Sunday, November 11, 2018


Filed under: General — m759 @ 11:00 PM

Warburg at Cornell U. Press

See also Warburg + Cornell in this journal.

"Yet if this Denkraum ,  this 'twilight region,'  is where the artist and
emblem-maker invent, then, as Gombrich well knew, Warburg also
constantly regrets the 'loss' of this 'thought-space,' which he also
dubs the Zwischenraum  and Wunschraum ."

Memory, Metaphor, and Aby Warburg's Atlas of Images ,
     Christopher D. Johnson, Cornell University Press, 2012, p. 56

Saturday, March 23, 2013

Art History

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

Quoted in the March 13 post Blackboard Jungle:

"Every morning you take your machete into the jungle
and explore and make observations, and every day
you fall more in love with the richness and splendor
of the place."

— Paul Lockhart, A Mathematician's Lament

More from Lockhart's jungle—

Mathematical objects, even if initially inspired by some aspect of reality (e.g., piles of rocks, the disc of the moon), are still nothing more than figments of our imagination.

Not only that, but they are created by us and are endowed by us with certain characteristics; that is, they are what we ask them to be….

… in Mathematical Reality, because it is an imaginary place, I actually can have pretty much whatever I want….

The point is that there is no reality to any of this, so there are no rules or restrictions other than the ones we care to impose…. Make up anything you want, so long as it isn’t boring. Of course this is a matter of taste, and tastes change and evolve. Welcome to art history!

— Lockhart, Paul (2009-04-01). A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form  (pp. 100-104). Bellevue Literary Press. Kindle Edition. 

Related material in this journal: Bellevue and Wechsler.

See also Gombrich in this journal and in the following:

Related material (Click for some background.) —

From a novel by Chinua Achebe

Monday, December 17, 2012

Nonlyric Stupidity

Filed under: General — m759 @ 5:35 PM

Or: Being There

(A sequel to last night's Lyric Intelligence )

IMAGE- Book reviews page of William Deresiewicz, showing reviews titled 'Be Here Now' and ''I Was There.''

William Deresiewicz reviews Kurt Vonnegut's 1952 novel Player Piano :

The novel’s prescience is chilling. Six years before the left-wing English
sociologist Michael Young published The Rise of the Meritocracy ,
a dystopian satire that coined that now-ubiquitous final word,
Vonnegut was already there.

Related material:

Intelligence Test , Gombrich,  and, more generally, Stupidity.

Saturday, December 8, 2012

Defining the Contest…

Filed under: General,Geometry — Tags: , , , , — m759 @ 5:48 AM

Chomsky vs. Santa

From a New Yorker  weblog yesterday—

"Happy Birthday, Noam Chomsky." by Gary Marcus—

"… two titans facing off, with Chomsky, as ever,
defining the contest"

"Chomsky sees himself, correctly, as continuing
a conversation that goes back to Plato, especially
the Meno dialogue, in which a slave boy is
revealed by Socrates to know truths about
geometry that he hadn’t realized he knew."

See Meno Diamond in this journal. For instance, from 
the Feast of Saint Nicholas (Dec. 6th) this year—

The Meno Embedding


For related truths about geometry, see the diamond theorem.

For a related contest of language theory vs. geometry,
see pattern theory (Sept. 11, 16, and 17, 2012).

See esp. the Sept. 11 post,  on a Royal Society paper from July 2012
claiming that

"With the results presented here, we have taken the first steps
in decoding the uniquely human  fascination with visual patterns,
what Gombrich* termed our ‘sense of order.’ "

The sorts of patterns discussed in the 2012 paper —

IMAGE- Diamond Theory patterns found in a 2012 Royal Society paper

"First steps"?  The mathematics underlying such patterns
was presented 35 years earlier, in Diamond Theory.

* See Gombrich-Douat in this journal.

Tuesday, September 11, 2012

Symmetry and Hierarchy

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

A followup to Intelligence Test (April 2, 2012).

