Are Square.

Tuesday, April 4, 2017

Plan 9 Continues

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

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

— Bill Murray in "Ed Wood"

For The Church of Plan 9

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

Wednesday, June 24, 2015

Scoring Plan 9

Filed under: General — Tags: , — m759 @ 6:33 PM

In keeping with the resurrection themes of the
previous post and of "Plan 9 from Outer Space,"
here is a link to the soundtrack of "Field of Dreams."

Related material:

A post of March 11, 2014, on
truth, cornfields, and Rebecca Goldstein —
Dark Fields of the Republic.

R.I.P., James Horner.

Sunday, November 30, 2014

Two Physical Models of the Fano Plane

Filed under: General,Geometry — Tags: , , — m759 @ 1:23 AM

The Regular Tetrahedron

The seven symmetry axes of the regular tetrahedron
are of two types: vertex-to-face and edge-to-edge.
Take these axes as the "points" of a Fano plane.
Each of the tetrahedron's six reflection planes contains 
two vertex-to-face axes and one edge-to-edge axis.
Take these six planes as six of the "lines" of a Fano
plane. Then the seventh line is the set of three 
edge-to-edge axes.

(The Fano tetrahedron is not original with me.
See Polster's 1998 A Geometrical Picture Book pp. 16-17.)

The Cube

There are three reflection planes parallel to faces
of the cube. Take the seven nonempty subsets of
the set of these three planes as the "points" of a
Fano plane. Define the Fano "lines" as those triples
of these seven subsets in which each member of
the triple is the symmetric-difference sum of the 
other two members.

(This is the eightfold cube  discussed at finitegeometry.org.)

Wednesday, November 26, 2014

A Tetrahedral Fano-Plane Model

Filed under: General,Geometry — Tags: — m759 @ 5:30 PM

Update of Nov. 30, 2014 —

It turns out that the following construction appears on
pages 16-17 of A Geometrical Picture Book , by 
Burkard Polster (Springer, 1998).

"Experienced mathematicians know that often the hardest
part of researching a problem is understanding precisely
what that problem says. They often follow Polya's wise
advice: 'If you can't solve a problem, then there is an
easier problem you can't solve: find it.'"

—John H. Conway, foreword to the 2004 Princeton
Science Library edition of How to Solve It , by G. Polya

For a similar but more difficult problem involving the
31-point projective plane, see yesterday's post
"Euclidean-Galois Interplay."

The above new [see update above] Fano-plane model was
suggested by some 1998 remarks of the late Stephen Eberhart.
See this morning's followup to "Euclidean-Galois Interplay" 
quoting Eberhart on the topic of how some of the smallest finite
projective planes relate to the symmetries of the five Platonic solids.

Update of Nov. 27, 2014: The seventh "line" of the tetrahedral
Fano model was redefined for greater symmetry.

Tuesday, September 16, 2014

Plan 9

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

(Continued from St. Augustine's Day, 2012)

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

Epigraph to "No Great Magic," a story by Fritz Leiber:

 To bring the dead to life
Is no great magic.
Few are wholly dead:
Blow on a dead man’s embers
And a live flame will start.


Friday, September 11, 2009

Friday September 11, 2009

Filed under: General — Tags: — m759 @ 1:00 PM
For 9/11

Cover of 'Underworld,' by Don DeLillo, First Edition, Advance Reader's Copy, 1997


Cover of Underworld,
 by Don DeLillo, First Edition,
 Advance Reader's Copy, 1997

"Time and chance
happeneth to them all."
Ecclesiastes 9:11  

Related material:

1. The previous entry, on
  Copenhagen physicist
Aage Bohr, and      
2. Notes from this journal
 from Bohr's birthday,
 June 19th, through  
        Midsummer Night, 2007…
 including notes on   
  Faust in Copenhagen
   3. Walpurgisnacht 2008 and
 Walpurgisnacht 2009

Friday September 11, 2009

Filed under: General,Geometry — Tags: — m759 @ 2:56 AM
 in memory of
physicist Aage Bohr,
who died at 87 on
Tuesday, Sept. 8, 2009

Swarthmore physics honors thesis, 136 pp., 2007–


"Quantum mechanics, which has no completely accepted interpretation but many seemingly strange physical results, has been interpreted in a number of bizarre and fascinating ways over the years. The two interpretations examined in this paper, [Aage] Bohr and [Ole] Ulfbeck's 'Genuine Fortuitousness' and Stuckey, Silberstein, and Cifone's 'Relational Blockworld,' seem to be two such strange interpretations; Genuine Fortuitousness posits that causality is not fundamental to the universe, and Relational Blockworld suggests that time does not act as we perceive it to act. In this paper, I analyze these two interpretations…."

Footnote 55, page 114:
"Thus far, I have been speaking in fairly abstract terms, which can sometimes be unhelpful on the issue of explaining anything about the structure of space-time. I want to pause for a moment to suggest a new potential view of the blockworld within a 'genuinely fortuitous' universe in more visual terms. Instead of the 'static spacetime jewel' of blockworld that is often invoked by eternalists to help their readers conceptualize of what a blockworld would 'look like' from the outside, now imagine that a picture on a slide is being projected onto the surface of this space-time jewel."

Interpolated figure
from Log24:


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

Cf. August 5, 2009.

From the perspective of one inside the jewel, one might ask 'Why is this section blue while this section is black?,' and from within the jewel, one could not formulate an answer since one could not see the entire picture projected on the jewel; however, from outside the jewel, an observer (some analogue of Newton's God, perhaps, looking down on his 'sensorium' from the 5th dimension) could easily see the pattern and understand that all of the 'genuinely fortuitous' events inside the space-time jewel are, in fact, completely determined by the pattern in the projector."

— "Genuine Fortuitousness, Relational Blockworld, Realism, and Time" (pdf), by Daniel J. Peterson, Honors Thesis, Swarthmore College, December 13, 2007

Monday, September 7, 2009

Monday September 7, 2009

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

Magic Boxes

"Somehow it seems to fill my head with ideas– only I don't exactly know what they are!…. Let's have a look at the garden first!"

— A passage from Lewis Carroll's Through the Looking-Glass. The "garden" part– but not the "ideas" part– was quoted by Jacques Derrida in Dissemination in the epigraph to Chapter 7, "The Time before First."

 on the passage:

Part I    "The Magic Box,"  shown on Turner Classic Movies earlier tonight

Part II: "Mimsy Were the Borogoves," a classic science fiction story:

"… he lifted a square, transparent crystal block, small enough to cup in his palm– much too small to contain the maze of apparatus within it. In a moment Scott had solved that problem. The crystal was a sort of magnifying glass, vastly enlarging the things inside the block. Strange things they were, too. Miniature people, for example– They moved. Like clockwork automatons, though much more smoothly. It was rather like watching a play."

Part III:  A Crystal Block

Cube, 4x4x4

Four coloring pencils, of four different colors

Image of pencils is by
Diane Robertson Design.

Related material:
"A Four-Color Theorem."

Part IV:

David Carradine displays a yellow book-- the Princeton I Ching.

"Click on the Yellow Book."

Saturday, September 5, 2009

Saturday September 5, 2009

Filed under: General,Geometry — Tags: , — m759 @ 10:31 PM
For the
Burning Man

'The Stars My Destination,' current edition (with cover slightly changed)

(Cover slightly changed.)

Background —

Part I:

Sophists (August 20th)

Part II:


Escher's 'Verbum'

Escher's Verbum

Solomon's Cube

Part III:

From August 25th

Equilateral triangle on a cube, each side's length equal to the square root of two

"Boo, boo, boo,
  square root of two.

Wednesday, August 26, 2009

Wednesday August 26, 2009

Filed under: General — Tags: — m759 @ 9:00 AM
A Puritan Settlement
in memory of
Sen. Edward Kennedy

“When New Haven was founded, the city was laid out into a grid of nine squares surrounded by a great wilderness.
Last year [2000] History of Art Professor Emeritus Vincent Scully said the original town plan reflected a feeling that the new city should be sacred.
Scully said the colony’s founders thought of their new Puritan settlement as a ‘nine-square paradise on Earth, heaven on earth, New Haven, New Jerusalem.'”

Yale Daily News, Jan. 11, 2001

“Real and unreal are two in one:
New Haven
Before and after one arrives….”

— Wallace Stevens,
“An Ordinary Evening
in New Haven,” XXVIII

See also Art and Man at Yale.

Wednesday, August 19, 2009

Wednesday August 19, 2009

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

Group Actions, 1984-2009

From a 1984 book review:

"After three decades of intensive research by hundreds of group theorists, the century old problem of the classification of the finite simple groups has been solved and the whole field has been drastically changed. A few years ago the one focus of attention was the program for the classification; now there are many active areas including the study of the connections between groups and geometries, sporadic groups and, especially, the representation theory. A spate of books on finite groups, of different breadths and on a variety of topics, has appeared, and it is a good time for this to happen. Moreover, the classification means that the view of the subject is quite different; even the most elementary treatment of groups should be modified, as we now know that all finite groups are made up of groups which, for the most part, are imitations of Lie groups using finite fields instead of the reals and complexes. The typical example of a finite group is GL(n, q), the general linear group of n dimensions over the field with q elements. The student who is introduced to the subject with other examples is being completely misled."

— Jonathan L. Alperin,
   review of books on group theory,
   Bulletin (New Series) of the American
   Mathematical Society
10 (1984) 121, doi:

A more specific example:

Actions of GL(2,3) on a 3x3 coordinate-array

The same example
at Wolfram.com:

Ed Pegg Jr.'s program at Wolfram.com to display a large number of actions of small linear groups over finite fields

Caption from Wolfram.com:
"The two-dimensional space Z3×Z3 contains nine points: (0,0), (0,1), (0,2), (1,0), (1,1), (1,2), (2,0), (2,1), and (2,2). The 48 invertible 2×2 matrices over Z3 form the general linear group known as GL(2, 3). They act on Z3×Z3 by matrix multiplication modulo 3, permuting the nine points. More generally, GL(n, p) is the set of invertible n×n matrices over the field Zp, where p is prime. With (0, 0) shifted to the center, the matrix actions on the nine points make symmetrical patterns."

Citation data from Wolfram.com:

"GL(2,p) and GL(3,3) Acting on Points"
 from The Wolfram Demonstrations Project,
 Contributed by: Ed Pegg Jr"

As well as displaying Cullinane's 48 pictures of group actions from 1985, the Pegg program displays many, many more actions of small finite general linear groups over finite fields. It illustrates Cullinane's 1985 statement:

"Actions of GL(2,p) on a p×p coordinate-array have the same sorts of symmetries, where p is any odd prime."

Pegg's program also illustrates actions on a cubical array– a 3×3×3 array acted on by GL(3,3). For some other actions on cubical arrays, see Cullinane's Finite Geometry of the Square and Cube.

Monday, August 10, 2009

Monday August 10, 2009

Filed under: General — Tags: — m759 @ 9:29 PM
For Maine Preacher
Stephen King

Union colonel Joshua Chamberlain, on the way to the battle at Gettysburg, remembers his boyhood.

"Maine… is silent and cold.

Maine in the winter: air is darker, the sky is a deeper dark. A darkness comes with winter that these Southern people don't know. Snow falls so much earlier and in the winter you can walk in a snowfield among bushes, and visitors don't know that the bushes are the tops of tall pines, and you're standing in thirty feet of snow. Visitors. Once long ago visitors in the dead of winter: a preacher preaching hell-fire. Scared the fool out of me. And I resented it and Pa said I was right.


