Friday, February 5, 2021

ABC Art Code

Filed under: General — m759 @ 7:04 PM

Continued from January 14

A colored version using CSS —

See https://codepen.io/m759/pen/wvoGwzx .

Thursday, January 14, 2021

ABC Art: A Portcullis for Mondrian

Filed under: General — m759 @ 3:58 PM

Links to related Log24 posts —

Don’t forget the portcullis, Dutch Boy!” and Mondrian.

Friday, September 21, 2018


Filed under: G-Notes,General,Geometry — Tags: — m759 @ 4:36 AM

Monday, August 22, 2016

Minimal ABC Art

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

Two portions of a post from Guy Fawkes Day 2015


Other art for Guy Fawkes Day

Cloak and Dagger

Saturday, April 16, 2016


Filed under: General — m759 @ 12:00 PM

A search in Log24 for Wallace Stevens's phrase
"the A B C of Being" suggests a related search, for
"Happy Birthday, Wallace Stevens." That search
in turn suggests a search for "Maori."

“Literature begins with geography.”

— Attributed to Robert Frost

Sunday, November 8, 2015


Filed under: General — m759 @ 7:00 PM

Thursday, November 5, 2015

ABC Art or: Guitart Solo

Filed under: General,Geometry — Tags: , — m759 @ 5:55 PM

“… the A B C of being….” — Wallace Stevens

Scholia —

Compare to my own later note, from March 4, 2010 —

“It seems that Guitart discovered these ‘A, B, C’ generators first,
though he did not display them in their natural setting,
the eightfold cube.” — Borromean Generators (Log24, Oct. 19)

See also Raiders of the Lost Crucible (Halloween 2015)
and “Guitar Solo” from the 2015 CMA Awards on ABC.

Thursday, January 8, 2015

ABC Verlag, Zurich

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

IMAGE- Dust jacket, 'Conceptions of International Exhibitions,' by Hans Neuburg, ABC Verlag, Zurich, 1969

"The motive for metaphor, shrinking from
The weight of primary noon,
The A B C of being…." — Wallace Stevens

See also Cube Trinity in this journal.

Wednesday, January 20, 2021

It’s Easy

Filed under: General — Tags: — m759 @ 4:18 PM

See as well ABC in this journal.

Sunday, July 5, 2020

Annals of Medicine:

Filed under: General — m759 @ 11:29 PM

Death by Ventilator

Related reading —

As doctors got a crash course in the new disease,
their stance on ventilators began to evolve.

Saturday, April 18, 2020


Filed under: General — m759 @ 6:30 PM

Thursday, November 7, 2019

Jagged Crest

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

"The man touched the white bishop, queen and king,
and ran his finger over the jagged crest of the rook.
Then, sitting down before the chess set owner could nod
his head, he made his first move with the white pawn."

The late Stephen Dixon, "The Chess House," in
The Paris Review Winter-Spring 1963 (early in 1963).

I Ching chessboard (original 1989 arrangement)

Friday, October 18, 2019


Filed under: General — Tags: — m759 @ 8:43 PM

Continued from September 24 —

From today's news . . .

" 'If the nesting doll fits '
'This is not some outlandish claim. This is reality.' " 

Related images from 4 AM ET today —

See as well today's previous post, "Vibe for Ray Bradbury."
Bradbury was the author of the 1955 classic The October Country .

Thursday, August 29, 2019

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


Friday, May 10, 2019

Desperately Seeking Resonance

Filed under: General — Tags: , , — m759 @ 10:46 AM


Also from Fall Equinox 2018 — Looney Tune for Physicists

Sunday, December 9, 2018

Quaternions in a Small Space

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

The previous post, on the 3×3 square in ancient China,
suggests a review of group actions on that square
that include the quaternion group.

Click to enlarge

Three links from the above finitegeometry.org webpage on the
quaternion group —

Related material —

Iain Aitchison on the 'symmetric generation' of R. T. Curtis

See as well the two Log24 posts of December 1st, 2018 —

Character and In Memoriam.

Sunday, September 23, 2018

Three Times Eight

Filed under: General,Geometry — Tags: — m759 @ 9:21 AM

The New York Times 's Sunday School today —

I prefer the three bricks of the Miracle Octad Generator —

Image result for mog miracle octad bricks

Saturday, September 22, 2018

Minimalist Configuration

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 11:03 PM

From the previous post

From Wikipedia

From Log24

The Venturi Manifesto

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 1:00 PM

Venturi reportedly died on Tuesday, September 18.*

See also this journal on that date.

* Fact check:

Symmetric Generation, by Curtis

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 10:15 AM

Norwegian artist Josefine Lyche —

Lyche's shirt honors the late Kurt Cobain.

"Here we are now, entertain us."

Symmetric Generation, by Netflix

Filed under: General — Tags: , — m759 @ 5:05 AM

Suggested by the previous post . . .

'Out of nothing' opening of 'Maniac' at Netflix

"The pattern is the pattern."

Friday, September 21, 2018

Symmetric Generation, by Nao

Filed under: General — Tags: , — m759 @ 1:30 PM

"The creation of a new world
        starts now.
Once again I am tied
        to the logic of this

Bill Murray and Scarlett Johansson in 'Lost in Translation'

Thursday, September 20, 2018

Clash of the Titans

Filed under: General — Tags: , — m759 @ 6:18 PM

Sunday, September 9, 2018

Plan 9 Continues.

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

"The role of Desargues's theorem was not understood until
the Desargues configuration was discovered. For example,
the fundamental role of Desargues's theorem in the coordinatization
of synthetic projective geometry can only be understood in the light
of the Desargues configuration.

Thus, even as simple a formal statement as Desargues's theorem
is not quite what it purports to be. The statement of Desargues's theorem
pretends to be definitive, but in reality it is only the tip of an iceberg
of connections with other facts of mathematics."

— From p. 192 of "The Phenomenology of Mathematical Proof,"
by Gian-Carlo Rota, in Synthese , Vol. 111, No. 2, Proof and Progress
in Mathematics
(May, 1997), pp. 183-196. Published by: Springer.

Stable URL: https://www.jstor.org/stable/20117627.

Related figures —

Note the 3×3 subsquare containing the triangles ABC, etc.

"That in which space itself is contained" — Wallace Stevens

Tuesday, June 26, 2018

Rock Notes

Filed under: General — m759 @ 9:34 AM

Photo caption

"Vinnie Paul of the band Hellyeah performs in concert
during Day 2 of the Rock Allegiance Festival at
Talen Energy Stadium on Sunday, Sept. 18, 2016, in
Chester, Pa. (Photo by Owen Sweeney/Invision/AP)"

News report

"Former SKID ROW singer Sebastian Bach played
a cover version of the PANTERA classic 
"Cemetery Gates" as a tribute to Vinnie Paul Abbott 
during his June 24 concert at The Pyramid Cabaret in
Winnipeg, Manitoba, Canada."

Some backstory

Sunday, October 29, 2017

Sunday in the Park

Filed under: General — Tags: — m759 @ 1:18 PM


Scholium —

Related material —  Sunday in the Park  in this  journal.

Wednesday, December 14, 2016

Graveyard Roses

Filed under: General — m759 @ 2:35 AM

Two deaths on Tuesday, Dec. 13, 2016 —

In memory of game show figure Alan Thicke —

Minimal ABC Art.

In memory of game theory author Thomas Schelling —

Barbara Rose in a Log24 search for Princeton + Art.

Saturday, August 27, 2016


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

See a search for the title in this journal.

Related material:

The incarnation of three permutations,
named A, B, and C,
on the 7-set of digits {1, 2, 3, 4, 5, 6, 7}
as  permutations on the eightfold cube.

See Minimal ABC Art, a post of August 22, 2016.

Tuesday, August 23, 2016

Puritan Contemplation:

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

For an authority on Japanese art —

Text Tiles*

Res ipsa loquitur.

Compare to and contrast with 

Remarks on art, contemplation. and Puritanism
from a recent Princeton University Press book —

“Lucy Lippard distinguished Asian art
(ego-less and contemplative)
from New York Minimalism
(moralistic and puritanical).”
Mathematics and Art ,
Princeton U. Press, Fall 2015

* Update of Aug. 24, 2016 — See also Nov. 2, 2014.

Sunday, August 21, 2016

Big Meeting

Filed under: General — m759 @ 10:00 PM

Grosses Treffen


See also Log24 on the above Berlin date — April 16, 2016 —

For some historical background, see
the post ABC Art of November 8, 2015.

Wednesday, March 9, 2016

Requiem for a Producer

Filed under: General — m759 @ 9:19 AM

                                                               Album cover by Richard Ward

Thursday, January 14, 2016

Exit Slytherin

Filed under: General — m759 @ 3:51 PM

This unfortunate title seems inevitable in light of the previous post.