Philosophical Transactions of the Royal Society
B  (2012) 367, 2007–2022
(theme issue of July 19, 2012

Gesche Westphal-Fitch [1], Ludwig Huber [2],
Juan Carlos Gómez [3], and W. Tecumseh Fitch [1]
[1]  Department of Cognitive Biology, University of Vienna,
      Althanstrasse 14, 1090 Vienna, Austria
[2]  Messerli Research Institute, University of Veterinary Medicine Vienna,
      Medical University of Vienna and University of Vienna,
      Veterinärplatz 1, 1210 Vienna, Austria
[3]  School of Psychology, St Mary’s College, University of St Andrews,
      South Street, St Andrews, KY16 9JP, UK
Excerpt (added in an update on Dec. 8, 2012) —
Conclusion —
"…  We believe that applying the theoretical
framework of formal language theory to two-dimensional
patterns offers a rich new perspective on the
human capacity for producing regular, hierarchically
organized structures. Such visual patterns may actually
prove more flexible than music or language for probing
the full extent of human pattern processing abilities.
      With the results presented here, we have taken the
first steps in decoding the uniquely human fascination
with visual patterns, what Gombrich termed our
‘sense of order’.
      Although the patterns we studied are most similar
to tilings or mosaics, they are examples of a much
broader type of abstract plane pattern, a type found
in virtually all of the world’s cultures [4]. Given that
such abstract visual patterns seem to represent
human universals, they have received astonishingly
little attention from psychologists. This neglect is particularly
unfortunate given their democratic nature,
their popular appeal and the ease with which they
can be generated and analysed in the laboratory.
With the current research, we hope to spark renewed
scientific interest in these ‘unregarded arts’, which
we believe have much to teach us about the nature of
the human mind."
[4]  Washburn, D. K. & Crowe, D. W.,1988
      Symmetries of Culture
      Theory and Practice of Plane Pattern Analysis
      Seattle, WA: University of Washington Press.
Commentary —
For hierarchy , see my assessment of Gombrich.
For culture , see T. S. Eliot and Russell Kirk on Eliot.

Friday, August 17, 2012


Filed under: General,Geometry — m759 @ 12:25 PM

Detail from last night's 1.3 MB image
"Search for the Lost Tesseract"—

The lost tesseract appears here on the cover of Wittgenstein's
Zettel  and, hidden in the form of a 4×4 array, as a subarray 
of the Miracle Octad Generator on the cover of Griess's
Twelve Sporadic Groups  and in a figure illustrating
the geometry of logic.

Another figure—

IMAGE- Serbian chess innovator Svetozar Gligoric dies at 89

Gligoric died in Belgrade, Serbia, on Tuesday, August 14.

From this journal on that date

"Visual forms, he thought, were solutions to 
specific problems that come from specific needs."

— Michael Kimmelman in The New York Times
    obituary of E. H. Gombrich (November 7th, 2001)

Tuesday, August 14, 2012

Space Odyssey

Filed under: General — m759 @ 1:00 PM

(An episode of Art Wars )

"Visual forms, he thought, were solutions to
specific problems that come from specific needs."

— Michael Kimmelman in The New York Times
    obituary of E. H. Gombrich (November 7th, 2001)

"… deep cultural fears within the art world— 
fears that art is elitist,
or some kind of confidence game,
or not a serious endeavor (a fear that has
dogged art since at least the time of Plato)."

Philip Kennicott, quoted here on July 22, 2012

See also today's date in 2003.

Saturday, April 7, 2012


Filed under: General,Geometry — Tags: — m759 @ 12:29 PM

From Joyce's 1912 Trieste lecture on Blake:

"Michelangelo's influence is felt in all of Blake's work, and especially in some passages of prose collected in the fragments, in which he always insists on the importance of the pure, clean line that evokes and creates the figure on the background of the uncreated void."

For a related thought from Michelangelo, see Marmo Solo .

For pure, clean lines, see Galois Geometry.

As for "the uncreated void," see the Ernst Gombrich link in Marmo Solo  for "an almost medieval allegory of how man confronts the void."

For some related religious remarks suited to the Harrowing of Hell on this Holy Saturday, see August 16, 2003

Friday, March 2, 2012

Douat Facsimile

Filed under: General,Geometry — Tags: — m759 @ 5:14 PM

Title of a treatise by Dominique Douat

"Méthode pour faire une infinité de desseins différens avec des carreaux mi-partis de deux couleurs par une ligne diagonale : ou observations du Père Dominique Doüat Religieux Carmes de la Province de Toulouse sur un mémoire inséré dans l'Histoire de l'Académie Royale des Sciences de Paris l'année 1704, présenté par le Révérend Père Sébastien Truchet religieux du même ordre, Académicien honoraire  " (Paris, 1722)

"The earliest (and perhaps the rarest) treatise on the theory of design"

— E. H. Gombrich, 1979, in The Sense of Order

A facsimile version (excerpts, 108 pp., Feb. 5, 2010) of this treatise is available from

http://jacques-andre.fr/ed/ in a 23.1 MB pdf.