When he thought of the old man he could see him suddenly in a field in the spring, trying to move a gray boulder. He always knew instinctively the ones you could move, even though the greater part was buried in the earth, and he expected you to move the rock and not discuss it. A hard and silent man, an honest man, a noble man. Little humor but sometimes the door opened and you saw the warmth within a long way off, a certain sadness, a slow, remote, unfathomable quality as if the man wanted to be closer to the world but did not know how. Once Chamberlain had a speech memorized from Shakespeare and gave it proudly, the old man listening but not looking, and Chamberlain remembered it still: 'What a piece of work is man… in action how like an angel!' And the old man, grinning, had scratched his head and then said stiffly, 'Well, boy, if he's an angel, he's sure a murderin' angel.' And Chamberlain had gone on to school to make an oration on the subject: Man, the Killer Angel. And when the old man heard about it he was very proud, and Chamberlain felt very good remembering it."

— Michael Shaara, The Killer Angels: A Novel of the Civil War


Monday August 10, 2009

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

Pictures Within Pictures

"The Chinese language is written in ideograms, pictures. Think of a DO NOT ENTER pictogram, a circle with a diagonal slash, a type of ideogram. It tells you what to do or not do, but not why. The why is part of a larger context, a bigger picture. Such is the nature of the Chinese language. Simple yet complex. Pictures within pictures."

Customer review at Amazon.com

See also the pictures in this journal on today's date five years ago.

Sunday, August 9, 2009

Sunday August 9, 2009

Filed under: General — Tags: — m759 @ 4:00 PM
WIVB TV Buffalo, 2:56 PM ET Aug. 9, 2009, Severe Weather Statement accompanied by Instant Action 'Ace of Aces' aerial dogfight game


See also "Chautauqua"
at Stormfront.org and
 the five entries ending with
"Unfriendly Persuasion"
this morning.

"Today's Sinner"

Sunday August 9, 2009

Filed under: General — Tags: — m759 @ 9:11 AM

Unfriendly Persuasion

"What disturbs Americans of all ideological persuasions is the fear that almost everything, not just government, is fixed or manipulated by some powerful hidden hand…."

Frank Rich in today's New York Times

Franz Liebkind (played by Kenneth Mars) in 'The Producers,' with helmet and pigeon

Author! Author!

Sunday August 9, 2009

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

On the Waterfront

"On the Hoboken waterfront, people scattered as pieces of debris fell from the sky. A wheel from one of the aircraft lay on Hoboken's Sinatra Drive." —Associated Press, August 8, 2009

So set 'em up, Joe…

Thursday, August 6, 2009

Thursday August 6, 2009

Filed under: General,Geometry — Tags: — m759 @ 1:44 PM
A Fisher of Men
Cover, Schulberg's novelization of 'Waterfront,' Bantam paperback
Update: The above image was added
at about 11 AM ET Aug. 8, 2009.

Dove logo, First United Methodist Church of Bloomington, Indiana

From a webpage of the First United Methodist Church of Bloomington, Indiana–


Dr. Joe Emerson, April 24, 2005–

"The Ultimate Test"

— Text: I Peter 2:1-9

Dr. Emerson falsely claims that the film "On the Waterfront" was based on a book by the late Budd Schulberg (who died yesterday). (Instead, the film's screenplay, written by Schulberg– similar to an earlier screenplay by Arthur Miller, "The Hook"–  was based on a series of newspaper articles by Malcolm Johnson.)

"The movie 'On the Waterfront' is once more in rerun. (That’s when Marlon Brando looked like Marlon Brando.  That’s the scary part of growing old when you see what he looked like then and when he grew old.)  It is based on a book by Budd Schulberg."


Emerson goes on to discuss the book, Waterfront, that Schulberg wrote based on his screenplay–

"In it, you may remember a scene where Runty Nolan, a little guy, runs afoul of the mob and is brutally killed and tossed into the North River.  A priest is called to give last rites after they drag him out."


Hook on cover of Budd Schulberg's novel 'Waterfront' (NY Times obituary, detail)

New York Times today

Dr. Emerson flunks the test.


Dr. Emerson's sermon is, as noted above (Text: I Peter 2:1-9), not mainly about waterfronts, but rather about the "living stones" metaphor of the Big Fisherman.

My own remarks on the date of Dr. Emerson's sermon

The 4x6 array used in the Miracle Octad Generator of R. T. Curtis

Those who like to mix mathematics with religion may regard the above 4×6 array as a context for the "living stones" metaphor. See, too, the five entries in this journal ending at 12:25 AM ET on November 12 (Grace Kelly's birthday), 2006, and today's previous entry.

Thursday August 6, 2009

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

The Running

"Budd Schulberg, who wrote the award-winning screenplay for 'On the Waterfront' and created a classic American archetype of naked ambition, Sammy Glick, in his novel What Makes Sammy Run?, died on Wednesday. He was 95…."

Running man with blue background on the cover of 'Eye of Cat,' by Roger Zelazny

Log24, Dec. 16, 2003:

See, too, Blue Matrices, and
a link for Beethoven's birthday:

Juliette Binoche with musical score from Kieslowski's 'Blue'

Song for the
Unification of Europe

Friday, July 24, 2009

Friday July 24, 2009

Filed under: General — Tags: — m759 @ 6:23 PM
Word Problem

“Philosophers ponder the idea
of identity: what it is to
give something a name on
Monday and have it respond
 to that name on Friday….”
Bernard Holland

Quoted here Monday:
Tom Wolfe on the moon
 landing forty years ago:

What NASA needs now
  is the power of the Word.”

30 OCTOBER 2000- NY- Charlize Theron, Matt Damon and Will Smith at the Oct. 29, 2000, NY premiere of 'Legend Of Bagger Vance.' --Ezio Petersen UPI

“It don’t mean a thing
 if it ain’t got that….”


This week’s
earlier entries.

Happy birthday,
Gus Van Sant.

Thursday, July 23, 2009

Thursday July 23, 2009

Filed under: General — Tags: — m759 @ 12:06 PM
Blade Singer
Director’s Cut

Replication of 'The Immortal Game' of chess in 'Blade Runner'

“Bishop to King 7, check.” – Roy Batty

On Chris Hipp, who died of an apparent heart attack at 47 on July 14 (Bastille Day), 2009:

“‘He was the father of blade technology when he was with RLX,’ Jim Hall, president of the Blade System Alliance, said in an interview. ‘He invented the blade server.'”

“Hall said Hipp was a natural inventor who wanted to be on the cutting edge.”

— Jeffrey Burt at eWeek.com

Epitaph by a friend:

“He was known as a determined, fearsome and fair competitor.”

Red Kite Prayer

Hipp’s motto was “pounding idiots.”*

From a website celebrating the life and family (cf. previous two entries) of Leonard Shlain, author of Art & Physics and pioneering surgeon:

“Shlain n: unique last name of Russian origins. Possible meanings: 1: Sound sword makes as it’s pulled from sheath” —Shlain.com

A more authentic sound:

The blade actually does sing. When it is withdrawn from the sheath it makes a ‘Tshuiiing’ sound as one hears in the movies. It rings like a bell.”

Armageddon blade by Trace Rinaldi
Steel Addiction, Custom Knives

A less authentic sound:

Wizard of Id, July 23, 2009-- The Drawn Blade

* The residents of Id (as in the above cartoon) are known, affectionately, as Idiots.

Thursday July 23, 2009

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

A Tangled Tale

Proposed task for a quantum computer:

"Using Twistor Theory to determine the plotline of Bob Dylan's 'Tangled up in Blue'"

One approach to a solution:

"In this scheme the structure of spacetime is intrinsically quantum mechanical…. We shall demonstrate that the breaking of symmetry in a QST [quantum space-time] is intimately linked to the notion of quantum entanglement."

— "Theory of Quantum Space-Time," by Dorje C. Brody and Lane P. Hughston, Royal Society of London Proceedings Series A, Vol. 461, Issue 2061, August 2005, pp. 2679-2699

(See also The Klein Correspondence, Penrose Space-Time, and a Finite Model.)

For some less technical examples of broken symmetries, see yesterday's entry, "Alphabet vs. Goddess."

That entry displays a painting in 16 parts by Kimberly Brooks (daughter of Leonard Shlain– author of The Alphabet Versus the Goddess— and wife of comedian Albert Brooks (real name: Albert Einstein)). Kimberly Brooks is shown below with another of her paintings, titled "Blue."


Click image to enlarge.

"She was workin' in a topless place
 And I stopped in for a beer,
 I just kept lookin' at the side of her face
 In the spotlight so clear.
 And later on as the crowd thinned out
 I's just about to do the same,
 She was standing there in back of my chair
 Said to me, 'Don't I know your name?'
 I muttered somethin' underneath my breath,
 She studied the lines on my face.
 I must admit I felt a little uneasy
 When she bent down to tie the laces of my shoe,
 Tangled up in blue."

-- Bob Dylan

Further entanglement with blue:

The website of the Los Angeles Police Department, designed by Kimberly Brooks's firm, Lightray Productions.

Further entanglement with shoelaces:

"Entanglement can be transmitted through chains of cause and effect– and if you speak, and another hears, that too is cause and effect.  When you say 'My shoelaces are untied' over a cellphone, you're sharing your entanglement with your shoelaces with a friend."

— "What is Evidence?," by Eliezer Yudkowsky

Wednesday, July 22, 2009

Wednesday July 22, 2009

Filed under: General,Geometry — Tags: — m759 @ 9:48 AM
Alphabet vs. Goddess


Roy Lichtenstein girl and Hand of God pointing to the letter B

… from June 11, 2008.

“Just as both tragedy and comedy can be written by using the same letters of the alphabet, the vast variety of events in this world can be realized by the same atoms through their different arrangements and movements. Geometry and kinematics, which were made possible by the void, proved to be still more important in some way than pure being.”

— Werner Heisenberg in
  Physics and Philosophy

Werner, Kimberly;
Kimberly, Werner.

Wechsler cubes, with 'Certainty,' by Kimberly Brooks

Happy Feast of
St. Mary Magdalene.

Tuesday, July 21, 2009

Tuesday July 21, 2009

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

Today's Readings:

Monday, July 20, 2009

Monday July 20, 2009

Filed under: General — Tags: — m759 @ 7:00 PM
The First Post
in this weblog:

The Diamond Theorem

Related material:

From Sunday’s New York Times, Tom Wolfe on the moon landing forty years ago:

What NASA needs now is the power of the Word. On Darwin’s tongue, the Word created a revolutionary and now well-nigh universal conception of the nature of human beings, or, rather, human beasts. On Freud’s tongue, the Word means that at this very moment there are probably several million orgasms occurring that would not have occurred had Freud never lived. Even the fact that he is proved to be a quack has not diminished the power of his Word.

July 20, 1969, was the moment NASA needed, more than anything else in this world, the Word. But that was something NASA’s engineers had no specifications for. At this moment, that remains the only solution to recovering NASA’s true destiny, which is, of course, to build that bridge to the stars.

Tom Wolfe is the author of “The Right Stuff,” an account of the Mercury Seven astronauts.


The Word according to St. John:

Jill St. John, star of 'Diamonds are Forever'

Sunday, July 19, 2009

Sunday July 19, 2009

Filed under: General — Tags: — m759 @ 7:11 AM
Finite Jest
(continued from
 Monday, July 13)

Blaise Pascal:

"L’unité jointe à l’infini ne l’augmente de rien, non plus qu’un pied à une mesure infinie. Le fini s’anéantit en présence de l’infini, et devient un pur néant….