Wednesday, November 18, 2015

Friday, October 2, 2015


Filed under: General,Geometry — m759 @ 9:28 PM

"The close of trading today will spell a new era for Google
as the search giant becomes a part of new holding company 
Alphabet Inc." — ABC News, 1:53 PM ET today

From an Aug. 10, 2015, letter by Larry Page announcing the change:

Other business philosophy:

Strategy Rules: Five Timeless Lessons from
Bill Gates, Andy Grove, and Steve Jobs

by David B. Yoffie, Michael A. Cusumano

On Sale: 04/14/2015

A not-so-timeless lesson: a synchronicity check
(of this journal, not of the oeuvre  of Joseph Jaworski) —

04/14/2015 — Sacramental Geometry.

Saturday, September 5, 2015

Operation Blockhead

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

New Yorker  writer on the new parent corporation of
Google, named Alphabet:

"In Larry Page’s letter explaining it to us, Alphabet
is illustrated with a bunch of kids’ building blocks. 
Operation Childlike Innocence, Phase One."

— Sarah Larson

Building blocks, Sarah, are not the same thing
as alphabet blocks.  For the distinction, see a
Log24 post of August 14, 2015, "Being Interpreted."

The New Yorker  apparently also has another fact wrong.
The official version of Page's letter is not  "illustrated."
Perhaps, Sarah, you mistook the new Alphabet website
abc.xyz, which did show alphabet blocks and quoted
Page's letter, for the letter itself.

Friday, August 14, 2015

Being Interpreted

Filed under: General,Geometry — Tags: — m759 @ 12:31 AM

The ABC of things —

Froebel's Third Gift: A cube made up of eight subcubes

The ABC of words —

A nutshell —

Book lessons —

IMAGE- History of Mathematics in a Nutshell

Tuesday, August 11, 2015

The XYZ of Being

Filed under: General — m759 @ 11:00 AM

"The Stone" column in yesterday's New York Times :

"But where, exactly, is the border between
the private exchange of money or gifts
and the impersonal profit-making of the market?"

Good question.

Some background on the market —

Thursday, July 23, 2015


Filed under: General — m759 @ 1:15 PM

   It's Space Week at Camp Google

“… the object sets up
 a kind of frame or space or field 
   within which there can be epiphany.”
— Charles Taylor       
Kylie Minogue does the Locomotion

“My little baby sister can do it with ease.
It’s easier to learn than those ABC’s.”

— Kylie Minogue           

Monday, February 23, 2015

For Katy Perry

Filed under: General — Tags: — m759 @ 10:15 PM

See also this  journal on the date of Mr. Howard's death:

"Mark my words
This love will make you levitate
Like a bird"

— Katy Perry, "Dark Horse"

“It’s the Super Bowl, I guess,”
Michael Keaton said in the first minutes
of ABC’s official Oscar red-carpet special."

— Hallie Cantor in the online New Yorker  today

Thursday, October 16, 2014

Seeking Kleos

Filed under: General — Tags: — m759 @ 6:22 PM

Rebecca Newberger Goldstein, quoted in a webpage dated
October 7, 2014 (presumably according to Australian time):

"For the Athenians, kleos  mattered more than anything,
according to Goldstein.

'Kleos  is fame: it’s the deed that brings fame, it’s the poem
that sings your triumphs, it’s having your life replicated in
other minds, acquiring a kind of moreness, a kind of
secular immortality.' "

Related material:

A check of Goldstein's definition…

… and an image for Broomsday:

Rebecca Goldstein and a Cullinane quaternion

From Argument for the Existence of Rebecca (Feb. 6, 2010)

Tuesday, September 30, 2014

Pythagorean Selfie

Filed under: General — m759 @ 5:01 PM

“Rarely is a TV show as brilliant and as terrible as Selfie .”

Kevin Fallon on a new ABC TV show that starts tonight at 8 PM ET

A recent selfie from Josefine Lyche’s Instagram page:

For some remarks related to Lyche’s pentagram, see
Lyche + Mathmagic* and also yesterday’s Michaelmas Mystery.

In today’s previous post, the late Harvey Cohn posed a question that
he said might have been asked by Pythagoras:

“It is an elementary observation that an integral right triangle
has an even area. Suppose the hypotenuse is prime.

Q.  How do we determine from the prime value of the hypotenuse
when the area is divisible by 4, 8, 16, or any higher power of 2?

A.  We use class fields constructed by means of transcendental
functions, of course!”

— From the preface to Introduction to the Construction of Class Fields ,
by Harvey Cohn (Cambridge University Press, 1985)


For a related song, see Prime Suspect (Dec. 13, 2007).

Footnote of 12:14 AM Oct. 1, 2014 —

* That search yields a link to…

This Lyche webpage’s pentagram  indicates an interest in Disney rather than
in SatanismOther Lyche webpages have been less reassuring.

Related material — Posts tagged Elegantly Packaged.

Friday, March 7, 2014

Field Dream

Filed under: General — m759 @ 7:11 PM

A field in China —

IMAGE- Chinese field from opening of TV series 'Resurrection'

The following link was suggested by today’s previous post
and by the ABC TV series “Resurrection” scheduled to start
at 9 PM ET Sunday, March 9, 2014 —

Field Dream

Tuesday, March 4, 2014


Filed under: General — m759 @ 12:00 AM

"… in Speedtalk it was… difficult not  to be logical."

— Robert A. Heinlein in Gulf 

Related material: ABC TV at 9 PM ET
on Sunday, March 9, 2014… 3/09.

See also page  309 in the previous post, Outside the Box.

Shades of Plan 9.

Saturday, November 16, 2013

Chapel (continued)

Filed under: General — m759 @ 11:30 PM

In memory of the translator of Foucault's Pendulum ,
who reportedly died on Tuesday, November 12th—

A detail from an image search (2 MB) linked to here 
on that date:

See also Milano  in this journal.

Tuesday, October 8, 2013

S in a Diamond

Filed under: General — m759 @ 10:00 PM

For Amy Adams, who in a recent
Superman film posed the question

"What's the S stand for?"

This logo appears on the new game
Beyond: Two Souls . (See this evening's
earlier post on the game.)

In a more appealing sort of computer
entertainment, the S might stand for Scarlett.

"Please wait as your operating system is initiated."

(From the October 5th post Dream Girls.) 

Monday, August 19, 2013


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

Last midnight's post quoted poet John Hollander
on Cervantes—

"… the Don’s view of the world is correct at midnight,
and Sancho’s at noon."

The post concluded with a figure that might, if
rotated slightly, be regarded as a sort of Star of
David or Solomon's Seal. The figure's six vertices
may be viewed as an illustration of Pascal's
"mystic hexagram."

Pacal's hexagram is usually described
as a hexagon inscribed in a conic
(such as a circle). Clearly the hexagon
above may be so inscribed.

The figure suggests that last midnight's Don be
played by the nineteenth-century mathematician
James Joseph Sylvester. His 1854 remarks on
the nature of geometry describe a different approach
to the Pascal hexagram—

"… the celebrated theorem of Pascal known under the name of the Mystic Hexagram, which is, that if you take two straight lines in a plane, and draw at random other straight lines traversing in a zigzag fashion between them, from A in the first to B in the second, from B in the second to C in the first, from C in the first to D in the second, from D in the second to E in the first, from E in the first to F in the second and finally from F in the second back again to A the starting point in the first, so as to obtain ABCDEF a twisted hexagon, or sort of cat's-cradle figure and if you arrange the six lines so drawn symmetrically in three couples: viz. the 1st and 4th in one couple, the 2nd and 5th in a second couple, the 3rd and 6th in a third couple; then (no matter how the points ACE have been selected upon one of the given lines, and BDF upon the other) the three points through which these three couples of lines respectively pass, or to which they converge (as the case may be) will lie all in one and the same straight line."

For a Sancho view of Sylvester's "cat's cradle," see some twentieth-century
remarks on "the most important configuration of all geometry"—

"Now look, your grace," said Sancho,
"what you see over there aren't giants,
but windmills, and what seems to be arms
are just their sails, that go around in the wind
and turn the millstone."
"Obviously," replied Don Quijote,
"you don't know much about adventures.”

― Miguel de Cervantes Saavedra

Monday, April 1, 2013

Desargues via Rosenhain

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

Background: Rosenhain and Göpel Tetrads in PG(3,2)


The Large Desargues Configuration

Added by Steven H. Cullinane on Friday, April 19, 2013

Desargues' theorem according to a standard textbook:

"If two triangles are perspective from a point
they are perspective from a line."

The converse, from the same book:

"If two triangles are perspective from a line
they are perspective from a point."

Desargues' theorem according to Wikipedia 
combines the above statements:

"Two triangles are in perspective axially  [i.e., from a line]
if and only if they are in perspective centrally  [i.e., from a point]."

A figure often used to illustrate the theorem, 
the Desargues configuration , has 10 points and 10 lines,
with 3 points on each line and 3 lines on each point.