Sample page—

For a treatise on the finite geometry underlying such designs (based on a monograph I wrote in 1976, before I had heard of Douat or his predecessor Truchet), see Diamond Theory.

Friday, May 28, 2010

Multispeech for Oxford

Filed under: General — m759 @ 7:00 PM

Happy Birthday,
Carey Mulligan


Star of "An Education"

In "An Education," Mulligan's character
applies for admission to Oxford.

Today's New York Times:

Education »

Oxford Tradition
Comes to This:
‘Death’ (Expound)

Related material:

Such words arrive on the page like suitcases at the baggage claim: You know there is something in them and they have travelled far, but you cannot tell what the writer means. The words are filled with unstated meaning. They are (the term is Ricoeur's) "packed" and need unpacking.

This method of using language, however, is not always a defect; radiantly evocative words have long been the language of myth, mysticism, and love. Also, in earlier centuries, educated readers expected to interpret writing on several different levels at once (e.g., literal, allegorical, moral, and anagogical or spiritual), so that multiple meanings were the norm. This was before the era of clear, expository, fully-explicit prose.

Visual thinkers are accustomed to their own kind of interpreting; the very act of visual perception, as Gregory (1966, 1970) and Gombrich (1959) have shown, is interpretive. When oral thinkers leave you to guess at something they have written, it is usually something that would have been obvious had the writing been a conversation. Such is not the case with visual thinkers, even whose spoken words can be mysterious references to visual thoughts invisible to anyone but the thinker.

Writing done in this "packed" manner makes more sense when read as poetry than when read as prose.


Gombrich, E. H. (1959). Art and Illusion: A Study in the Psychology of Pictorial Representation. London: Phaidon.

Gregory, R. L. (1966). Eye and Brain: The Psychology of Seeing. New York: McGraw-Hill.

Gregory, R. L. (1970). The Intelligent Eye. New York: McGraw-Hill.

"Stacking, Packing, and Enfolding Words," by Gerald Grow in "The Writing Problems of Visual Thinkers"

Those wishing to emulate Mulligan's
character in "An Education" might,
having read the Times article above,
consult this journal's post of May 17,
"Rolling the Stone."

That post contains the following
image from the Times


May 17 was, by the way, the day
that R. L. Gregory, author of
The Intelligent Eyedied.

Friday, February 22, 2008

Friday February 22, 2008

Filed under: General — m759 @ 11:00 AM
Philosophers Ponder

“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 in
   The New York Times
Monday, May 20, 1996

Associated Press,
Today in History,
Monday, Feb. 18, 2008:

On this date:

In 1564,
artist Michelangelo
died in Rome.

Images of time and eternity in a 1x4x9 black monolith

Non ha l’ottimo artista in se alcun concetto,
Ch’un marmo solo in se non circoscriva
Col suo soverchio; e solo a quello arriva
La man che ubbidisce all’intelletto.
(The best artist has in himself no concept
in a single block of marble not contained;
only the hand obeying mind will find it.)
— Michelangelo, as quoted
by Erwin Panofsky in

Idea: A Concept
in Art Theory

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

— Rubén Darío

Related material:
Yesterday’s entry
and Anthony Lane
in this week’s
New Yorker:

“… the whole of ‘Jumper’ comes across as vastly incurious about the cultures at its command. When David takes Millie (Rachel Bilson), a school friend from Michigan, for a dirty day out in Rome, she stands in awe before the Colosseum. ‘This place is amazing,’ she declares. ‘It’s so cool.’ I wasn’t expecting Ernst Gombrich….”

Thursday, February 21, 2008

Thursday February 21, 2008

Filed under: General — m759 @ 11:07 AM

The New Yorker's Anthony Lane reviewing the new film "Jumper"–

"I wasn’t expecting Ernst Gombrich, but surely three writers, among them, could inject a touch of class."