Nous connaissons qu’il y a un infini, et ignorons sa nature. Comme nous savons qu’il est faux que les nombres soient finis, donc il est vrai qu’il y a un infini en nombre. Mais nous ne savons ce qu’il est: il est faux qu’il soit pair, il est faux qu’il soit impair; car, en ajoutant 1 unité, il ne change point de nature; cependant c’est un nombre, et tout nombre est pair ou impair (il est vrai que cela s’entend de tout nombre fini). Ainsi…."

"Unity joined to infinity adds nothing to it, no more than one foot to an infinite measure. The finite is annihilated in the presence of the infinite, and becomes a pure nothing….

We know that there is an infinite, and are ignorant of its nature. As we know it to be false that numbers are finite, it is therefore true that there is an infinity in number. But we do not know what it is. It is false that it is even, it is false that it is odd; for the addition of a unit can make no change in its nature. Yet it is a number, and every number is odd or even (this is certainly true of every finite number). So…."

Pensées (trans. W. F. Trotter), Courier Dover Publications, 2003

"Le fini s’anéantit
 en présence de l’infini,
      et devient un pur néant

Un Pur Néant:

"So did God cause the big bang?
Overcome by metaphysical lassitude,
I finally reach over to my bookshelf
for The Devil's Bible.
Turning to Genesis I read:
'In the beginning
there was nothing.
And God said,
'Let there be light!'
And there was still nothing,
but now you could see it.'"

— Jim Holt, Big-Bang Theology,
   Slate's "High Concept" department


Fiat Lux, and After


"In the garden of Adding,
 Live Even and Odd"      
— E. L. Doctorow    


The Cross of Five Ninths

  4 + 5 = 9.

Wednesday, July 15, 2009

Wednesday July 15, 2009

Filed under: General — Tags: — m759 @ 11:09 AM
The Plot Thickens

Thanks to David Lavery
see previous entry— the
word for today is…
Cover of 'Zaddik,' a novel by David Rosenbaum

"As the story develops, an
 element of magical realism
 enters the picture."
Amazon review   

Related material:

For background on magical
realism, see the update to
today's previous entry.

See also
A Year of Magical Thinking
(June 6, 2009) and
the entries of May 19-22,
featuring Judy Davis in…

Poster for 'Diamonds' miniseries on ABC starting May 24, 2009

(Cf. St. Bridget's Day, 2003)

Wednesday July 15, 2009

Filed under: General — Tags: — m759 @ 4:01 AM
of obituaries page,
New York Times,
Monday morning:

Detail, obits page, NY Times Monday morning, July 13, 2009

Detail of arts page,
New York Times, Wednesday morning:

(Click ad for more on the Monday night death of Dash Snow.)

Arts page detail, morning of Wednesday, July 15, 2009

Headlines collage by Dash Snow

Hurt yet?

Update of 5:01 AM:

Lavery Hits
Literary Jackpot

From the top right of
this morning's online
New York Times front page:

Christoph Niemann on witchcraft and snow

Click on voodoo doll
for further details.

See also…

1. Monday's link to a
Wallace Stevens poem,
"Snow and Stars"

2. The conclusion of this
morning's Times obituary
for artist Dash Snow, which
gives his daughter's name…

3. David Lavery's excellent
of the classic
 Conrad Aiken story
"Silent Snow, Secret Snow."

Wednesday, June 17, 2009

Wednesday June 17, 2009

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

Back to the Real

Colum McCann on yesterday’s history:

“Fiction gives us access to a very real history.”

The Associated Press thought for today:

“Journalism allows its readers to witness history; fiction gives its readers an opportunity to live it.”

— John Hersey, American author (born on this date in 1914, died 1993).

From John Hersey’s The Child Buyer (1960):

“I was wondering about that this morning… About forgetting. I’ve always had an idea that each memory was a kind of picture, an insubstantial picture. I’ve thought of it as suddenly coming into your mind when you need it, something you’ve seen, something you’ve heard, then it may stay awhile, or else it flies out, then maybe it comes back another time…. If all the pictures went out, if I forgot everything, where would they go? Just out into the air? Into the sky? Back home around my bed, where my dreams stay?”

“We keep coming back and coming back
To the real: to the hotel instead of the hymns….”

— Wallace Stevens

Hotel Bella Vista, Cuernavaca, Morelos, Mexico

Postcard from eBay
From Under the Volcano, by Malcolm Lowry, 1947, Chapter I: 

Faustus is gone: regard his hellish fall —
Shaken, M. Laruelle replaced the book on the table… he reached to the floor for a folded sheet of paper that had fluttered out of it. He picked the paper up between two fingers and unfolded it, turning it over. Hotel Bella Vista, he read. There were really two sheets of uncommonly thin hotel notepaper….

I sit now in a little room off the bar at four-thirty in the morning drinking ochas and then mescal and writing this on some Bella Vista notepaper I filched the other night…. But this is worst of all, to feel your soul dying. I wonder if it is because to-night my soul has really died that I feel at the moment something like peace. Or is it because right through hell there is a path, as Blake well knew, and though I may not take it, sometimes lately in dreams I have been able to see it? …And this is how I sometimes think of myself, as a great explorer who has discovered some extraordinary land from which he can never return to give his knowledge to the world: but the name of this land is hell. It is not Mexico of course but in the heart.

Thursday, June 4, 2009

Thursday June 4, 2009

Filed under: General — Tags: , — m759 @ 1:24 PM

The Grasshopper
Lies Heavy

David Carradine dies at 72

“‘Oracle, why did you write
The Grasshopper Lies Heavy?
What are we supposed to learn?'”

— Philip K. Dick

She began throwing the coins.

I Ching Hexagram 61: Inner Truth

Click on image
for further details.

Thursday June 4, 2009

Filed under: General — Tags: — m759 @ 10:30 AM
A Passage to Egypt

The First Draft: Reviews flood in
after Obama's Cairo speech

The conclusion:
a tribute to E. M. Forster

Test-- 'To prove you're a person and not a script'-- type the word 'connect.'

(Image only; not for use.)

Those who prefer spam scripts
to persons may consult
the entry from midnight.

Thursday June 4, 2009

Filed under: General,Geometry — Tags: — m759 @ 12:00 AM
continued from
October 16, 2008

New collection release:
Pattern in Islamic Art
from David Wade

October 16, 2008

David Wade has partnered with ARTstor to distribute approximately 1,500 images of Islamic art, now available in the Digital Library. These images illustrate patterns and designs found throughout the Islamic world, from the Middle East and Europe to Central and South Asia. They depict works Wade photographed during his travels, as well as drawings and diagrams produced for publication. Reflective of Wade's particular interest in symmetry and geometry, these images analyze and break down common patterns into their basic elements, thereby revealing the underlying principles of order and balance in Islamic art. Islamic artists and craftsmen employed these intricate patterns to adorn all types of surfaces, such as stone, brick, plaster, ceramic, glass, metal, wood, and textiles. The collection contains examples of ornamentation from monumental architecture to the decorative arts.

To view the David Wade: Pattern in Islamic Art collection: go to the ARTstor Digital Library, browse by collection, and click "David Wade: Pattern in Islamic Art;" or enter the Keyword Search: patterninislamicart.

For more detailed information about this collection, visit the David Wade: Pattern in Islamic Art collection page.

The above prose illustrates
the institutional mind at work.

Those who actually try to view
the Wade collection will
encounter the following warning:

To access the images in the ARTstor Digital Library you need to be affiliated with a participating institution (university, college, museum, public library or K-12 school).
You say
"go to the ARTstor Digital Library,"
I say

Tuesday, May 19, 2009

Tuesday May 19, 2009

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

"By far the most important structure in design theory is the Steiner system S(5, 8, 24)."

"Block Designs," 1995, by Andries E. Brouwer

"The Steiner system S(5, 8, 24) is a set S of 759 eight-element subsets ('octads') of a twenty-four-element set T such that any five-element subset of T is contained in exactly one of the 759 octads. Its automorphism group is the large Mathieu group M24."

The Miracle Octad Generator (MOG) of R.T. Curtis (webpage)

"… in 1861 Mathieu… discovered five multiply transitive permutation groups…. In a little-known 1931 paper of Carmichael… they were first observed to be automorphism groups of exquisite finite geometries."

William M. Kantor, 1981

The 1931 paper of Carmichael is now available online from the publisher for $10.

Saturday, April 25, 2009

Saturday April 25, 2009

Filed under: General,Geometry — Tags: — m759 @ 9:22 PM
State of Play

Russell Crowe in 'State of Play'

The Russell Crowe
Hotel Puzzle

by John Tierney

"Russell Crowe arrives at the Hotel Infinity looking tired and ornery. He demands a room. The clerk informs him that there are no vacancies…."

Footprints from California today
(all by a person or persons using Firefox browsers):

7:10 AM
Concepts of Space: Euclid vs. Galois

8:51 AM
Art Wars continued: Behind the Picture

1:33 PM
A Riff for Dave: Me and My Shadow

2:11 PM
A Death of Kings: In Memory of Bobby Fischer

2:48 PM
Art Wars in review– Through the Looking Glass: A Sort of Eternity

3:28 PM and
Annals of Philosophy: The Dormouse of Perception

4:28 PM
Epiphany for Roy, Part I

6:03 PM
At the Still Point: All That Jazz

6:22 PM
Where Entertainment is Not God: The Just Word

7:14 PM
Happy New Yorker Day– Class Galore

7:16 PM
The Politics of Change: Jumpers

"Relax," said the night man.
"We are programmed to receive."
— Hotel California

Saturday April 25, 2009

Filed under: General — Tags: , — m759 @ 11:09 AM
April is Awareness Month

for both

Mathematics and Autism.

Welcome to the
Black Hole Café

"Our lifelong friendship made me not only an admirer of the depth, scholarship, and sheer energy of his mathematical work (and of his ceaseless activities as an editorial entrepreneur on behalf of mathematics) but one in awe of his status as the ultimate relaxed sophisticate."

The late Jacob T. Schwartz 
  on Gian-Carlo Rota


by Alfred Bester
and Roger Zelazny:

His manner was all charm and grace; pure café 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."

"After Davis and Hersh,
it will be hard to uphold
the Glasperlenspiel
view of mathematics."
— Gian-Carlo Rota  

"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon  



Thursday, April 23, 2009

Thursday April 23, 2009

Filed under: General — Tags: — m759 @ 5:24 PM
Star Quality

Eight-pointed star, background image for the E! Online logo

This deliberately cryptic entry is to thank an anonymous reader in Sweden for the following footprint:

…&uid=37798719 4/23/2009
4:33 PM

“Speedy” is the browser name supplied to the server. The link is to a Columbus Day, 2003, entry with the song phrase “spinnin’ wheel, spinnin’ true.” The time is Eastern Daylight.

Related material:

Vide today’s midday PA lottery number, 177, the 1919 edition of The Oxford Book of English Verse, and the time (interpreted, in a Joycean manner, as a date) of this morning’s first entry.

Happy birthday to Judy Davis
and happy Day of the Book.

Oxford Book of English Verse 1250-1900

Thursday April 23, 2009

Filed under: General,Geometry — Tags: , — m759 @ 10:00 AM


The Geometry
of Language

(continued from April 16)


Professor Arielle Saiber with chess set

Click on the image for an
interview with the author of
Giordano Bruno and
the Geometry of Language

Related material:

Joyce on language —

The sigla of 'Finnegans Wake'

Bruno, Joyce, and coincidentia oppositorum

Cullinane on geometry —

Geometry of the I Ching (for comparison to Joyce's 'sigla')

Click on images for details.