A discussion of the "if and only if" version of the theorem
in light of Galois geometry requires a larger configuration—
15 points and 20 lines, with 3 points on each line 
and 4 lines on each point.

This large  Desargues configuration involves a third triangle,
needed for the proof   (though not the statement ) of the 
"if and only if" version of the theorem. Labeled simply
"Desargues' Theorem," the large  configuration is the
frontispiece to Volume I (Foundations)  of Baker's 6-volume
Principles of Geometry .

Point-line incidence in this larger configuration is,
as noted in the post of April 1 that follows
this introduction, described concisely 
by 20 Rosenhain tetrads  (defined in 1905 by
R. W. H. T. Hudson in Kummer's Quartic Surface ).

The third triangle, within the larger configuration,
is pictured below.

IMAGE- The proof of the converse of Desargues' theorem involves a third triangle.



A connection discovered today (April 1, 2013)—

(Click to enlarge the image below.)

Update of April 18, 2013

Note that  Baker's Desargues-theorem figure has three triangles,
ABC, A'B'C', A"B"C", instead of the two triangles that occur in
the statement of the theorem. The third triangle appears in the
course of proving, not just stating, the theorem (or, more precisely,
its converse). See, for instance, a note on a standard textbook for 
further details.

(End of April 18, 2013 update.)

Update of April 14, 2013

See Baker's Proof (Edited for the Web) for a detailed explanation 
of the above picture of Baker's Desargues-theorem frontispiece.

(End of April 14, 2013 update.)

Update of April 12, 2013

A different figure, from a site at National Tsing Hua University,
shows the three triangles of Baker's figure more clearly:

IMAGE- Desargues' theorem with three triangles, and Galois-geometry version

(End of update of April 12, 2013)

Update of April 13, 2013

Another in a series of figures illustrating
Desargues's theorem in light of Galois geometry:
IMAGE- Veblen and Young 1910 Desargues illustration, with 2013 Galois-geometry version

See also the original Veblen-Young figure in context.

(End of update of April 13, 2013)

Rota's remarks, while perhaps not completely accurate, provide some context
for the above Desargues-Rosenhain connection.  For some other context,
see the interplay in this journal between classical and finite geometry, i.e.
between Euclid and Galois.

For the recent  context of the above finite-geometry version of Baker's Vol. I
frontispiece, see Sunday evening's finite-geometry version of Baker's Vol. IV
frontispiece, featuring the Göpel, rather than the Rosenhain, tetrads.

For a 1986 illustration of Göpel and Rosenhain tetrads (though not under
those names), see Picturing the Smallest Projective 3-Space.

In summary… the following classical-geometry figures
are closely related to the Galois geometry PG(3,2):

Volume I of Baker's Principles  
has a cover closely related to 
the Rosenhain tetrads in PG(3,2)
Volume IV of Baker's Principles 
has a cover closely related to
the Göpel tetrads in PG(3,2) 
(click to enlarge)




Higher Geometry
(click to enlarge)





Sunday, January 20, 2013

Field of Dreams

Filed under: General — m759 @ 12:48 AM

The Presidential Medal of Freedom, the highest honor
that can be bestowed on a civilian, was presented to
Stan Musial at the White House on Feb 15, 2011.


Tuesday, November 6, 2012

Bend Sinister

Filed under: General — m759 @ 6:30 AM

This morning's New York Times  obituaries—

These suggest a look at Solving Nabokov's Lolita Riddle ,
by Joanne Morgan (Sydney: Cosynch Press, 2005).

That book discusses Lolita as a character like Lewis Carroll's Alice.

(The Red Queen and Alice of course correspond to figures in
the first two thumbnails above.)

From the obituary associated with the third thumbnail above:

"Front-page headlines combined concision and dark humor." 

The title of this post, Bend Sinister , is not unlike such a headline.
It is the title of a novel by Nabokov (often compared with Orwell's 1984 )
that is discussed in the Lolita Riddle  book.

Related material— The bend sinister found in Log24 searches
for Hexagram 14 and for the phrase Hands-On

IMAGE- Magician's hands on his wand, viewed as a diagonal of a square

Tuesday, October 23, 2012

The Lovely Bones

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


"… and crown thy good with brotherhood…"

"The brothers are charged with murder,
conspiracy to commit murder,
disposing a body,
and tampering with evidence,
according to police."

Tuesday, May 8, 2012

Exit, Pursued by Wild Thing

Filed under: General — m759 @ 1:00 PM

In memory of author Maurice Sendak,
who has died at 83—

"President Obama and his family read from
Where the Wild Things Are  at this year’s
White House Easter Egg Roll." —ABC News

See also Easter Act and Shaggy Dance.

Thursday, March 22, 2012

Square-Triangle Theorem continued

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

Last night's post described a book by Alexander Soifer
on questions closely related to— and possibly
suggested by— a Miscellanea  item and a letter to
the editor
in the American Mathematical Monthly ,
June-July issues of 1984 and 1985.

Further search yields a series of three papers by
Michael Beeson on the same questions. These papers are
more mathematically  presentable than Soifer's book.

Triangle Tiling I 


       March 2, 2012

Triangle Tiling II 


       February 18, 2012

Triangle Tiling III 


       March 11, 2012 

These three recent preprints replace some 2010 drafts not now available.
Here are the abstracts of those drafts—

"Tiling triangle ABC with congruent triangles similar to ABC"
 (March 13, 2010),

"Tiling a triangle with congruent triangles"
(July 1, 2010).

Beeson, like Soifer, omits any reference to the "Triangles are square" item
of 1984 and the followup letter of 1985 in the Monthly .

Thursday, March 1, 2012

Block That Metaphor:

Filed under: General,Geometry — Tags: — m759 @ 11:09 PM

The Cube Model and Peano Arithmetic

The eightfold cube  model of the Fano plane may or may not have influenced a new paper (with the date Feb. 10, 2011, in its URL) on an attempted consistency proof of Peano arithmetic—

The Consistency of Arithmetic, by Storrs McCall

"Is Peano arithmetic (PA) consistent?  This paper contains a proof that it is. …

Axiomatic proofs we may categorize as 'syntactic', meaning that they concern only symbols and the derivation of one string of symbols from another, according to set rules.  'Semantic' proofs, on the other hand, differ from syntactic proofs in being based not only on symbols but on a non-symbolic, non-linguistic component, a domain of objects.    If the sole paradigm of 'proof ' in mathematics is 'axiomatic proof ', in which to prove a formula means to deduce it from axioms using specified rules of inference, then Gödel indeed appears to have had the last word on the question of PA-consistency.  But in addition to axiomatic proofs there is another kind of proof.   In this paper I give a proof of PA's consistency based on a formal semantics for PA.   To my knowledge, no semantic consistency proof of Peano arithmetic has yet been constructed.

The difference between 'semantic' and 'syntactic' theories is described by van Fraassen in his book The Scientific Image :

"The syntactic picture of a theory identifies it with a body of theorems, stated in one particular language chosen for the expression of that theory.  This should be contrasted with the alternative of presenting a theory in the first instance by identifying a class of structures as its models.  In this second, semantic, approach the language used to express the theory is neither basic nor unique; the same class of structures could well be described in radically different ways, each with its own limitations.  The models occupy centre stage." (1980, p. 44)

Van Fraassen gives the example on p. 42 of a consistency proof in formal geometry that is based on a non-linguistic model.  Suppose we wish to prove the consistency of the following geometric axioms:

A1.  For any two lines, there is at most one point that lies on both.
A2.  For any two points, there is exactly one line that lies on both.
A3.  On every line there lie at least two points.

The following diagram shows the axioms to be consistent:

Figure 1

The consistency proof is not a 'syntactic' one, in which the consistency of A1-A3 is derived as a theorem of a deductive system, but is based on a non-linguistic structure.  It is a semantic as opposed to a syntactic proof.  The proof constructed in this paper, like van Fraassen's, is based on a non-linguistic component, not a diagram in this case but a physical domain of three-dimensional cube-shaped blocks. ….

… The semantics presented in this paper I call 'block semantics', for reasons that will become clear….  Block semantics is based on domains consisting of cube-shaped objects of the same size, e.g. children's wooden building blocks.  These can be arranged either in a linear array or in a rectangular array, i.e. either in a row with no space between the blocks, or in a rectangle composed of rows and columns.  A linear array can consist of a single block, and the order of individual blocks in a linear or rectangular array is irrelevant. Given three blocks A, B and C, the linear arrays ABC and BCA are indistinguishable.  Two linear arrays can be joined together or concatenated into a single linear array, and a rectangle can be re-arranged or transformed into a linear array by successive concatenation of its rows.  The result is called the 'linear transformation' of the rectangle.  An essential characteristic of block semantics is that every domain of every block model is finite.  In this respect it differs from Tarski’s semantics for first-order logic, which permits infinite domains.  But although every block model is finite, there is no upper limit to the number of such models, nor to the size of their domains.