The "Jumper" theme, teleportation, has been better developed by three other writers– Bester, Zelazny, and King–

"As a long-time fan of both Alfie Bester and Roger Zelazny, I was delighted to find this posthumous collaboration. Psychoshop is, I think, true to both authors' bodies of work. After all, Bester's influence on Zelazny is evident in a a number of works, most notably Eye of Cat with its dazzling experimental typography so reminiscent of what Bester had done in The Demolished Man and The Stars My Destination."

— Amazon.com customer review

"'This is the last call for Jaunt-701,' the pleasant female voice echoed through the Blue Concourse of New York's Port Authority Terminal."

— Stephen King, "The Jaunt"

From another
Log24, Feb. 7:

The Football

New York Lottery, 2008:

NY Lottery Feb. 6, 2008: Mid-day 064, Evening 701

The Mandorla (vesica piscis) as Football


"He pointed at the football
  on his desk. 'There it is.'"
Glory Road   

Wu  Li
Masters know
that physicists are
doing  more  than
'discovering  the endless
 diversity of nature.' They
 are  dancing with Kali,
 the Divine Mother of
 Hindu  mythology."
 — Gary Zukav,

"What happened?"
  one of the scientists shouted….

"It's eternity in there,"
 he said, and dropped dead….

— Stephen King, "The Jaunt"

for  Ernst
Gombrich, see
his  link in  the
Log24 entries
of June 15,

Related material:
the previous entry.

Friday, June 15, 2007

Friday June 15, 2007

Filed under: General,Geometry — Tags: , — m759 @ 1:00 PM
A Study in
Art Education

Rudolf Arnheim, a student of Gestalt psychology (which, an obituary notes, emphasizes "the perception of forms as organized wholes") was the first Professor of the Psychology of Art at Harvard.  He died at 102 on Saturday, June 9, 2007.

The conclusion of yesterday's New York Times obituary of Arnheim:

"… in The New York Times Book Review in 1986, Celia McGee called Professor Arnheim 'the best kind of romantic,' adding, 'His wisdom, his patient explanations and lyrical enthusiasm are those of a teacher.'"

A related quotation:

"And you are teaching them a thing or two about yourself. They are learning that you are the living embodiment of two timeless characterizations of a teacher: 'I say what I mean, and I mean what I say' and 'We are going to keep doing this until we get it right.'"

Tools for Teaching

Here, yet again, is an illustration that has often appeared in Log24– notably, on the date of Arnheim's death:

The 3x3 square

Related quotations:

"We have had a gutful of fast art and fast food. What we need more of is slow art: art that holds time as a vase holds water: art that grows out of modes of perception and whose skill and doggedness make you think and feel; art that isn't merely sensational, that doesn't get its message across in 10 seconds, that isn't falsely iconic, that hooks onto something deep-running in our natures. In a word, art that is the very opposite of mass media. For no spiritually authentic art can beat mass media at their own game."

Robert Hughes, speech of June 2, 2004

"Whether the 3×3 square grid is fast art or slow art, truly or falsely iconic, perhaps depends upon the eye of the beholder."

Log24, June 5, 2004

If the beholder is Rudolf Arnheim, whom we may now suppose to be viewing the above figure in the afterlife, the 3×3 square is apparently slow art.  Consider the following review of his 1982 book The Power of the Center:

"Arnheim deals with the significance of two kinds of visual organization, the concentric arrangement (as exemplified in a bull's-eye target) and the grid (as exemplified in a Cartesian coordinate system)….

It is proposed that the two structures of grid and target are the symbolic vehicles par excellence for two metaphysical/psychological stances.  The concentric configuration is the visual/structural equivalent of an egocentric view of the world.  The self is the center, and all distances exist in relation to the focal spectator.  The concentric arrangement is a hermetic, impregnable pattern suited to conveying the idea of unity and other-worldly completeness.  By contrast, the grid structure has no clear center, and suggests an infinite, featureless extension…. Taking these two ideal types of structural scaffold and their symbolic potential (cosmic, egocentric vs. terrestrial, uncentered) as given, Arnheim reveals how their underlying presence organizes works of art."