Thursday April 23, 2009

Filed under: General — Tags: — m759 @ 7:22 AM
Theology for Holst

“Timothy J. Holst, who joined the Ringling Brothers and Barnum & Bailey Circus as a lowly Keystone Kops clown, rose to the role of singing ringmaster, and ultimately became the show’s talent czar, died April 16 in São Paulo, Brazil, during a visit to sign up circus acts. He was 61.”

Tiene angel.

Timothy J. Holst, who died April 16, 2009
But seriously…. 

Wednesday, April 8, 2009

Wednesday April 8, 2009

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

Good’s Singularity

Irving John “I.J.” Good died Sunday, April 5, 2009.

The date of his death was also Palm Sunday and the day of the Academy of Country Music Awards.

Information from Wikipedia:

Good, 92, was a cryptanalyst at Bletchley Park during World War II.

“He was born as Isidore Jacob Gudak to a Jewish family in London. In his publications he was called I. J. Good. He studied mathematics at Jesus College, Cambridge, graduating in 1938. He did research work under G.H. Hardy and Besicovitch before moving to Bletchley Park in 1941 on completing his doctorate.

At Bletchley Park, he was initially in Hut 8 under the supervision of Alan Turing…”

[Related material: the death of Turing (a major fan of the Evil Queen in Snow White) and yesterday’s entry]

Wikipedia states that “I. J. Good’s vanity car license plate, hinting at his spylike wartime work, was ‘007 IJG’…. He played chess to county standard, and helped to popularise Go, an Asian boardgame, through a 1965 article in New Scientist (he had learned the rules from Turing). In 1965, he described a concept similar to today’s meaning of technological singularity, in that it included in it the advent of superhuman intelligence:

Let an ultraintelligent machine be defined as a machine that can far surpass all the intellectual activities of any man however clever. Since the design of machines is one of these intellectual activities, an ultraintelligent machine could design even better machines; there would then unquestionably be an ‘intelligence explosion,’ and the intelligence of man would be left far behind. Thus the first ultraintelligent machine is the last invention that man need ever make….
— Good, I. J. (1965). ‘Speculations Concerning the First Ultraintelligent Machine‘, Advances in Computers, Vol. 6.”
“Some say the symbol
of Apple Computers,
the apple with a bite out of it,
is a nod to Alan Turing.”– from “Alan Turing and
the Apple
at Flickr, uploaded
on Epiphany 2006 by guano

Alan Turing and the Apple


Above: Composite by “guano” at Flickr

Will: Do you like apples?
Clark: Yeah.
Will: Well, I got her number.
How do you like them apples?

— “Good Will Hunting

Happy Spy Wednesday.

Sunday, April 5, 2009

Sunday April 5, 2009

Filed under: General — Tags: — m759 @ 7:35 AM
Reba's Widget

Click to enlarge.

Reba McEntire to host Academy of Country Music Awards Sunday, April 5, 2009

Sunday April 5, 2009

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

About the People:
Race to Witch Mountain

"As Robert Kennedy once told a crowd of students in South Africa, it is a revolutionary world that we live in and, thus, it is young people who must take the lead– [applause]– because young people are unburdened by the biases or prejudices of the past."

President Obama in Strasbourg on Friday, April 3, 2009

"George Bernard Shaw once wrote, 'Some people see things as they are and say why? I dream things that never were and say, why not?'"

— Robert Kennedy, University of Kansas, March 18, 1968

George Bernard Shaw:

THE SNAKE. I can talk of many things. I am very wise. It was I who whispered the word to you that you did not know. Dead. Death. Die.

EVE [shuddering] Why do you remind me of it? I forgot it when I saw your beautiful hood. You must not remind me of unhappy things.

THE SERPENT. Death is not an unhappy thing when you have learnt how to conquer it.

EVE. How can I conquer it?

THE SERPENT. By another thing, called birth.

EVE. What? [Trying to pronounce it] B-birth?

THE SERPENT. Yes, birth.

EVE. What is birth?

THE SERPENT. The serpent never dies. Some day you shall see me come out of this beautiful skin, a new snake with a new and lovelier skin. That is birth.

EVE. I have seen that. It is wonderful.

THE SERPENT. If I can do that, what can I not do? I tell you I am very subtle. When you and Adam talk, I hear you say 'Why?' Always 'Why?' You see things; and you say 'Why?' But I dream things that never were; and I say 'Why not?' I made the word dead to describe my old skin that I cast when I am renewed. I call that renewal being born.

EVE. Born is a beautiful word.

THE SERPENT. Why not be born again and again as I am, new and beautiful every time?

EVE. I! It does not happen: that is why.

THE SERPENT. That is how; but it is not why. Why not?

EVE. But I should not like it. It would be nice to be new again; but my old skin would lie on the ground looking just like me; and Adam would see it shrivel up and–

THE SERPENT. No. He need not. There is a second birth.

EVE. A second birth?

THE SERPENT. Listen. I will tell you a great secret….

"Listen, I tell you a mystery…."
Saul of Tarsus   

About the People
(with apologies to
Zenna Henderson):

'Spaceships, Toddlers, Model T Cars, and Jars of Beer'

"We've got to stop meeting like this."

Saturday, March 21, 2009

Saturday March 21, 2009

Filed under: General — Tags: , — m759 @ 11:30 PM
Interpreter's Booth

Tonight's online New York Times:

NY Times  online March 21, 2009: Pope in Angola tells clergy to work against belief in witchcraft

Click to enlarge.

Mary Karr,
"Facing Altars:
    Poetry and Prayer"–

"There is a body
on the cross
  in my church."

Sean Penn gives Nicole Kidman his card in 'The Interpreter'

Sean Penn and Nicole Kidman
in "The Interpreter."

Click to enlarge.

"My card."

"Is Heart of Darkness the story of Kurtz or the story of Marlow’s experience of Kurtz?  Was Marlow invented as a rhetorical device for heightening the meaning of Kurtz’s moral collapse, or was Kurtz invented in order to provide Marlow with the centre of his experience in the Congo?  Again a seamless web, and we tell ourselves that the old-fashioned question 'Who is the protagonist?' is a meaningless one."

Wayne C. Booth, p. 346 in
The Rhetoric of Fiction
as quoted by Paul Wake in
"The Storyteller in Chance"

Saturday March 21, 2009

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

Counters in Rows

"Music, mathematics, and chess are in vital respects dynamic acts of location. Symbolic counters are arranged in significant rows. Solutions, be they of a discord, of an algebraic equation, or of a positional impasse, are achieved by a regrouping, by a sequential reordering of individual units and unit-clusters (notes, integers, rooks or pawns)."

— George Steiner
   (See March 10, "Language Game.")

For example:

Model of the 21-point projective plane consisting of the 1- and 2- subsets of a 6-set

Click to enlarge.


Notes on Finite Geometry
(Section on 6-set structures)

Monday, March 2, 2009

Monday March 2, 2009

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


From this journal’s Sunday sermon:

“Flowers’s thoughts stray to Brown,
with affectionate pity, as he
drinks port and eats walnuts
for the first time in
Senior Combination Room.”

— G. H. Hardy recounting the plot
of A Fellow of Trinity

A Glossary of Cambridge:

Combination Room
Attached to the High Table end of the largely unheated medieval college halls, this was a warm place for Fellows to gather before and after meals. Now known as the Senior Combination Room to distinguish it from the Junior and Middle combination rooms.


From Stanley Fish’s weblog
in The New York Times
(Sunday, March 1, 2009, 10 PM):


George Herbert’s “Redemption” —

“‘I resolved to be bold,/And make a suit unto him, to afford/A new small-rented lease and cancel th’old.’

But first he has to find him…. Either he’s just left or he hasn’t been seen, but then, unexpectedly and in the most unlikely circumstances, he turns up:

‘At length I heard a ragged noise and mirth/Of thieves and murderers: there I him espied.’

Before he or his reader can ask ‘what on earth are you doing here?,’ the final line provides an answer with a compact swiftness that is literally breathtaking:

 ‘Who straight, “Your suit is granted,” said, and died.'”

For Senior Combination Room as
a den of thieves and murderers,
see That Hideous Strength.

Related material:

The Painted Word

G. H. Hardy died at 70
on December 1, 1947.
That date is now observed as
“Day Without Art.”

Day Without Art logo: X'd-out frame

Click on image
for further details.

Monday March 2, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 11:30 AM

Joyce’s Nightmare

Today in History – March 2

Today is Monday, March 2, the 61st day of 2009. There are 304 days left in the year.

Today’s Highlight in History:

On March 2, 1939, Roman Catholic Cardinal Eugenio Pacelli was elected Pope on his 63rd birthday; he took the name Pius XII.

Angels and Demons, Illuminati Diamond, pages 359-360

Log24 on June 9, 2008

From Gravity’s Rainbow (Penguin Classics, 1995), page 563:

“He brings out the mandala he found.
‘What’s it mean?’

Slothrop gives him the mandala. He hopes it will work like the mantra that Enzian told him once, mba-kayere (I am passed over), mba-kayere… a spell […]. A mezuzah. Safe passage through a bad night….”

In lieu of Slothrop’s mandala, here is another…

Christ and the four elements, 1495

Christ and the Four Elements

This 1495 image is found in
The Janus Faces of Genius:
The Role of Alchemy
in Newton’s Thought,
by B. J. T. Dobbs,
Cambridge University Press,
2002, p. 85


Related mandalas:Diamond arrangement of the four elements

Logo by Steven H. Cullinane for website on finite geometry


For further details,
click on any of the
three mandalas above.

Angels and Demons cross within a diamond (page 306), and Finite Geometry logo

Happy birthday to
Tom Wolfe, author of
The Painted Word.

Friday, February 20, 2009

Friday February 20, 2009

Filed under: General,Geometry — Tags: , , — m759 @ 11:01 PM

The Cross
of Constantine

mentioned in
this afternoon's entry
"Emblematizing the Modern"
was the object of a recent
cinematic chase sequence
(successful and inspiring)
starring Mira Sorvino
at the Metropolitan
Museum of Art.

In memory of
Dr. Hunter S. Thompson,
dead by his own hand
on this date
four years ago

Rolling Stone memorial to Dr. Hunter S. Thompson

Click for details.

There is
another sort of object
we may associate with a
different museum and with
a modern Constantine
See "Art Wars for MoMA"
(Dec. 14, 2008).

This object, modern
rather than medieval,
is the ninefold square:

The ninefold square

It may suit those who,
like Rosalind Krauss
(see "Emblematizing"),
admire the grids of modern art
but view any sort of Christian
cross with fear and loathing.

For some background that
Dr. Thompson might appreciate,
see notes on Geometry and Death
in this journal, June 1-15, 2007,
and the five Log24 entries
 ending at 9 AM Dec. 10. 2006,
which include this astute
observation by J. G. Ballard:

"Modernism's attempt to build a better world with the aid of science and technology now seems almost heroic. Bertolt Brecht, no fan of modernism, remarked that the mud, blood and carnage of the first world war trenches left its survivors longing for a future that resembled a white-tiled bathroom."


Friday February 20, 2009

Filed under: General — Tags: , — m759 @ 6:00 PM
A Kind of Cross

Descartes portrait

"For every kind of vampire,
there is a kind of cross."