It should be emphasized that block models are physical models, the elements of which can be physically manipulated.  Their manipulation differs in obvious and fundamental ways from the manipulation of symbols in formal axiomatic systems and in mathematics.  For example the transformations described above, in which two linear arrays are joined together to form one array, or a rectangle of blocks is re-assembled into a linear array, are physical transformations not symbolic transformations. …" 

Storrs McCall, Department of Philosophy, McGill University

See also…

Monday, August 8, 2011

Diamond Theory vs. Story Theory (continued)

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

Some background

Richard J. Trudeau, a mathematics professor and Unitarian minister, published in 1987 a book, The Non-Euclidean Revolution , that opposes what he calls the Story Theory of truth [i.e., Quine, nominalism, postmodernism] to what he calls the traditional Diamond Theory of truth [i.e., Plato, realism, the Roman Catholic Church]. This opposition goes back to the medieval "problem of universals" debated by scholastic philosophers.

(Trudeau may never have heard of, and at any rate did not mention, an earlier 1976 monograph on geometry, "Diamond Theory," whose subject and title are relevant.)

From yesterday's Sunday morning New York Times

"Stories were the primary way our ancestors transmitted knowledge and values. Today we seek movies, novels and 'news stories' that put the events of the day in a form that our brains evolved to find compelling and memorable. Children crave bedtime stories…."

Drew Westen, professor at Emory University

From May 22, 2009

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

The above ad is by
  Diane Robertson Design—

Credit for 'Diamonds' miniseries poster: Diane Robertson Design, London

Diamond from last night’s
Log24 entry, with
four colored pencils from
Diane Robertson Design:

Diamond-shaped face of Durer's 'Melencolia I' solid, with  four colored pencils from Diane Robertson Design
See also
A Four-Color Theorem.

For further details, see Saturday's correspondences
and a diamond-related story from this afternoon's
online New York Times.

Thursday, November 4, 2010

Rhetoric, continued

Filed under: General — m759 @ 9:00 PM

"Is our children learning?"
— George W. Bush, January 11, 2000 (according to TIME)

"… our politics seems so tough right now, and
 facts and science and argument does not seem to be winning the day…."
— Barack Obama, October 16, 2010 (according to whitehouse.gov)


The same Obama quotation appeared in The New York Times.

Related material on facts and science and argument —

"If you’re interested in particle physics and not regularly reading
 Tommaso Dorigo’s blog, you should be."
 — Peter Woit at Not Even Wrong , March 21, 2009


Click on the above for further details.

See also Plotting Obama's Passage to India (AP)

Sunday, October 31, 2010

Heaven’s Gate continues

Filed under: General — m759 @ 9:48 AM

In memory of Dutch author Harry Mulisch

The Discovery of Heaven


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

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

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

See also "starflight" in this journal.

Sunday, May 23, 2010

For Your Consideration —

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

Cannes Festival Readies for Awards Night

Uncertified Copy

Image-- Uncertified copy of 1986 figures by Cullinane in a 2009 art exhibit in Oslo

The pictures in the detail are copies of
figures created by S. H. Cullinane in 1986.
They illustrate his model of hyperplanes
and points in the finite projective space
known as PG(3,2) that underlies
Cullinane's diamond theorem.

The title of the pictures in the detail
is that of a film by Burkard Polster
that portrays a rival model of PG(3,2).

The artist credits neither Cullinane nor Polster.

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)

Friday, May 22, 2009

Friday May 22, 2009

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

New York Times
banner this morning:

NYT banner, 9:21 AM Friday, May 22, 2009-- Ears are ads for HSBC.

Click to enlarge.

Related material from
July 11, 2008:

HSBC logo with framed version

The HSBC Logo Designer —

Henry Steiner

Henry Steiner, designerHe is an internationally recognized corporate identity consultant. Based in Hong Kong, his work for clients such as HongkongBank, IBM and Unilever is a major influence in Pacific Rim design.

Born in Austria and raised in New York, Steiner was educated at Yale under Paul Rand and attended the Sorbonne as a Fulbright Fellow. He is a past President of Alliance Graphique Internationale. Other professional affiliations include the American Institute of Graphic Arts, Chartered Society of Designers, Design Austria, and the New York Art Directors' Club.

His Cross-Cultural Design: Communicating in the Global Marketplace was published by Thames and Hudson (1995).



Charles Taylor,
"Epiphanies of Modernism,"
Chapter 24 of Sources of the Self
  (Cambridge U. Press, 1989, p. 477):


"… the object sets up
 a kind of frame or space or field
   within which there can be epiphany."


Related material suggested by
an ad last night on
ABC's Ugly Betty season finale:

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

Credit for 'Diamonds' miniseries poster: Diane Robertson Design, London

Diamond from last night's
Log24 entry, with
four colored pencils from
Diane Robertson Design:

Diamond-shaped face of Durer's 'Melencolia I' solid, with  four colored pencils from Diane Robertson Design
See also
A Four-Color Theorem.

Saturday, July 26, 2008

Saturday July 26, 2008

Filed under: General — m759 @ 3:09 PM
Tinker Shuffle

Cover of book 'Irish Travellers'

Peter  O'Toole

Peter Seamus O’Toole,
born Connemara, 1932

“O body swayed to music,
O brightening glance,
How can we know the dancer
from the dance?”

William Butler Yeats

“My little baby sister
can do it with ease.
It’s easier to learn
  than those ABC’s.”

Kylie Minogue 

Happy birthday,
Kate Beckinsale

Wednesday, June 25, 2008

Wednesday June 25, 2008

Filed under: General — m759 @ 8:06 AM
Prize Dance

“I would not know what the spirit
of a philosopher might wish more
 to be than a good dancer.
For the dance is his ideal,
also his art, and finally also his
only piety, his ‘service of God.'”


Charles Taylor, winner
of this year’s Kyoto Prize
in arts and philosophy:

“… the object sets up
 a kind of frame or space or field
   within which there can be epiphany.”

Kylie Minogue does the Locomotion

“My little baby sister
can do it with ease.
It’s easier to learn
  than those ABC’s.”

Kylie Minogue 

Tuesday, May 20, 2008

Tuesday May 20, 2008

Filed under: General — m759 @ 10:00 PM

The China Candidate

In honor of the 100th birthday of actor James Stewart,
Turner Classic Movies is now showing
The Man Who Shot Liberty Valance.

In light of an ABC News story tonight,
Report: U.S. Soldiers Did 'Dirty Work' for Chinese Interrogators,
the following film seems more relevant:

Welcome to the Garden Club, Pilgrim


Related material:

The Dictatorship of Talent, by David Brooks
in The New York Times of December 4, 2007—

"When you talk to Americans, you find that they have all these weird notions about Chinese communism. You try to tell them that China isn’t a communist country anymore. It’s got a different system: meritocratic paternalism. You joke: Imagine the Ivy League taking over the shell of the Communist Party and deciding not to change the name. Imagine the Harvard Alumni Association with an army."

— and Harvard mathematician

Professor Yau of Harvard

See also Sylvia Nasar's 2006 New Yorker article on Yau
and the screenplay of The Manchurian Candidate:

A long pause.
Finally, Yen Lo laughs.

YEN LO With humor, my dear Zilkov.
Always with a little humor.

Tuesday, August 7, 2007

Tuesday August 7, 2007

Filed under: General — m759 @ 8:00 AM
The Horse Whisperer

Scarlett Johansson and friend in The Horse Whisperer

Scarlett Johansson and friend
in “The Horse Whisperer” (1998)

Thanks to University Diaries (Aug. 6) for the following:

“‘The University of Sydney has ordered an independent review into allegations that the dean of the Conservatorium of Music hired a horse whisperer to conduct management workshops.’ [Are you, like UD, a bit vague on exactly what a horse whisperer is? And are you having trouble figuring out what a horse whisperer would have to offer a management workshop? But then, what exactly is a management workshop? Read on.]”

For some background on horse whispering and management workshops, see IABC Steal Sheet, March 2004.

Related material:

The recent Log24 entries

University Diaries:
“God, isn’t there already
enough crap in this story?”

See also Log24,
Dec. 10, 2003:

Putting Descartes Before Dehors


“Descartes déclare que
c’est en moi, non hors de moi,
en moi, non dans le monde,
que je pourrais voir
si quelque chose existe
hors de moi.”