— Review of Rudolf Arnheim's The Power of the Center: A Study of Composition in the Visual Arts (Univ. of Calif. Press, 1982). Review by David A. Pariser, Studies in Art Education, Vol. 24, No. 3 (1983), pp. 210-213

Arnheim himself says in this book (pp. viii-ix) that "With all its virtues, the framework of verticals and horizontals has one grave defect.  It has no center, and therefore it has no way of defining any particular location.  Taken by itself, it is an endless expanse in which no one place can be distinguished from the next.  This renders it incomplete for any mathematical, scientific, and artistic purpose.  For his geometrical analysis, Descartes had to impose a center, the point where a pair of coordinates [sic] crossed.  In doing so he borrowed from the other spatial system, the centric and cosmic one."

Students of art theory should, having read the above passages, discuss in what way the 3×3 square embodies both "ideal types of structural scaffold and their symbolic potential."

We may imagine such a discussion in an afterlife art class– in, perhaps, Purgatory rather than Heaven– that now includes Arnheim as well as Ernst Gombrich and Kirk Varnedoe.

Such a class would be one prerequisite for a more advanced course– Finite geometry of the square and cube.

Friday, February 20, 2004

Friday February 20, 2004

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

The Da Vinci Code
Symbology at Harvard

The protagonist of the recent bestseller The Da Vinci Code is Robert Langdon, "a professor of Religious Symbology at Harvard University."  A prominent part in the novel is played by the well-known Catholic organization Opus Dei.  Less well known (indeed, like Langdon, nonexistent) is the academic discipline of "symbology."  (For related disciplines that do exist, click here.) What might a course in this subject at Harvard be like?

Harvard Crimson, April 10, 2003:

While Opus Dei members said that they do not refer to their practices of recruitment as "fishing," the Work’s founder does describe the process of what he calls "winning new apostles" with an aquatic metaphor.

Point #978 of The Way invokes a passage in the New Testament in which Jesus tells Peter that he will make him a "fisher of men." The point reads:

" ‘Follow me, and I will make you into fishers of men.’ Not without reason does our Lord use these words: men—like fish—have to be caught by the head. What evangelical depth there is in the ‘intellectual apostolate!’ ”

IMAGE- Escher, 'Fishes and Scales'

IMAGE- Cullinane, 'Invariance'

Exercise for Symbology 101:

Describe the symmetry
in each of the pictures above.
Show that the second picture
retains its underlying structural
symmetry under a group of
322,560 transformations.

Having reviewed yesterday's notes
on Gombrich, Gadamer, and Panofsky,
discuss the astrological meaning of
the above symbols in light of
today's date, February 20.

Extra credit:

Relate the above astrological
symbolism to the four-diamond
symbol in Jung's Aion.

Happy metaphors!

Robert Langdon

Thursday, February 19, 2004

Thursday February 19, 2004

Filed under: General — m759 @ 9:22 PM

What is Poetry, Part II —

Gombrich vs. Gadamer

Excerpts from
Tetsuhiro Kato on

Gombrich and the
Hermeneutics of Art

Kato on Gombrich

“… according to Gombrich, an image is susceptible to become a target for ‘symbol detectives’…. But the hidden authorial intention… ([for example]… astrology, recalling the famous warning of Panofsky [1955: 32]), almost always tends to become a reproduction of the interpreter’s own ideological prejudice. Not to give into the irrationalism such psychological overinterpretation might invite…. we have to look for the origin of meaning… in…  the social context…. The event of image making is not the faithful transcription of the outside world by an innocent eye, but it is the result of the artist’s act of selecting the ‘nearest equivalence’… based on social convention….”

Kato on Gadamer 

“For [Gadamer], picture reading is a process where a beholder encounters a picture as addressing him or her with a kind of personal question, and the understanding develops in the form of its answer (Gadamer 1981: 23-24; Gadamer 1985: 97,102-103).  But, it must be noted that by this Gadamer does not mean to identify the understanding of an image with some sort of ‘subsumption’ of the image into its meaning (Gadamer 1985: 100). He insists rather that we can understand an image only by actualizing what is implied in the work, and engage in a dialogue with it. This process is ideally repeated again and again, and implies different relations than the original conditions that gave birth to the work in the beginning (Gadamer 1985: 100).

What matters here for Gadamer is to let the aesthetic aspect of image take its own ‘Zeitgestalt’ (Gadamer 1985: 101).”

Example (?) — the Zeitgestalt
of today’s previous entry:

See, too,
 The Quality of Diamond.