— Thomas Pynchon in  
Gravity's Rainbow

Descartes's Cross

Click for source.

Related material:

A memorial service
held at 2 PM today at the
U.S. Space & Rocket Center
in Huntsville, Alabama, and
 today's previous entry.

Friday February 20, 2009

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

The following meditation was
inspired by the recent fictional
recovery, by Mira Sorvino
in "The Last Templar,"

of a Greek Cross —
"the Cross of Constantine"–
and by the discovery, by
art historian Rosalind Krauss,
of a Greek Cross in the
art of Ad Reinhardt.


The Cross of Descartes  

Note that in applications, the vertical axis
of the Cross of Descartes often symbolizes
the timeless (money, temperature, etc.)
while the horizontal axis often symbolizes time.

T.S. Eliot:

"Men’s curiosity searches past and future
And clings to that dimension. But to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint…."

There is a reason, apart from her ethnic origins, that Rosalind Krauss (cf. 9/13/06) rejects, with a shudder, the cross as a key to "the Pandora's box of spiritual reference that is opened once one uses it." The rejection occurs in the context of her attempt to establish not the cross, but the grid, as a religious symbol:

"In suggesting that the success [1] of the grid
is somehow connected to its structure as myth,
I may of course be accused of stretching a point
beyond the limits of common sense, since myths
are stories, and like all narratives they unravel
through time, whereas grids are not only spatial
to start with, they are visual structures
that explicitly reject a narrative
or sequential reading of any kind.

[1] Success here refers to
three things at once:
a sheerly quantitative success,
involving the number of artists
in this century who have used grids;
a qualitative success through which
the grid has become the medium
for some of the greatest works
of modernism; and an ideological
success, in that the grid is able–
in a work of whatever quality–
to emblematize the Modern."

— Rosalind Krauss, "Grids" (1979)

Related material:

Time Fold and Weyl on
objectivity and frames of reference.

See also Stambaugh on
The Formless Self
as well as
A Study in Art Education
Jung and the Imago Dei.

Thursday, February 19, 2009

Thursday February 19, 2009

Filed under: General — Tags: — m759 @ 7:07 AM

A Sunrise
for Sunrise

“If we open any tract– Plastic Art and Pure Plastic Art or The Non-Objective World, for instance– we will find that Mondrian and Malevich are not discussing canvas or pigment or graphite or any other form of matter. They are talking about Being or Mind or Spirit.  From their point of view, the grid is a staircase to the Universal, and they are not interested in what happens below in the Concrete.”

Rosalind Krauss, “Grids”

Yesterday’s entry featured a rather simple-minded example from Krauss of how the ninefold square (said to be a symbol of Apollo)

The 3x3 grid

may be used to create a graphic design– a Greek cross, which appears also in crossword puzzles:

Crossword-puzzle design that includes Greek-cross elements

Illustration by
Paul Rand
(born Peretz Rosenbaum)

A more sophisticated example
of the ninefold square
in graphic design:

“That old Jew
gave me this here.”

— A Flag for Sunrise  

The 3x3 grid as an organizing frame for Chinese calligraphy. Example-- the character for 'sunrise'
From Paul-Rand.com

Wednesday, February 18, 2009

Wednesday February 18, 2009

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

Raiders of
the Lost Well

“The challenge is to
keep high standards of
scholarship while maintaining
showmanship as well.”

— Olga Raggio, a graduate of the Vatican library school and the University of Rome who, at one point in her almost 60 years with the Metropolitan Museum of Art, organized “The Vatican Collections,” a blockbuster show. Dr. Raggio died on January 24.

The next day, “The Last Templar,” starring Mira Sorvino, debuted on NBC.

Mira Sorvino in 'The Last Templar'
“The story, involving the Knights Templar, the Vatican, sunken treasure, the fate of Christianity and a decoding device that looks as if it came out of a really big box of medieval Cracker Jack, is the latest attempt to combine Indiana Jones derring-do with ‘Da Vinci Code’ mysticism.”

The New York Times

Sorvino in “The Last Templar”
at the Church of the Lost Well:

Mira Sorvino at the Church of the Lost Well in 'The Last Templar'

One highlight of Secretary of State Hillary Clinton’s first overseas trip will be a stop in China. Her main mission in Beijing will be to ensure that US-China relations under the new Obama administration get off to a positive start.”

— Stephanie Ho, Voice of America Beijing bureau chief, today

Symbol of The Positive,
from this journal
on Valentine’s Day:

'Enlarge' symbol from USA Today

“Stephanie started at the Voice of America as an intern in 1991. She left briefly to attend film school in London in 2000. Although she didn’t finish, she has always wanted to be a film school dropout, so now she’s living one of her dreams.

Stephanie was born in Ohio and grew up in California. She has a bachelor’s degree in Asian studies with an emphasis on Chinese history and economics, from the University of California at Berkeley.”

“She is fluent in
Mandrin Chinese.”

As is Mira Sorvino.

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

Those who, like Clinton, Raggio, and
Sorvino’s fictional archaeologist in
“The Last Templar,” prefer Judeo-
Christian myths to Asian myths,
may convert the above Chinese
“well” symbol to a cross
(or a thick “+” sign)
by filling in five of
the nine spaces outlined
by the well symbol.

In so doing, they of course
run the risk, so dramatically
portrayed by Angelina Jolie
as Lara Croft, of opening
Pandora’s Box.

(See Rosalind Krauss, Professor
of Art and Theory at Columbia,
for scholarly details.)

Rosalind Krauss


Greek Cross, adapted from painting by Ad Reinhardt

The Krauss Cross

Tuesday, February 17, 2009

Tuesday February 17, 2009

Filed under: General,Geometry — Tags: , , , — m759 @ 1:06 PM

of the Rock

A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:

For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:

The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...

The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,

Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.

The rock is the habitation of the whole,
Its strength and measure, that which is near,
     point A
In a perspective that begins again

At B: the origin of the mango's rind.

                    (Collected Poems, 528)

A mathematical version of
this poetic concept appears
in a rather cryptic note
from 1981 written with
Stevens's poem in mind:


For some explanation of the
groups of 8 and 24
motions referred to in the note,
see an earlier note from 1981.

For the Perlis "diamond facets,"
see the Diamond 16 Puzzle.

For a much larger group
of motions, see
Solomon's Cube.

As for "the mind itself"
and "possibilities for
human thought," see
Geometry of the I Ching.

Saturday, February 14, 2009

Saturday February 14, 2009

Filed under: General — Tags: — m759 @ 9:29 PM
The Devil
in the Details


Here are clearer pictures of
the Einstein-Gutkind letter
discussed here February 7.

The pictures are from
the Bloomsbury Auctions site.



The Bloomsbury Auctions caption for these images is as follows:

303. Einstein (Albert, theoretical physicist, 1879-1955) Autograph Letter signed to Eric B. Gutkind, in German, 1½pp. & envelope, 4to, Princeton, 3rd January 1954, thanking him for a copy of his book and expressing his view of God and Judaism, [The word God is for me nothing more than the expression and product of human weaknesses, the Bible a collection of honorable, but still primitive legends which are nevertheless pretty childish… . For me the Jewish religion like all other religions is an incarnation of the most childish superstitions. And the Jewish people to whom I gladly belong and with whose mentality I have a deep affinity have no different quality for me than all other people…], folds, slightly browned ; and a photograph of Gutkind, v.s., v.d.

est. £6000 – £8000

Einstein’s view of God and Judaism.
Eric B. Gutkind (1877-1965), philosopher; author of Choose Life: The Biblical Call to Revolt, 1952.
Albert Einstein – see also lot 497

Sold for £170000
Sale 649, 15th May 2008

Here is a close reading of the part of the letter itself that Bloomsbury gives in English, transcribed from the above images.

Line-by-line transcription of paragraph 2, starting at line 4 of that paragraph:                        

                   ... Das Wort Gott ist für mich nichts als Ausdruck
und Produkt menschlicher Schwächen, die Bibel eine Sammlung
ehrwürdiger, aber doch reichlich primitiver Legenden. Keine noch
so feinsinnige Auslegung kann (für mich) etwas daran ändern.
Diese verfeinerten Auslegungen sind naturgemäß höchst mannigfaltig
und haben so gut wie nichts mit dem Urtext zu schaffen. Für
mich ist die unverfälschte jüdische Religion, wie alle anderen
Religionen, eine Inkarnation des primitiven Aberglaubens. Und das
jüdische Volk, zu dem ich gern gehöre und mit dessen Mentalität ich
tief verwachsen bin, hat für mich doch keine andersartige
Qualität als alle anderen Völker. So weit meine Erfahrung reicht,
ist es auch um nichts besser als andere menschliche Gruppierungen,
wenn es auch durch Mangel an Macht gegen die schlimmsten
Auswüchse gesichert ist. Ansonsten kann ich nichts "Auserwähltes"
an ihm wahrnehmen.

The Guardian of May 13, 2008 stated that the following was "translated from German by Joan Stambaugh"–

... The word God is for me nothing more than the expression
and product of human weaknesses, the Bible a collection
of honourable, but still primitive legends which are nevertheless pretty childish. No
interpretation no matter how subtle can (for me) change this.
These subtilised interpretations are highly manifold
according to their nature and have almost nothing to do with the original text. For
me the Jewish religion like all other
religions is an incarnation of the most childish [German: primitiven] superstitions. And the
Jewish people to whom I gladly belong and with whose mentality I
have a deep affinity have no different
quality for me than all other people. As far as my experience goes,
they are also no better than other human groups,
although they are protected from the worst
cancers by a lack of power. Otherwise I cannot see anything 'chosen'
about them.

Phrases by Stambaugh that do not appear in the German text are highlighted.

Stambaugh, a philosophy professor, is the author of a work on Buddhism, The Formless Self. For some related material on young men who "go crying 'The world is myself, life is myself'" in May, see Wallace Stevens's "The Pediment of Appearance."

Wednesday, November 19, 2008

Wednesday November 19, 2008

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

"Through the unknown,
remembered gate…."

Four Quartets

(Epigraph to the introduction,
Parallelisms of Complete Designs
by Peter J. Cameron,
Merton College, Oxford)

"It's still the same old story…."
— Song lyric

The Great Gatsby
Chapter 6:

"An instinct toward his future glory had led him, some months before, to the small Lutheran college of St. Olaf in southern Minnesota. He stayed there two weeks, dismayed at its ferocious indifference to the drums of his destiny, to destiny itself, and despising the janitor’s work with which he was to pay his way through."

There is a link to an article on St. Olaf College in Arts & Letters Daily  today:

"John Milton, boring? Paradise Lost  has a little bit of something for everybody. Hot sex! Hellfire! Some damned good poetry, too…" more»

The "more" link is to The Chronicle of Higher Education.

For related material on Paradise Lost  and higher education, see Mathematics and Narrative.

Wednesday November 19, 2008

Filed under: General — Tags: — m759 @ 2:56 AM

Sympathy for Baird Bryant

"Pleased to meet you
Hope you guess my name
But what's puzzling you
Is the nature of my game"

The Rolling Stones

"'Don't you want to
hear him call your name
when you're standing
at the pearly gates?'
I told the Preacher 'Yes, I do,
but I hope he don't call today.'"

— Kenny Chesney, song at the CMA Awards on Wednesday, November 12, quoted here at 9:00 AM on Thursday, Novermber 13

Related material:

LA Times obituary for the experienced bohemian writer and filmmaker Baird Bryant, who died at 80 on Thursday, November 13. Bryant filmed parts of "Easy Rider" in 1968 and of the Altamont concert in 1969. He was apparently a member of the Harvard College Class of 1950.