ATRIUM, Philosophie     

For further details,

Sunday, May 27, 2007

Sunday May 27, 2007

Filed under: General — m759 @ 8:00 AM
Random Number
The previous entry links back to May 18’s “Devil in the Details,” an entry quoting Peter Woit.  Yesterday afternoon Woit, who sometimes writes on pure mathematics as well as physics, posted an entry on a talk said to be related to something called “the ABC-conjecture,” which has been called “the most important unsolved problem in diophantine analysis.” (Dorian Goldfeld,  “Beyond the Last Theorem,” The Sciences, March/April 1996, 34-40)

On the ABC-conjecture in number theory:

“We hope to elucidate the beautiful connections between elliptic curves, modular forms and the ABC–conjecture.” —Dorian Goldfeld (pdf)

An Edinburgh postgraduate student on the conjecture:

“… abc brings us full circle to Fermat’s Last Theorem….” —Graeme Taylor at Everything2.com

I regret I can add nothing to Taylor’s admirable exposition and to Goldfeld’s “beautiful connections” except the following observation of a rather ugly connection.

The previous Log24 entry, from yesterday afternoon, related the May 18 “details” entry to Friday’s PA evening lottery number, 005.  A  followup seems (if only to honor the madcap tradition of John Nash) to be called for.  The PA evening number yesterday evening, Saturday, was 443.  Nash, in his younger days, might have been pleased to note that this number is associated (if only by coincidence) with a topic Woit mentioned earlier yesterday– Fermat’s famed conjecture:

The image “http://www.log24.com/log/pix07/070527-Fermat.jpg” cannot be displayed, because it contains errors.
Page 443

in The Annals of Mathematics,
2nd Ser., Vol. 141, No. 3 (May, 1995)
This is the first page of a rather
 famous paper by Andrew Wiles.

Such coincidences are, of course, anathema to believers in the religion of Scientism.  But one such believer, Natalie Angier (yesterday morning’s entry), at least acknowledges the charm of “the atheist’s favorite Christmas movie, ‘Coincidence on 34th Street.'” (pdf)

Saturday, October 14, 2006

Saturday October 14, 2006

Filed under: General — m759 @ 10:31 AM

The image “http://www.log24.com/log/pix06A/061014-Snowglobe.jpg” cannot be displayed, because it contains errors.

On a novel by this year’s winner of the Nobel Prize in Literature:

“In Snow, translated by Maureen Freely, the line between playful farce and gruesome tragedy is very fine. For instance, the town’s newspaper publisher, Serdar Bey, prints an article describing Ka’s public performance of his poem ‘Snow.’ When Ka protests that he hasn’t written a poem called ‘Snow’ and is not going to perform it in the theater, Serdar Bey replies: ‘Don’t be so sure. There are those who despise us for writing the news before it happens…. Quite a few things do happen only because we’ve written them up first. This is what modern journalism is all about.’ And sure enough….”

Margaret Atwood in the New York Times Book Review of Aug. 15, 2004

The image “http://www.log24.com/log/pix06A/061014-SnowABC2.gif” cannot be displayed, because it contains errors.

Related material:


(Thursday, Oct. 12, 2006)

and a novel by
the author of the
above review,
Margaret Atwood:

The image “http://www.log24.com/log/pix06A/CatsEye3.jpg” cannot be displayed, because it contains errors.

Click on pictures for details.

Friday, September 29, 2006

Friday September 29, 2006

Filed under: General — m759 @ 8:00 AM
for the High Holy Days

(Rosh Hashanah began at sundown September 22; Yom Kippur begins at sundown October 1.  —holidays.net)

Mark Finkelstein today:

"Today comes more evidence of the left's painful struggle to deal with its diminished standing and repeated rejection at the polls. In the subscription-required Why Voters Like Values, [New York] Times columnist Judith Warner claims that "the Christian right's ability to stir voter passions is based not on values, but on psychology." Warner describes having bravely gone inside the belly of the conservative beast, recently attending a Values Voters Summit in DC, and declaring it "imbued with so much intolerance and hate." This is presumably in contrast with liberal love-ins, where Bush & Co. are regularly depicted as liars, murderers, Hitlers, etc.

She later describes a schadenfreude-provoking scene of the day after Kerry's 2004 defeat, picking through the rubble with Harvard psychology professor emeritus, Jerome Kagan, who tried to console Warner and presumably himself. As she describes it:

"Our conversation drifted to the Republicans' 'values' [note scare quotes] agenda, and Kagan's belief that values sell because they're an antidote to the endemic mental health problem of our time: depression.

"'Humans demand that there be a clear right and wrong,' he said. 'You've got to believe that the track you've taken is the right track. You get depressed if you're not certain as to what it is you're supposed to be doing or what's right and wrong in the world."

"People need to divide the world into good and evil, us and them, Kagan continued. To do otherwise– to entertain the possibility that life is not black and white, but variously shaded in gray– is perhaps more honest, rational and decent. But it's also, psychically, a recipe for disaster."

Got it? Liberalism is "more honest, rational and decent" than conservativism, but that's just not what the benighted public wants. They're looking for political Prozac, a Manichean worldview they can cling to, and that's what conservatism cunningly offers.

Less controversial values are provided by yesterday evening's Pennsylvania lottery— namely, the values 4, 5, and 6.

For a discussion of these values under the guise of musical intervals, see Professor Kagan again, in a paper (pdf) he wrote with Marcel R. Zentner, "Infants' Perception of Consonance and Dissonance in Music" (Infant Behavior & Development, Vol. 21, No. 3, 1998):

Adults judge as most consonant either the octave (difference of 12 semitones) [or the unison, difference of 0 semitones], the fifth (7 semitones), or the major third (4 semitones).

Illustration (see also yesterday evening):

The image “http://www.log24.com/music/images/Keys-Values.gif” cannot be displayed, because it contains errors.

Notes and frequency ratios

The paper discusses consonant intervals
as an example of alleged
"perceptual universals."

Related material on universals
suitable for today, the Feast of
St. Michael and All Angels:

Shining Forth and
Midsummer Eve's Dream.

The material in Shining Forth
is also related, tangentially, to the
following presentation of the
Warner "values" essay
in today's online New York Times:

The image “http://www.log24.com/log/pix06A/060929-NYT.jpg” cannot be displayed, because it contains errors.

The above three Times items,
taken together, suggest that
those in search of "values"
should consult Betty Suarez:

The image “http://www.log24.com/log/pix06A/060929-BettyPoncho.gif” cannot be displayed, because it contains errors.

Click on picture for further details.

Friday, July 21, 2006

Friday July 21, 2006

Filed under: General — m759 @ 1:00 PM

For Hemingway’s birthday:

Mathematics and Narrative, continued

“We know many little things about the relation between mathematics and narrative, but lack one big comprehensive insight.”

— John Allen Paulos (pdf)

“On Wednesday, Sept. 11, 2002– 9/11/02– the New York State lottery numbers were 911, an eerie coincidence that set many people to thinking or, perhaps more accurately, to not thinking.”

—  John Allen Paulos

“Time and chance happeneth to them all.”

— Ecclesiastes 9:11

Monday, May 29, 2006

Monday May 29, 2006

Filed under: General — m759 @ 2:45 AM

Strange Bedfellows

Ted Berkman, author of books about the Israeli military, died at 92 on May 12, 2006.

Dennis Hevesi in today’s New York Times:

“In World War II he served as the Middle East chief of the Foreign Broadcast Intelligence Service, a predecessor of the Central Intelligence Agency. In 1946, as a radio correspondent for ABC, he provided an eyewitness account of the bombing of the King David Hotel in Jerusalem by Jewish terrorists.”

He also worked as a screenwriter (with his brother-in-law Raphael Blau) on the films “Girl of the Night” (1960), starring Anne Francis, and  “Bedtime for Bonzo” (1951), starring Diana Lynn.

These are two of my all-time favorite actresses, and I am grateful to Berkman for providing them with roles.  I am less grateful for his Zionist politics.  Who he is in bed with now, God only knows.

The image “http://www.log24.com/log/pix06A/060529-AnneFrancis.jpg” cannot be displayed, because it contains errors.
Anne Francis

The image “http://www.log24.com/log/pix06A/060529-DianaLynn2.jpg” cannot be displayed, because it contains errors.
Diana Lynn

Wednesday, April 26, 2006

Wednesday April 26, 2006

Filed under: General — m759 @ 2:00 PM

Plagiarist or Fraud?

The weekly Harvard Independent points out that Kaavya Viswanathan’s recent novel may have been ghostwritten.  Therefore the ghostwriter, rather than the purported author, may have committed the original plagiarism.  Viswanathan maintains that she herself wrote the novel, and said that “any phrasing similarities… were completely unintentional and unconscious.” (Harvard Crimson, April 24)  (The use of ghostwriters is not generally called plagiarism, although one definition says plagiarism is “passing off someone else’s work as your own.”  This would of course make all recent U.S. presidents guilty of the crime.)

Related material:

Tuesday, January 17, 2006

Tuesday January 17, 2006

Filed under: General — m759 @ 11:00 PM
Bang Splat

The image “http://www.log24.com/log/pix05B/BangSplat.gif” cannot be displayed, because it contains errors.

School Book Depository



“Many people look at the Kennedy assassination as a turning point, when people started realizing and thinking and believing their government would lie to them and lie to them repeatedly,” said Gary Mack, curator of the Sixth Floor Museum at Dealey Plaza in Dallas.

AP, Dallas, Nov. 21, 2003   

Better late than never.

Tuesday, December 20, 2005

Tuesday December 20, 2005

Filed under: General — m759 @ 12:00 AM

“Heaven– Where Is It?
  How Do We Get There?”

To air on ABC
Tuesday, Dec. 20
(John Spencer’s birthday)

Fred Stein, 1945

“And we may see
the meadow in December,
icy white and crystalline.”

— Johnny Mercer,
“Midnight Sun”
See also a Brooklyn version.

Sunday, December 18, 2005

Sunday December 18, 2005

Filed under: General — m759 @ 8:11 AM

The Meadow

“Heaven– Where Is It?
  How Do We Get There?”

To air on ABC
Tuesday, Dec. 20
(John Spencer’s birthday)

By Trevanian, who died on
Wednesday, Dec. 14, 2005:


“Well… the flow of the play was just right, and it began to bring me to the meadow. It always begins with some kind of flowing motion… a stream or river, maybe the wind making waves in a field of ripe rice, the glitter of leaves moving in a breeze, clouds flowing by. And for me, if the structure of the Go stones is flowing classically, that too can bring me to the meadow.”

“The meadow?”

“Yes. That’s the place I expand into. It’s how I recognize that I am resting.”

“Is it a real meadow?”

“Yes, of course.”

“A meadow you visited at one time? A place in your memory?”

“It’s not in my memory. I’ve never been there when I was diminished.”


“You know… when I’m in my body and not resting.”

“You consider normal life to be a diminished state, then?”

“I consider time spent at rest to be normal. Time like this… temporary, and… yes, diminished.”

“Tell me about the meadow, Nikko.”

“It is triangular. And it slopes uphill, away from me. The grass is tall. There are no animals. Nothing has ever walked on the grass or eaten it. There are flowers, a breeze… warm. Pale sky. I’m always glad to be the grass again.”

“You are the grass?”

“We are one another. Like the breeze, and the yellow sunlight. We’re all… mixed in together.”

“I see. I see. Your description of the mystic experience resembles others I have read. And this meadow is what the writers call your ‘gateway’ or ‘path.’ Do you ever think of it in those terms?”


“So. What happens then?”

“Nothing. I am at rest. I am everywhere at once. And everything is unimportant and delightful. And then… I begin to diminish. I separate from the sunlight and the meadow, and I contract again back into my bodyself. And the rest is over.” Nicholai smiled uncertainly. “I suppose I am not describing it very well, Teacher. It’s not… the kind of thing one describes.”

“No, you describe it very well, Nikko. You have evoked a memory in me that I had almost lost. Once or twice when I was a child… in summer, I think… I experienced brief transports such as you describe. I read once that most people have occasional mystic experiences when they are children, but soon outgrow them. And forget them….”

“And we may see
the meadow in December,
icy white and crystalline.”

— Johnny Mercer,
  “Midnight Sun

Thursday, November 17, 2005

Thursday November 17, 2005

Filed under: General — m759 @ 2:22 PM
All the King’s Men

(See also Time and
All the King’s Horses.)


Now you better do some thinkin’
    then you’ll find
You got the only daddy
    that’ll walk the line

The image “http://www.log24.com/log/pix05B/051117-Ridin1.jpg” cannot be displayed, because it contains errors.


I’ve always been different
    with one foot over the line….
I’ve always been crazy
    but it’s kept me from going insane.

For related material, see

The Line: Notes on Iconology,

and last night’s winner of

The image “http://www.log24.com/log/pix05B/051117-Award2.jpg” cannot be displayed, because it contains errors.

the National Book Award
for nonfiction, i.e.,
“all hard facts, all reality, with
no illusions and no fantasy.”  

A Story That Works

  • “There is the dark, eternally silent, unknown universe;
  • there are the friend-enemy minds shouting and whispering their tales and always seeking the three miracles —
    • that minds should really touch, or
    • that the silent universe should speak, tell minds a story, or (perhaps the same thing)
    • that there should be a story that works, that is all hard facts, all reality, with no illusions and no fantasy;
  • and lastly, there is lonely, story-telling, wonder-questing, mortal me.”

    Fritz Leiber in “The Button Molder

Monday, October 3, 2005

Monday October 3, 2005

Filed under: General — m759 @ 10:00 AM
On This Date

“In 1955, 50 years ago, ‘Captain Kangaroo’
and ‘The Mickey Mouse Club’
premiered on CBS and ABC, respectively.”
— Today in History, Associated Press

Part I

For a Christian meditation on Captain Kangaroo, see the Log24 entries of Jan. 24, 2004.

Part II

“Rosh Hashana, the Jewish New Year, begins at sunset.”
— Today in History, Associated Press

A Rosh Hashana catechism:


(See Chorus from the Rock.)

How does one stand
To behold the sublime,
To confront the mockers,
The mickey mockers
And plated pairs?
— Wallace Stevens,
   “The American Sublime”


“Spear Daddy!” in yesterday’s entry,
Happy Birthday, Wallace Stevens

Thursday, September 15, 2005

Thursday September 15, 2005

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

Square Wheel, continued

For director Robert Wise,
who died yesterday on
The Feast of The Holy Cross:

The Maltese Cross

The image “http://www.log24.com/log/pix05B/050915-Maltese2.jpg” cannot be displayed, because it contains errors.

From Cabaret Mechanical Theatre

See also Sept. 8, 2002,  Sept. 12, 2002, and Time Fold.

Saturday, January 8, 2005

Saturday January 8, 2005

Filed under: General — m759 @ 7:26 PM
Splendor of the Light

The Beginning of a Story
by Guy Davenport

Lo Splendore della Luce a Bologna

“The locomotive bringing a trainload of philosophers to Bologna hissed and ground to a standstill in the long Appenine dusk to have its headlamps lit and to be dressed in the standards of the city and the university.”

Eclogues, by Guy Davenport
(Johns Hopkins paperbacks
   ed. edition, 1993, page 125)

Related material:

The train wreck at 12:50 pm local time (6:50 AM EST) Friday, Jan. 7, 2005, 25 miles north of Bologna.

A northbound freight train collided with a passenger train traveling south from Verona to Bologna.

From an essay on Davenport I found Friday morning, well before I learned on Friday afternoon (Eastern Standard Time) of the train wreck:

“A disciple of Ezra Pound, he adapts to the short story the ideogrammatic method of The Cantos, where a grammar of images, emblems, and symbols replaces that of logical sequence. This grammar allows for the grafting of particulars into a congeries of implied relation without subordination. In contrast to postmodernists, Davenport does not omit causal connection and linear narrative continuity for the sake of an aleatory play of signification but in order to intimate by combinational logic kinships and correspondences among eras, ideas and forces.”

— “When Novelists Become Cubists:
    The Prose Ideograms of Guy Davenport,”
by Andre Furlani

See also
Friday’s Log24 entries and
Davenport’s Express.

Sunday, March 28, 2004

Sunday March 28, 2004

Filed under: General — m759 @ 12:12 PM

American Heaven

Headlines from today’s Google News:

Singer Jan Berry, 62; Half of Surf Music Duo

Screeching for heaven at Mach 7

March 25 news story:

“The promise of 70 virgins in paradise and the equivalent of about $20 was all it took to convince a Palestinian teenager to turn himself into a suicide bomber…”

A more modest paradise, from a Jan Berry obituary today:

With Brian Wilson of the Beach Boys, William Jan Berry co-wrote the lyrics for “Surf City” with its lines about taking the station wagon to a place where there are “two girls for every boy.”*

* Theological footnote for feminists:
In some other regions of American Heaven, there may be two boys for every girl.

Monday, March 22, 2004

Monday March 22, 2004

Filed under: General — m759 @ 10:00 PM

The Hairy Palm Academy

The previous two entries were prompted by a picture in the Washington Post of Spain’s Interior Minister, a member of the secular arm of the Legion of Christ.

Both entries mentioned a school run by the Legion of Christ, the Royal Palm Academy.  As the following excerpt from my March 20 entry indicates, a different sort of palm might also be honored by the Legion — the hairy palm.

“Los Legionarios de Cristo…  es una organización fundada en 1941 en Méjico por el padre Marcel [Marcial] Maciel (rehabilitado por el Vaticano en 1958 tras ser acusado de ayudarse en sus visiones con ampollas de morfina; también fue acusado de pederastia, le gustaba masturbar a jovencitos y que ellos le masturbaran a él).”


Related readings from The New York Review of Books, issue dated April 8, 2004:

God in the Hands of Angry Sinners, by Garry Wills, on the Legion of Christ and on Mel Gibson flogging his God,

and a related article, a review of

Solitary Sex: A Cultural History of Masturbation.