A more complete account of Bryant's life

Thirty references to the Devil in a book by Bryant

Solace With Interruptions

(Log24 entries for November 12, 13, and 14 — the day before Bryant's death, the day of his death, and the day after)

Tuesday, August 19, 2008

Tuesday August 19, 2008

Filed under: General,Geometry — Tags: , , — m759 @ 8:30 AM
Three Times

"Credences of Summer," VII,

by Wallace Stevens, from
Transport to Summer (1947)

"Three times the concentred
     self takes hold, three times
The thrice concentred self,
     having possessed
The object, grips it
     in savage scrutiny,
Once to make captive,
     once to subjugate
Or yield to subjugation,
     once to proclaim
The meaning of the capture,
     this hard prize,
Fully made, fully apparent,
     fully found."

Stevens does not say what object he is discussing.

One possibility —

Bertram Kostant, Professor Emeritus of Mathematics at MIT, on an object discussed in a recent New Yorker:

"A word about E(8). In my opinion, and shared by others, E(8) is the most magnificent 'object' in all of mathematics. It is like a diamond with thousands of facets. Each facet offering a different view of its unbelievable intricate internal structure."

Another possibility —

The 4x4 square

  A more modest object —
the 4×4 square.

Update of Aug. 20-21 —

Symmetries and Facets

Kostant's poetic comparison might be applied also to this object.

The natural rearrangements (symmetries) of the 4×4 array might also be described poetically as "thousands of facets, each facet offering a different view of… internal structure."

More precisely, there are 322,560 natural rearrangements– which a poet might call facets*— of the array, each offering a different view of the array's internal structure– encoded as a unique ordered pair of symmetric graphic designs. The symmetry of the array's internal structure is reflected in the symmetry of the graphic designs. For examples, see the Diamond 16 Puzzle.

For an instance of Stevens's "three times" process, see the three parts of the 2004 web page Ideas and Art.

* For the metaphor of rearrangements as facets, note that each symmetry (rearrangement) of a Platonic solid corresponds to a rotated facet: the number of symmetries equals the number of facets times the number of rotations (edges) of each facet–

Platonic solids' symmetry groups

The metaphor of rearrangements as facets breaks down, however, when we try to use it to compute, as above with the Platonic solids, the number of natural rearrangements, or symmetries, of the 4×4 array. Actually, the true analogy is between the 16 unit squares of the 4×4 array, regarded as the 16 points of a finite 4-space (which has finitely many symmetries), and the infinitely many points of Euclidean 4-space (which has infinitely many symmetries).

If Greek geometers had started with a finite space (as in The Eightfold Cube), the history of mathematics might have dramatically illustrated Halmos's saying (Aug. 16) that

"The problem is– the genius is– given an infinite question, to think of the right finite question to ask. Once you thought of the finite answer, then you would know the right answer to the infinite question."

The Greeks, of course, answered the infinite questions first– at least for Euclidean space. Halmos was concerned with more general modern infinite spaces (such as Hilbert space) where the intuition to be gained from finite questions is still of value.

Saturday, May 19, 2007

Saturday May 19, 2007

Filed under: General — Tags: , , — m759 @ 9:29 AM
Point of View

"In a sense, too, Wallace Stevens has spent a lifetime writing a single poem. What gives his best work its astonishing power and vitality is the way in which a fixed point of view, maturing naturally, eventually takes in more than a constantly shifting point of view could get at.

The point of view is romantic, 'almost the color of comedy'; but 'the strength at the center is serious.'  Behind Wallace Stevens stand Wordsworth and Coleridge as well as Rimbaud and Mallarmé, and, surprisingly enough, La Fontaine and Pope. This poetic lineage is important only in so far as it proves that a master can claim the world as ancestor. Knowing where he stands, the poet can move as a free man in the company of free men."

Samuel French Morse, review 
of The Collected Poems
of Wallace Stevens, in
The New York Times
(October 3, 1954)
Related material

The point of view
expressed in Log24 on
  today's date in 2004:

For a related gloss on Stevens's remark
"the strength at the center is serious,"
see "Serious" (also on an October 3).

Monday, October 9, 2006

Monday October 9, 2006

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

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

“This is the garden of Apollo,
the field of Reason….”
John Outram, architect

To Apollo (10/09/02)
Art Wars: Apollo and Dionysus
Balanchine’s Birthday
Art Theory for Yom Kippur
A Form
A Form, continued
Deep Game
Gameplayers of Zen
And So To Bed
Translation Plane for Rosh Hashanah
Derrida Dead
The Nine
From Tate to Plato
Art History
A Miniature Rosetta Stone
High Concept
High Concept, Continued
Analogical Train of Thought
Today’s Sermon: Magical Thinking
Seven is Heaven, Eight is a Gate
Nine is a Vine
Apollo and Christ
Hamilton’s Whirligig
On Beauty
Sunday Morning
New Haven
Washington Ballet
Catholic Schools Sermon
The Logic of Apollo
Game Boy
Art Wars Continued: The Krauss Cross
Art Wars Continued: Pandora’s Box
The Pope in Plato’s Cave
Today’s Birthdays
Symbology 101

Saturday, August 19, 2006

Saturday August 19, 2006

Filed under: General — Tags: — m759 @ 4:28 PM

"With no means to verify its truth, superstring theory, in the words of Burton Richter, director emeritus of the Stanford Linear Accelerator Center, may turn out to be 'a kind of metaphysical wonderland.' Yet it is being pursued as vigorously as ever, its critics complain, treated as the only game in town."

— "The Inelegant Universe," by George Johnson, in the Sept. 2006 Scientific American

Some may prefer metaphysics of a different sort:

"To enter Cervantes’s world, we cross a threshold that is Shakespearean and quixotic into a metaphysical wonderland where time expands to become space and vast vaulted distances bend back on themselves, where the threads of fiction and the strands of history shuttle back and forth in the great loom of the artist’s imagination."

As wonderlands go, I personally prefer Clive Barker's Weaveworld.

Wednesday, March 29, 2006

Wednesday March 29, 2006

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

The image “http://www.log24.com/theory/images/Carmichael440.gif” cannot be displayed, because it contains errors.
Note: Carmichael's reference is to
A. Emch, "Triple and multiple systems, their geometric configurations and groups," Trans. Amer. Math. Soc. 31 (1929), 25–42.

"There is such a thing as a tesseract."
A Wrinkle in Time

Wednesday March 29, 2006

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

It turns out that Medawar (see previous entry) also wrote a deeply hostile review of Koestler’s The Act of Creation.  (See Pluto’s Republic.)

There are plenty more like Medawar, so it may be that a further effort at documentation of Diamond Theory is needed.  See this evening’s entry, to follow.

Thursday, February 9, 2006

Thursday February 9, 2006

Filed under: General — Tags: — m759 @ 9:00 PM
The Vanishing (?) President
The image “http://www.log24.com/log/pix06/060209-Summers.jpg” cannot be displayed, because it contains errors.

Karen E. Fields, translator’s introduction to Elementary Forms of the Religious Life, by Emile Durkheim:

“Durkheim breathed the air of turn-of-the-century Paris, a place that fizzed with experiments in artistic representation, and a time when philosophy, science, and art existed in nothing like today’s isolation from one another.24


24  Judith Ryan provides an illuminating account of the links joining physics, psychology, philosophy, painting, and literature in The Vanishing Subject: Early Psychology and Literary Modernism, Chicago, University of Chicago Press, 1991.”

And today’s Crimson provides an illuminating account of Judith Ryan and (implicitly) forms of the religious life at Harvard.

Related material:
The Crucifixion of John O’Hara,
The Crimson Passion,
Supper at Eight,

Thursday February 9, 2006

Filed under: General — Tags: — m759 @ 12:24 PM

Space, Time, and Scarlett

From last night’s Grammy awards, lyrics performed by Christina Aguilera and Herbie Hancock:

“a place where there’s no space or time”
Leon Russell

Not bad, but as Kat358 noted on May 4, 2005,

The image “http://www.log24.com/log/pix06/060209-Blondes.jpg” cannot be displayed, because it contains errors.

“Scarlett Johansson does this ‘old Hollywood glam’ look much better.”

For a reference to the place described in Russell’s lyrics, see the riff on the number “265”
linked to in last night’s “Midnight in the Garden of the Soul.”

Related material– Jazz Improvisation:

“Once an appropriate group of people has been assembled, you must decide what to play.”

Thursday February 9, 2006

Filed under: General — Tags: — m759 @ 12:00 AM
Midnight in the Garden
of the Soul

(continued)This time slot, reserved at midnight,
seems to belong to Frank Goodman,
who, according to this morning’s
(3 AM) New York Times, was
“one of the last of the old-time
Broadway press agents.”

Related material:

Yesterday afternoon’s entry
on a fictional “press agent
for ‘The Garden of the Soul,'”
and the entry on death
and gardens from Friday,
Feb. 3, 2006, the day
Frank Goodman died.

Friday, August 19, 2005

Friday August 19, 2005

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

Mathematics and Narrative

"There is a pleasantly discursive treatment of Pontius Pilate's unanswered question 'What is truth?'"

H. S. M. Coxeter, 1987, introduction to Richard J. Trudeau's remarks on the "Story Theory" of truth as opposed to  the "Diamond Theory" of truth " in The Non-Euclidean Revolution

"I had an epiphany: I thought 'Oh my God, this is it! People are talking about elliptic curves and of course they think they are talking mathematics. But are they really? Or are they talking about stories?'"

An organizer of last month's "Mathematics and Narrative" conference

"A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the 'Story Theory' of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.' The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes*…."

Richard J. Trudeau in The Non-Euclidean Revolution

"'Deniers' of truth… insist that each of us is trapped in his own point of view; we make up stories about the world and, in an exercise of power, try to impose them on others."

— Jim Holt in this week's New Yorker magazine.  Click on the box below.

The image “http://www.log24.com/log/pix05B/050819-Critic4.jpg” cannot be displayed, because it contains errors.

* Many stripes

   "What disciplines were represented at the meeting?"
   "Apart from historians, you mean? Oh, many: writers, artists, philosophers, semioticians, cognitive psychologists – you name it."


An organizer of last month's "Mathematics and Narrative" conference

Thursday, August 19, 2004

Thursday August 19, 2004

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

The Tiffany Code

5:01:58 AM ET:

A link for Jill St. John's birthday —

The Geometrics of Brilliance

Twinkle, twinkle…

Beach reading for
 brilliant redheads…

and for everyone else:

Click on pictures for details.

Thursday August 19, 2004

Filed under: General — Tags: — m759 @ 1:06 AM

Instantia Crucis

"Francis Bacon used the phrase instantia crucis, 'crucial instance,' to refer to something in an experiment that proves one of two hypotheses and disproves the other. Bacon's phrase was based on a sense of the Latin word crux, 'cross,' which had come to mean 'a guidepost that gives directions at a place where one road becomes two,' and hence was suitable for Bacon's metaphor."

The American Heritage® Dictionary of the English Language, Fourth Edition

The high notes hit by Harriet Wheeler, Jen Slocumb, and Alanis Morissette can, I am sorry to say, be excruciating. (See previous entry.) I greatly prefer the mellow tones of Mary Chapin Carpenter:

"I guess you're never really all alone,
        or too far from the pull of home,
An' the stars upon that painted dome
        still shine."