It seems the founder of the Legion of Christ, like many other Catholic priests, may have regarded masturbation as a group sport rather than solitary recreation.

For further details, see an ABC News 20/20 story dated April 26, 2002:

Priestly Sin, Cover-Up

When approached by ABC News’s Brian Ross in Rome with questions of allegations against Father Marcial Maciel, Cardinal Joseph Ratzinger became visibly upset and actually slapped Ross’s hand. — ABCNEWS.com

Thursday, March 11, 2004

Thursday March 11, 2004

Filed under: General — m759 @ 3:19 PM

Men of Respect



“I caught Alan Dershowitz defending Martha Stewart on ABC TV this morning. Most Americans who pay any attention at all to the news of her trial think she is being charged with insider trading. She is not. She is accused of asserting her innocence to federal prosecutors who accused her of insider trading. She is on trial for allegedly lying about her innocence.

Think about that. The Constitution supposedly gives us the presumption of innocence. A federal bureaucrat shows up and says, in effect, ‘We haven’t defined insider trading yet, Mrs. Stewart, but we think you’re guilty of it and should go to prison for it.’ Martha says ‘I’m innocent’ and for that she’s prosecuted.

Dershowitz was right on the money when he announced on ABC, ‘This is like the Soviet Union!’ “

Thomas DiLorenzo, February 4, 2004

DiLorenzo is a professor of economics
at Loyola College in Maryland.

Dershowitz is a professor of law
at Harvard.

Sunday, January 11, 2004

Sunday January 11, 2004

Filed under: General — m759 @ 1:11 PM

In Summary

To sum up the last two entries:

“I returned and saw under the sun
 that the race is not to the swift,
 nor the battle to the strong,
 nor bread to the wise,
 nor riches to men of understanding,
 nor favor to men of skill;
 but time and chance
 happeneth to them all”

Ecclesiastes 9:11.

Friday, November 21, 2003

Friday November 21, 2003

Filed under: General — m759 @ 7:04 PM

School Book Depository



“Many people look at the Kennedy assassination as a turning point, when people started realizing and thinking and believing their government would lie to them and lie to them repeatedly,” said Gary Mack, curator of the Sixth Floor Museum at Dealey Plaza in Dallas.

AP, Dallas, Nov. 21, 2003

Better late than never.

Saturday, September 6, 2003

Saturday September 6, 2003

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

The Tempest

IMAGE- 'Wind over Water,' i.e. 'Feng Shui'

A tropical storm over Florida (lower left)
and a hurricane at Bermuda (upper right)
at 3:15 p.m. EDT on Friday, Sept. 5, 2003:

Wind over Water

as described by William Shakespeare in 1611.

“Wind over Water” in the I Ching,
the Classic of Transformations,
signifies huan, “dissolving.”


Our revels now are ended. These our actors, as I foretold you, were all spirits and are melted into air, into thin air: and, like the baseless fabric of this vision, the cloud-capp’d towers, the gorgeous palaces, the solemn temples, the great globe itself, yea, all which it inherit, shall dissolve and, like this insubstantial pageant faded, leave not a rack behind. We are such stuff as dreams are made on, and our little life is rounded with a sleep. (Prospero, IV.i)

Friday, August 8, 2003

Friday August 8, 2003

Filed under: General — m759 @ 12:12 PM


From The New Yorker magazine, issue dated August 11, 2003:

Talk of the Town

As in the rest of the country, political talk radio here is dominated by the hard right. On the AM band, whose low-fidelity signal is perfect for shrill jabber, no fewer than four powerful stations feature “conservative talk.” Two of them, WMCA and WWDJ, are “Christian” and heavily salted with attacks on homosexuality, abortion rights, and stem-cell research and support for school prayer, President Bush’s judicial nominees, and Israeli maximalism. The other two pump out a steadier flow of viscous, untreated political sewage. WOR carries four hours daily of Bob Grant and Bill O’Reilly, reliable voices of irritable reaction. The biggie is WABC, which claims the largest talk-radio audience in the country. The station features fifteen hours a week of Limbaugh, fifteen of Sean Hannity, and ten of Mark Levin (“one of America’s preëminent conservative commentators”).

— Hendrik Hertzberg

For more on this alleged “sewage,” click on the names mentioned.

Those who wish may easily find sites attacking some of these commentators (particularly Bob Grant).

Others may feel that the word “sewage” might be better applied to The New Yorker itself under the recent editorship of Tina Brown.  See

Tina Brown and the Coming Decline
of Celebrity Journalism

at the

Columbia Journalism Review.

Monday, July 28, 2003

Monday July 28, 2003

Filed under: General — m759 @ 9:00 AM

City of God

Today's site music is

Nous Voici Dans La Ville.

The central aim of Western religion —

"Each of us has something to offer the Creator... 
the bridging of                  
masculine and feminine,                       
life and death. It's redemption.... 
nothing else matters." 
-- Martha Cooley in The Archivist (1998) 

The central aim of Western philosophy —

                 Dualities of Pythagoras 
                 as reconstructed by Aristotle: 

                 Limited     Unlimited                      
                 Odd         Even           
                 Male        Female                    
                 Light       Dark                 
                 Straight    Curved                   
                 ... and so on .... 

"Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy."
— Jamie James in
   The Music of the Spheres (1993)

"In the garden of Adding,
Live Even and Odd….
And the song of love's recision
is the music of the spheres."
— The Midrash Jazz Quartet in
   City of God, by E. L. Doctorow (2000)

Today is the feast of St. Johann Sebastian Bach.

Sunday, June 29, 2003

Sunday June 29, 2003

Filed under: General — m759 @ 4:22 PM

Every Boy Has a Daddy

Today is the Feast of Saint Peter.

The most timely quote I know of for today’s religious observances is from Oh What a Web They Weave, by F. John Loughnan:

Every boy has a daddy.

This was written as part of an attack on the father of a Latin-Mass Catholic who authored the website Ecclesia Militans, which has the logo

Note the resemblance to the Iron Cross.

Soldier of Fortune magazine, April 2002, contains a brief discussion of the German motto “Gott mit uns” that is relevant to the concept of The Church Militant.

Soldier of Fortune,
April 2002

The actor on the cover, Mel Gibson, also serves to illustrate our meditation for today, “Every boy has a daddy.”  See Christopher Noxon’s article in the New York Times Magazine of March 9, 2003:

Is the Pope Catholic… Enough?

Noxon attacks Gibson’s father Hutton — like his son Mel, a Latin-Mass Catholic, and author of

Is the Pope Catholic?

A related “Every boy has a daddy” attack appears in the June 2003 issue of Playboy magazine.  An entertaining excerpt from this attack on Joseph P. Kennedy, father of JFK, may be found at Orwell Today.  

Finally, let us meditate on the ultimate “Every boy has a daddy” attack — by novelist Robert Stone on the alleged father of Jesus of Nazareth:

Excerpt from
Damascus Gate,
by Robert Stone,
Houghton Mifflin, 1998,
Chapter 40

From the mosques, from the alleys, from the road: “Allahu Akbar!” ….

Then a voice shouted: “Itbah al-Yahud!” …. Kill the Jew! ….

Itbah al-Yahud!” the crowd screamed….

Then Lucas saw the things they had taken up: trowels and mallets and scythes, some dripping blood.  Everyone was screaming, calling on God.  On God, Lucas thought.  He was terrified of falling, of being crushed by the angry swarm that was whirling around him.  He wanted to pray.  “O Lord,” he heard himself say.  The utterance filled him with loathing, that he was calling on God, on that Great Fucking Thing, the Lord of Sacrifices, the setter of riddles.  Out of the eater comes forth meat.  The poser of parables and shibboleths.  The foreskin collector, connoisseur of humiliations, slayer by proxy of his thousands, his tens of thousands.  Not peace but a sword.  The Lunatic Spirit of the Near East, the crucified and crucifier, the enemy of all His own creation.  Their God-Damned God.

The New York Times Magazine article mentioned above was prompted, in part, by Mel Gibson’s current movie production, “The Passion,” about the final 12 hours in the (first, or possibly second) life of Jesus.  If I were producing a Passion play, as Peter I would certainly cast Stone.

See also the 11 PM sequel to the above.

Monday, May 19, 2003

Monday May 19, 2003

Filed under: General — m759 @ 11:45 PM

Part II: A Mighty Wind

I just saw the John Travolta film “Phenomenon” for the first time.  (It was on the ABC Family Channel from 8 to 11.)

Why is it that tellers of uplifting stories (like Zenna Henderson, in “Day of the Mother Ship, Part I,” or the authors of “Phenomenon” or the Bible) always feel they have to throw in some cockamamie and obviously false miracles to hold people’s attention?

On May 11 (Mother’s Day), Mother Nature got my attention with a mighty wind waving the branches of nearby trees, just before a tornado watch was issued for the area I was in.  This made me recall a Biblical reference I had come across in researching references to “Our Lady of the Woods” for my Beltane (May 1) entry

Isaiah 7:2

…And his heart was moved, and the heart of his people, as the trees of the wood are moved with the wind.

This is what I thought of on May 11 watching branches swaying in the wind on Mother’s Day — which some might regard as a festival of Our Lady of the Woods.  John Travolta in “Phenomenon” sees a very similar scene partway through the picture; then, at the end, explains to his girlfriend how the swaying branches made him feel — without mentioning the branches — by asking her to describe how she would cradle and rock a child in her arms.  At the very end of the film, she herself is reminded of his question by the swaying branches of another tree.

Events like these are miracle enough for me.

Thursday, April 17, 2003

Thursday April 17, 2003

Filed under: General — m759 @ 2:14 PM

Holiday Affair

From a site recommended by oOMisfitOo:

In The Star of Bethlehem: The Legacy of the Magi (Rutgers University Press, 1999), Michael R. Molnar explains how the purchase of a $50 Roman coin led him to discover the real date of Jesus’s birth.

The coin that provided the clue portrayed Aries the Ram looking back at a star.

From Molnar’s own site, Star of Bethlehem:

“On April 17, 6 BC, two years before King Herod died, Jupiter emerged in the east as a morning star in the sign of the Jews, Aries the Ram.”

Therefore, according to Molnar, today is Christmas.  Accordingly, let us sing a (slightly improved) carol in memory of the late Murray L. Bob (see April 15 entries):

God rest ye, merry gentleman.

Let us also voice a rousing chorus of one of my personal all-time favorites, in memory of a film director (see previous entry), who gave us a vision of Robert Mitchum (Ram) and Sarah Miles (“Lady Caroline Lamb“) united in marriage (Ding-Dong):

Who put the Ram in the
Ram-a-Lamb-a Ding-Dong?

Why, David Lean, of course.

Update of April 21, 2003:

When You Care Enough
to Send the Very Best

“Jan Scott, 88, a television art director and production designer who had won 11 Emmy Awards, died April 17 at her home in Hollywood Hills, Calif. The cause of death was not reported.

She started working in television in the 1950s and earned her first Emmy nomination in 1956 for a “Hallmark Hall of Fame” production. Her first Emmy Award came in 1968 for her work as an art director for “Kismet,” which appeared on ABC. Her last Emmy was awarded in 1989 for “I’ll Be Home for Christmas,” on NBC.”

The Washington Post, April 21, 2003

Saturday, August 3, 2002

Saturday August 3, 2002

Filed under: General — m759 @ 10:42 PM

Miss Sauvé

Homily on Flannery O’Connor

for the Sunday following Corpus Christi Day, 2002:

The part of her fiction that most fascinates me, then and now, is what many critics referred to as “the grotesque,” but what she herself called “the reasonable use of the unreasonable.” [Flannery O’Connor, Mystery and Manners: Occasional Prose, Robert and Sally Fitzgerald, eds. (New York: Farrar, Straus, 1969)] 

 A modest example comes to mind. In a short story  ….  the setting sun appears like a great red ball, but she sees it as “an elevated Host drenched in blood” leaving a “line like a red clay road in the sky.” [Flannery O’Connor, “A Temple of the Holy Ghost” from A Good Man is Hard to Find (New York: Harcourt, Brace & World, 1971)] 

In a letter to a friend of hers, O’Connor would later write, “…like the child, I believe the Host is actually the body and blood of Christ, not just a symbol. If the story grows for you it is because of the mystery of the Eucharist in it.” In that same correspondence, O’Connor relates this awkward experience:

I was once, five or six years ago, taken by [Robert Lowell and Elizabeth Hardwick] to have dinner with Mary McCarthy…. She departed the Church at the age of 15 and is a Big Intellectual. We went and eight and at one, I hadn’t opened my mouth once, there being nothing for me in such company to say…. Having me there was like having a dog present who had been trained to say a few words but overcome with inadequacy had forgotten them. Well, toward morning the conversation turned on the Eucharist, which I, being the Catholic, was obviously supposed to defend. [McCarthy] said that when she was a child and received the Host, she thought of it as the Holy Ghost, He being the “most portable” person of the Trinity; now she thought of it as a symbol and implied that it was a pretty good one. I then said, in a very shaky voice, “Well, if it’s a symbol, to hell with it.” That was all the defense I was capable of but I realize now that this is all I will ever be able to say about it, outside of a story, except that it is the center of existence for me; all the rest of life is expendable. [Sally Fitzgerald, ed., The Habit of Being: The Letters of Flannery O’Connor (Vintage: New York, 1979) 124-125] 

….There is, of course, something entirely preposterous and, well, unreasonable, almost grotesque, about the Catholic doctrine of the Real Presence. We claim, with a perfectly straight face, to eat the body and drink the blood of the Eternal Word of God, the second person of the Most Holy Trinity who, according to some, shouldn’t even have a body to begin with. But therein lies precisely the most outlandish feature of the Eucharist: namely, that it embodies the essential scandal of the Incarnation itself.  

             — Friar Francisco Nahoe, OFM Conv.

From James Joyce

A Portrait Of The Artist As A Young Man

Chapter 3 :

Why was the sacrament of the eucharist instituted under the two species of bread and wine if Jesus Christ be present body and blood, soul and divinity, in the bread alone and in the wine alone? Does a tiny particle of the consecrated bread contain all the body and blood of Jesus Christ or a part only of the body and blood? If the wine change into vinegar and the host crumble into corruption after they have been consecrated, is Jesus Christ still present under their species as God and as man?

— Here he is! Here he is!

From The Gazette, Montreal,

of Sunday, August 20, 1995, page C4:

“Summer of ’69,” a memoir by Judy Lapalme on the death by accidental drowning of her 15-year-old younger brother:

“I had never tasted pizza until Jeff died.  Our family, of staunch Irish Catholic stock with more offspring than money, couldn’t cope with the luxury or the spice.

The Hallidays, neighbors from across the street, sent it over to us the day after the funeral, from Miss Sauvé’s Pizzeria, on Sauvé St., just east of Lajeunesse St. in Ahuntsic.  An all-dressed pizza with the hard hat in the centre….

I was 17 that summer and had just completed Grade 12 at Holy Names High School in Rosemont….

…. Jeff was almost 16, a handsome football star, a rebellious, headstrong, sturdy young man who was forever locking horns with my father…. On Friday, Aug. 1, Jeff went out on the boat… and never came back….    

The day after the funeral, a white Volkswagen from Miss Sauvé’s Pizzeria delivered a jumbo, all-dressed pizza to us. The Hallidays’ daughter,  Diane, had been smitten with Jeff and wanted to do something special.

My father assured us that we wouldn’t like it, too spicy and probably too garlicky. There could not be a worse indictment of a person to my father than to declare them reeking of garlic. 

The rest of us tore into the cardboard and began tasting this exotic offering — melted strands of creamy, rubbery, burn-your-palate mozzarrella that wasn’t Velveeta, crisp, dry, and earthy mushrooms, spicy and salty pepperoni sliding off the crust with each bite, green peppers…. Bread crust both crisp and soggy with tomato sauce laden with garlic and oregano. 

It was an all-dressed pizza, tasted for the first time, the day after we buried Jeff….

The fall of 1969, I went to McGill…. I never had another pizza from Miss Sauvé’s.  It’s gone now — like so many things.”

     Ten thousand places

AS kingfishers catch fire, dragonflies dráw fláme;
As tumbled over rim in roundy wells
Stones ring; like each tucked string tells, each hung bell’s
Bow swung finds tongue to fling out broad its name;
Each mortal thing does one thing and the same:         
Deals out that being indoors each one dwells;
Selves—goes itself; myself it speaks and spells,
Crying Whát I do is me: for that I came.
Í say móre: the just man justices;
Kéeps gráce: thát keeps all his goings graces;         
Acts in God’s eye what in God’s eye he is—
Chríst—for Christ plays in ten thousand places,
Lovely in limbs, and lovely in eyes not his
To the Father through the features of men’s faces.

   — Gerard Manley Hopkins, 1844-1889

American Literature Web Resources:

Flannery O’Connor

She died on August 3, 1964 at the age of 39.

In almost all of her works the characters were led to a place where they had to deal with God’s presence in the world.

She once said “in the long run, a people is known, not by its statements or statistics, but by the stories it tells. Fiction is the most impure and the most modest and the most human of the arts.”

Encounter – 02/17/2002:

Flannery OConnor – Southern Prophet:

When a woman wrote to Flannery O’Connor saying that one of her stories “left a bad taste in my mouth,” Flannery wrote back: “You weren’t supposed to eat it.”

Etes-vous sauvé? 

Powered by WordPress