MCC, Grand Central Station

From an entry of 12/22/02:


As if

A white horse comes as if on wings.

— I Ching, Hexagram 22: Grace

See also

Plato, Pegasus, and the Evening Star,

Shining Forth, and

Music for Pegasus.

Carpenter's song quoted above
is from the album
Between Here and Gone,
released April 27, 2004.

Wednesday, May 19, 2004

Wednesday May 19, 2004

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


In memory of Lynn H. Loomis:

The above diagram is from a
(paper) journal note of October 21, 1999.

It pictures the relationship of my own discovery, diamond theory (at center), to the field, harmonic analysis, of Professor Loomis, a writer whose style I have long admired.

A quotation from the 1999 note:

"…it is not impossible to draw a fairly sharp dividing line between our mental disposition in the case of esthetic response and that of the responses of ordinary life.  A far more difficult question arises if we try to distinguish it from the responses made by us to certain abstract mental constructions such as those of pure mathematics…. Perhaps the distinction lies in this, that in the case of works of art the whole end and purpose is found in the exact quality of the emotional state, whereas in the case of mathematics the purpose is the constatation of the universal validity of the relations without regard to the quality of the emotion accompanying apprehension.  Still, it would be impossible to deny the close similarity of the orientation of faculties and attention in the two cases."
— Roger Fry, Transformations (1926), Doubleday Anchor paperback, 1956, p. 8

In other words, appreciating mathematics is much like appreciating art.

(Digitized diagram courtesy of Violet.)

Tuesday, August 19, 2003

Tuesday August 19, 2003

Filed under: General — Tags: — m759 @ 10:23 PM

O'Hara's Fingerpost

In The New York Times Book Review of next Sunday (August 24, 2003), Book Review editor Charles McGrath writes that author John O'Hara

"… discovered a kind of story… in which a line of dialogue or even a single observed detail indicates that something crucial has changed."

From the Online Etymology Dictionary:

crucial – 1706, from Fr. crucial… from L. crux (gen. crucis) "cross." The meaning "decisive, critical" is extended from a logical term, Instantias Crucis, adopted by Francis Bacon (1620); the notion is of cross fingerboard signposts at forking roads, thus a requirement to choose.

The remainder of this note deals with the "single observed detail" 162.



Instantias Crucis

Francis Bacon says

"Among Prerogative Instances I will put in the fourteenth place Instances of the Fingerpost, borrowing the term from the fingerposts which are set up where roads part, to indicate the several directions. These I also call Decisive and Judicial, and in some cases, Oracular and Commanding Instances. I explain them thus. When in the investigation of any nature the understanding is so balanced as to be uncertain to which of two or more natures the cause of the nature in question should be assigned on account of the frequent and ordinary concurrence of many natures, instances of the fingerpost show the union of one of the natures with the nature in question to be sure and indissoluble, of the other to be varied and separable; and thus the question is decided, and the former nature is admitted as the cause, while the latter is dismissed and rejected. Such instances afford very great light and are of high authority, the course of interpretation sometimes ending in them and being completed. Sometimes these instances of the fingerpost meet us accidentally among those already noticed, but for the most part they are new, and are expressly and designedly sought for and applied, and discovered only by earnest and active diligence."

The original:

Inter praerogativas instantiarum, ponemus loco decimo quarto Instantias Crucis; translato vocabulo a Crucibus, quae erectae in biviis indicant et signant viarum separationes. Has etiam Instantias Decisorias et Judiciales, et in casibus nonnullis Instantias Oraculi et Mandati, appellare consuevimus. Earum ratio talis est. Cum in inquisitione naturae alicujus intellectus ponitur tanquam in aequilibrio, ut incertus sit utri naturarum e duabus, vel quandoque pluribus, causa naturae inquisitae attribui aut assignari debeat, propter complurium naturarum concursum frequentem et ordinarium, instantiae crucis ostendunt consortium unius ex naturis (quoad naturam inquisitam) fidum et indissolubile, alterius autem varium et separabile ; unde terminatur quaestio, et recipitur natura illa prior pro causa, missa altera et repudiata. Itaque hujusmodi instantiae sunt maximae lucis, et quasi magnae authoritatis; ita ut curriculum interpretationis quandoque in illas desinat, et per illas perficiatur. Interdum autem Instantiae Crucis illae occurrunt et inveniuntur inter jampridem notatas; at ut plurimum novae sunt, et de industria atque ex composito quaesitae et applicatae, et diligentia sedula et acri tandem erutae.

— Francis Bacon, Novum Organum, Book Two, "Aphorisms," Section XXXVI

A Cubist Crucifixion

An alternate translation:

"When in a Search of any Nature the Understanding stands suspended, the Instances of the Fingerpost shew the true and inviolable Way in which the Question is to be decided. These Instances afford great Light…"

From a review by Adam White Scoville of Iain Pears's novel titled An Instance of the Fingerpost:

"The picture, viewed as a whole, is a cubist description, where each portrait looks strikingly different; the failings of each character's vision are obvious. However, in a cubist painting the viewer often can envision the subject in reality. Here, even after turning the last page, we still have a fuzzy view of what actually transpired. Perhaps we are meant to see the story as a cubist retelling of the crucifixion, as Pilate, Barabbas, Caiaphas, and Mary Magdalene might have told it. If so, it is sublimely done so that the realization gradually and unexpectedly dawns upon the reader. The title, taken from Sir Francis Bacon, suggests that at certain times, 'understanding stands suspended' and in that moment of clarity (somewhat like Wordsworth's 'spots of time,' I think), the answer will become apparent as if a fingerpost were pointing at the way. The final narrative is also titled An Instance of the Fingerpost, perhaps implying that we are to see truth and clarity in this version. But the biggest mystery of this book is that we have actually have no reason to credit the final narrative more than the previous three and so the story remains an enigma, its truth still uncertain."

For the "162" enigma, see


The Matthias Defense, and

The Still Point and the Wheel.

See also the December 2001 Esquire and

the conclusion of my previous entry.

Tuesday August 19, 2003

Filed under: General,Geometry — Tags: — m759 @ 5:23 PM

Intelligence Test

From my August 31, 2002, entry quoting Dr. Maria Montessori on conciseness, simplicity, and objectivity:

Above: Dr. Harrison Pope, Harvard professor of psychiatry, demonstrates the use of the Wechsler Adult Intelligence Scale "block design" subtest.

Another Harvard psychiatrist, Armand Nicholi, is in the news lately with his book The Question of God: C.S. Lewis and Sigmund Freud Debate God, Love, Sex, and the Meaning of Life






For the meaning of the Old-Testament logos above, see the remarks of Plato on the immortality of the soul at


For the meaning of the New-Testament logos above, see the remarks of R. P. Langlands at

The Institute for Advanced Study.

For the meaning of life, see

The Gospel According to Jill St. John,

whose birthday is today.

"Some sources credit her with an I.Q. of 162."

Thursday, January 9, 2003

Thursday January 9, 2003

Filed under: General — Tags: , , — m759 @ 4:48 PM

Balanchine's Birthday

Today seems an appropriate day to celebrate Apollo and the nine Muses.

From a website on Balanchine's and Stravinsky's ballet, "Apollon Musagete":

In his Poetics of Music (1942) Stravinsky says: "Summing up: What is important for the lucid ordering of the work– for its crystallization– is that all the Dionysian elements which set the imagination of the artist in motion and make the life-sap rise must be properly subjugated before they intoxicate us, and must finally be made to submit to the law: Apollo demands it."  Stravinsky conceived Apollo as a ballet blanc– a "white ballet" with classical choreography and monochromatic attire. Envisioning the work in his mind's eye, he found that "the absence of many-colored hues and of all superfluities produced a wonderful freshness." Upon first hearing Apollo, Diaghilev found it "music somehow not of this world, but from somewhere else above." The ballet closes with an Apotheosis in which Apollo leads the Muses towards Parnassus. Here, the gravely beautiful music with which the work began is truly recapitulated "on high"– ceaselessly recycled, frozen in time.

— Joseph Horowitz




Another website invoking Apollo:

The icon that I use… is the nine-fold square…. The nine-fold square has centre, periphery, axes and diagonals.  But all are present only in their bare essentials.  It is also a sequence of eight triads.  Four pass through the centre and four do not.  This is the garden of Apollo, the field of Reason…. 

In accordance with these remarks, here is the underlying structure for a ballet blanc:

A version of 'grid3x3.gif.'

This structure may seem too simple to support movements of interest, but consider the following (click to enlarge):

As Sir Arthur Quiller-Couch, paraphrasing Horace, remarks in his Whitsun, 1939, preface to the new edition of the Oxford Book of English Verse, "tamen usque recurret Apollo."

The alert reader will note that in the above diagrams, only eight of the positions move.

Which muse remains at the center?

Consider the remark of T. S. Eliot, "At the still point, there the dance is," and the fact that on the day Eliot turned 60, Olivia Newton-John was born.  How, indeed, in the words of another "sixty-year-old smiling public man," can we know the dancer from the dance?

Sunday, April 5, 2015

Night at the Museum and…

Filed under: General — m759 @ 11:52 PM

Plan 9 Resurrection

in memory of a labor leader who reportedly
died Sunday evening —

Saturday, May 1, 2021

Geometry Battlefield

Filed under: General — Tags: , — m759 @ 1:33 PM

Thursday, April 29, 2021

56 Three-Sets, 56 Spreads:

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

The Steiner Quadruple System S(3,4,8)
underlies the Steiner System S(5,8,24).

A previous update to the Oct. 29, 2019, post Triangles, Spreads, Mathieu:

Update of November 2, 2019 —

See also p. 284 of Geometry and Combinatorics:
Selected Works of J. J. Seidel
  (Academic Press, 1991).
That page is from a paper published in 1970.

That page, 284, contained an excerpt from

Bussemaker, F. C., & Seidel, J. J. (1970).
“Symmetric Hadamard matrices of order 36.”
(EUT report. WSK, Dept.of Mathematics and
Computing Science; Vol. 70-WSK-02).
Technische Hogeschool Eindhoven.

That paper is now available online:

https://pure.tue.nl/ws/files/1804543/252823.pdf .

Tuesday, April 27, 2021

New Site

Filed under: General — Tags: , — m759 @ 7:02 PM

Thursday, April 22, 2021

A New Concrete Model for an Old Abstract Space

Filed under: General — Tags: , — m759 @ 4:31 AM

The April 20 summary I wrote for ScienceOpen.com suggests
a different presentation of an Encyclopedia of Mathematics
article from 2013 —

(Click to enlarge.)

Introduction to the Square Model of Fano's 1892 Finite 3-Space

Keywords: PG(3,2), Fano space, projective space, finite geometry, square model,
Cullinane diamond theorem, octad group, MOG.

Cite as

Cullinane, Steven H. (2021).
“The Square Model of Fano’s 1892 Finite 3-Space.”
https://doi.org/10.5281/zenodo.4718182 .

An earlier version of the square model of PG(3,2) —

Friday, November 13, 2020


Filed under: General — Tags: , — m759 @ 1:15 PM

Raiders of the Lost Dorm Room

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

“That really is, really, I think, the Island of the Misfit Toys at that point.
You have crossed the Rubicon, you jumped on the crazy train and
you’re headed into the cliffs that guard the flat earth at that time, brother,”
said Rep. Denver Riggleman, a Republican congressman from Virginia,
in an interview.”

— Jon Ward, political correspondent, Yahoo News , Nov. 12, 2020

The instinct for heaven had its counterpart:
The instinct for earth, for New Haven, for his room,
The gay tournamonde as of a single world

In which he is and as and is are one.

— Wallace Stevens, “An Ordinary Evening in New Haven


Related material for comedians

See as well Sallows in this  journal.

“There exists a considerable literature
devoted to the Lo shu , much of it infected
with the kind of crypto-mystic twaddle
met with in Feng Shui.”

— Lee C. F. Sallows, Geometric Magic Squares ,
Dover Publications, 2013, page 121

Wednesday, November 11, 2020

An Ordinary Evening in New Haven

Filed under: General — Tags: — m759 @ 9:09 PM

Anthony Hopkins in 'The Human Stain'

Prof. Coleman Silk introducing  freshmen to academic values

“The communication
of the dead is tongued with fire
beyond the language of the living.”

— T. S. Eliot, Four Quartets

Wednesday, April 1, 2020

The Ghost

Filed under: General — Tags: — m759 @ 2:10 PM

Related material —

Sunday’s Plan 9 from Yale  as well as

http://www.arcadiainstitution.org/?page_id=16  and


Sunday, March 29, 2020

Metatextuality at Yale

Filed under: General — Tags: — m759 @ 5:37 PM

See also this  journal on the date — February 19, 2009
of the above Ibsen opening, as well as today’s previous post.

Monday, March 9, 2020

“Archimedes at Hiroshima” Continues.

Filed under: General — Tags: , , — m759 @ 7:34 PM

The title is from a post of January 10, 2019.

A figure from this journal on June 1, 2019

The following figure may help relate labelings of the
truncated octahedron (“permutahedron”) to labelings
of its fellow Archimedean solid, the cuboctahedron.

See as well other posts tagged Aitchison.

Max von Sydow

Filed under: General — Tags: , — m759 @ 9:08 AM

The Bucharest Wheel

Filed under: General — Tags: , — m759 @ 8:14 AM

From the Bucharest author in last night's 12:12 AM post

From this  journal on the above date, Feb. 16, 2011 —

The Bucharest Cross

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

For fans of "The Zero Theorem" —

The 24 permutations of S4 arranged on a cube
by Cristi Stoica of Bucharest at

Friday, February 21, 2020

To and Fro, Back and …

Filed under: General — Tags: , , — m759 @ 11:44 PM

Also on January 27, 2017 . . .

For other appearances of John Hurt here,
see 1984 Cubes.

Update of 12:45 AM Feb. 22 —

A check of later obituaries reveals that Hurt may well
have died on January 25, 2017, not January 27 as above.

Thus the following remarks may be more appropriate:

Not to mention what, why, who, and how.

Tuesday, December 24, 2019

Stille Nacht

Filed under: General — Tags: , — m759 @ 11:55 PM

Later in the film "He's not Einstein You're  Einstein."

Related material at the University of Iowa —

See as well this  journal on the above Daily Iowan  date.

Lucy Noir …

Filed under: General — Tags: , — m759 @ 10:21 AM

… Continued from August 26

Heidegger, "Hölderlin and the Essence of Poetry,"
translated by Douglas Scott, in Existence and Being  ,
Regnery, 1949, pp. 291-316—

IMAGE- Page 304 of Heidegger's 'Existence and Being' - Heidegger's essay 'Hölderlin and the Essence of Poetry,' tr. by Douglas Scott, publ. by Henry Regnery Company, Chicago, in 1949

See as well Readings for St. Patrick's Day, March 17, 2005.

Saturday, November 9, 2019


Filed under: General — Tags: , — m759 @ 6:34 AM

"Nor again will I pretend that, as Bacon asserts, `the pleasure and delight of knowledge and learning far surpasseth all other in nature'. This is too much the language of a salesman crying his own wares. The pleasures of the intellect are notoriously less vivid than either the pleasures of sense or the pleasures of the affections; and therefore, especially in the season of youth, the pursuit of knowledge is likely enough to be neglected and lightly esteemed in comparison with other pursuits offering much stronger immediate attractions. But the pleasure of learning and knowing, though not the keenest, is yet the least perishable of pleasures; the least subject to external things, and the play of chance, and the wear of time. And as a prudent man puts money by to serve as a provision for the material wants of his old age, so too he needs to lay up against the end of his days provision for the intellect. As the years go by, comparative values are found to alter: Time, says Sophocles, takes many things which once were pleasures and brings them nearer to pain. In the day when the strong men shall bow themselves, and desire shall fail, it will be a matter of yet more concern than now, whether one can say `my mind to me a kingdom is'; and whether the windows of the soul look out upon a broad and delightful landscape, or face nothing but a brick wall."

– A.E. Housman, Inaugural Lecture as Professor of Latin,
University College, London, 1892
, as quoted at . . .


Hello, Mr. Chips

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

A geometric diagram by the late Andrew Jobbings (1951-2019) —

From a book review quoted here on the date of Jobbings's death —

"Dodge is eventually brought back to life, or a kind of virtual afterlife,
in the 'Bitworld' where he exists as ones and zeros. Initially inchoate,
Dodge’s mind evolves, along with the digital environment he creates
around him, a kind of information-age Genesis story that Stephenson
describes evocatively."


Filed under: General — Tags: , — m759 @ 5:00 AM

"Something there is that doen't love a wall."

Wednesday, October 2, 2019

Struck by the Fusion

Filed under: General — Tags: — m759 @ 2:50 PM

"… I was struck by the fusion of drama and music.”

— Autobiographical recollection by a music critic who
reportedly died on Sunday at 83.

Related material — The previous post and

Social Climbing

Filed under: General — Tags: — m759 @ 2:13 PM

"When the queen came, they said she was wanton.
Or a witch, or a saint."

Ursula Whitcher,  "Alphabet of Signs"

Related images —

A Long Literary Tradition

Filed under: General — Tags: , — m759 @ 12:38 PM

"There's a long literary tradition associating
certain kinds of geometry with horror."

— American Mathematical Society yesterday:

See also yesterday's Log24 post "Transylvania Revisited."

A related post —

Harvard Showbiz.

Tuesday, October 1, 2019

Transylvania Revisited

Filed under: General — Tags: — m759 @ 2:10 PM

The previous post suggests . . .

Jim Holt reviewing Edward Rothstein's Emblems of Mind: The Inner Life of Music and Mathematics  in The New Yorker  of June 5, 1995:

"The fugues of Bach, the symphonies of Haydn, the sonatas of Mozart: these were explorations of ideal form, unprofaned by extramusical associations. Such 'absolute music,' as it came to be called, had sloughed off its motley cultural trappings. It had got in touch with its essence. Which is why, as Walter Pater famously put it, 'all art constantly aspires towards the condition of music.'

The only art that can rival music for sheer etheriality is mathematics. A century or so after the advent of absolute music, mathematics also succeeded in detaching itself from the world. The decisive event was the invention of strange, non-Euclidean geometries, which put paid to the notion that the mathematician was exclusively, or even primarily, concerned with the scientific universe. 'Pure' mathematics came to be seen by those who practiced it as a free invention of the imagination, gloriously indifferent to practical affairs– a quest for beauty as well as truth." [Links added.]

A line for James McAvoy —

"Pardon me boy, is this the Transylvania Station?"

Bolyai 'worlds out of nothing' quote

See as well Worlds Out of Nothing ,  by Jeremy Gray.

Hijacking the Vatican

Filed under: General — Tags: , — m759 @ 12:42 PM

Rothstein's 'Emblems of Mind,' 1995, cover illustrations by Pinturicchio from Vatican

Cover illustration— Arithmetic and Music,
Borgia Apartments, the Vatican.

See also Rothstein in this journal.

Related posts: The Eightfold Hijacking.

Monday, September 30, 2019

Defining a Space

Filed under: General — Tags: , — m759 @ 8:57 PM

See also Nada Brahma  in this  journal.

Multiplicity on Michaelmas

Filed under: General — Tags: , — m759 @ 5:54 AM

"We need a multiplicity of viewpoints."

— Philip Pullman in a New Yorker  interview
     published yesterday 

See as well Pullman's "Golden Compass"
in posts tagged

Nothing New.

Sunday, September 29, 2019

The Analyst

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

"The analyst, by freeing himself from the 'enchainment to past and future',
casts off the arbitrary pattern and waits for new aesthetic form to emerge,
which will (it is hoped) transform the content of the analytic encounter."

— From Psychoanalytic Aesthetics: The British School ,
by Nicola GloverChapter 4  

Shana Tova .

Dominus Illuminatio (from the Oxford motto)

Filed under: General — Tags: — m759 @ 10:01 AM

Related literary remarks — Raiders of the Lost Birthday.

Monday, September 23, 2019

Rabbit Hole Meets Memory Hole:

Filed under: General — Tags: , , — m759 @ 9:11 AM

The disappearance of "Christo et Ecclesiae" at Harvard

Rabbit Hole 

Memory Hole

The above Harvard seal in a PDF —

The same page, minus the seal, today at the Internet Archive — 

For a larger image of the seal-less page, click here.

Happy Fall 2019!

Click to enlarge.

Sunday, September 22, 2019

Colorful Tale

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

“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”

— Hermann Weyl, Philosophy of  Mathematics and
    Natural Science 
, Princeton, 1949, p. 237

"The bond with reality is cut."

— Hans Freudenthal, 1962

Indeed it is.

From page 180, Logicomix — It was a dark and stormy night


Whitehead and the Relativity Problem

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

"This is the relativity problem: to fix objectively a class of
equivalent coordinatizations and to ascertain the group of
transformations S mediating between them."
— Hermann Weyl, The Classical Groups,
    Princeton University Press, 1946, p. 16

Thursday, August 29, 2019

Spirits Rise

Filed under: General — Tags: — m759 @ 7:33 PM

"In real life, Sophia Lillis loves horror…."

— https://www.cheatsheet.com/entertainment/

"Spirits rise and their dance is unrehearsed…." 

— A nightmare song by Barbra Streisand

But not, perhaps, horror in real life . . .

Poe Street Dead End

As Well

Filed under: General — Tags: , , — m759 @ 12:45 PM

For some backstory, see
http://m759.net/wordpress/?s=”I+Ching”+48+well .

See as well elegantly packaged” in this journal.

“Well” in written Chinese is the hashtag symbol,
i.e., the framework of a 3×3 array.

My own favorite 3×3 array is the ABC subsquare
at lower right in the figure below —

'Desargues via Rosenhain'- April 1, 2013- The large Desargues configuration mapped canonically to the 4x4 square



Filed under: General — Tags: , — m759 @ 11:59 AM

See "Anastas…" in this journal.

Fashion News for Fury Road

Filed under: General — Tags: , — m759 @ 1:25 AM

Charlize Theron in 'Mad Max: Fury Road' says 'Redemption.'

The Fashion Eagle…

Filed under: General — Tags: — m759 @ 12:33 AM

Or:   404 Found!  continued.

For Carol Danvers* (Battle Angel )**

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

* See Wikipedia and the previous post.

** See Into the Sunset (Aug. 24).

Wednesday, August 28, 2019

Le Supplement

Filed under: General — Tags: — m759 @ 3:46 PM

Click TLS image for the source.

Sunday, August 25, 2019

Design Theory

Filed under: General — Tags: , , — m759 @ 7:58 PM

"Mein Führer Steiner"

See Hitler Plans and Quadruple System.

"There is  such a thing as a quadruple system."

— Saying adapted from a 1962 young-adult novel

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