Kato’s References:

Gadamer, Hans-Georg. 1981. “Philosophie und Literatur: Was ist die Literatur?,” Phänomenologische Forschungen 11 (1981): 18-45.

Gadamer, Hans-Georg. 1985. “Über das Lesen von Bauten und Bildern.” Modernität und Tradition: Festschrift für Max Imdahl zum 60. Geburtstag. Ed. Gottfried Boehm, Karlheinz Stierle, Gundorf Winter. Munchen: Wilhelm Fink. 97-103.

Panofsky, Erwin. 1955. Meaning in the Visual Arts: Papers in and on Art History. New York: Anchor.

Thursday, January 29, 2004

Thursday January 29, 2004

Filed under: General,Geometry — Tags: , — m759 @ 2:30 PM

in the Theory of Design

"Whether or not we can follow the theorist in his demonstrations, there is one misunderstanding we must avoid at all cost.  We must not confuse the analyses of geometrical symmetries with the mathematics of combination and permutation….

The earliest (and perhaps the rarest) treatise on the theory of design drives home this insight with marvellous precision."

— E. H. Gombrich, 1979, in
   The Sense of Order

This is perhaps the stupidest remark I have ever read.  The "treatise on the theory of design" that Gombrich refers to is

  • Dominique Douat, Méthode Pour Faire une Infinité de Desseins Differents…. Paris, 1722.

For some background, see

Truchet Tiling,  

Truchet & Types:
Tiling Systems and Ornaments
, and

Douat Designs

Certain of the Truchet/Douat patterns have rather intriguing mathematical properties, sketched in my website Diamond Theory.  These properties become clear if and only if we we do what Gombrich declares that we must not do:  "confuse the analyses of geometrical symmetries with the mathematics of combination and permutation."  (The verb "confuse" should, of course, be replaced by the verb "combine.")

Saturday, August 16, 2003

Saturday August 16, 2003

Filed under: General,Geometry — Tags: — m759 @ 2:16 AM

My Personal Thorny Crown

Kirk Varnedoe, 57, art historian and former curator of the Museum of Modern Art, died Thursday, August 14, 2003.

From his New York Times obituary:

" 'He loved life in its most tangible forms, and so for him art was as physical and pleasurable as being knocked down by a wave,' said Adam Gopnik, the writer and a former student of his who collaborated on Mr. Varnedoe's first big show at the Modern, 'High & Low.' 'Art was always material first — it was never, ever bound by a thorny crown of ideas.' "

For some background on the phrase "thorny crown of ideas," see the web page


The phrase "thorny crown of ideas" is also of interest in the light of recent controversy over Mel Gibson's new film, "The Passion."

For details of the controversy, see Christopher Orlet's Aug. 14 essay at Salon.com,

Mel Gibson vs. "The Jews"

For a real "thorny crown of ideas," consider the following remarks by another art historian:

"Whether or not we can follow the theorist in his demonstrations, there is one misunderstanding we must avoid at all cost.  We must not confuse the analyses of geometrical symmetries with the mathematics of combination and permutation….

The earliest (and perhaps the rarest) treatise on the theory of design drives home this insight with marvellous precision."

— E. H. Gombrich, 1979, in
   The Sense of Order

This is perhaps the most stupid remark I have ever read.  The "treatise on the theory of design" that Gombrich refers to is

  • Dominique Douat, Methode pour faire une infinité de desseins differents avec des carreaux mipartis de deux couleurs par une ligne diagonale : ou observations du Pere Dominique Douat Religieux Carmes de la Province de Toulouse sur un memoire inséré dans l'Histoire de l'Académie Royale des Sciences de Paris l'année 1704, présenté par le Reverend Sebastien Truchet religieux du même ordre, Academicien honoraire, imprimé chez Jacques Quillau, Imprimeur Juré de l'Université, Paris 1722.

This is the title given at the web page

Truchet & Types:
Tiling Systems and Ornaments

which gives some background. 

Certain of the Truchet/Douat patterns have rather intriguing mathematical properties, sketched in my website Diamond Theory.  These properties become clear if and only we we do what Gombrich moronically declares that we must not do:  "confuse the analyses of geometrical symmetries with the mathematics of combination and permutation."  (The verb "confuse" should, of course, be replaced by the verb "combine.") 

What does all this have to do with

Mel Gibson vs. "The Jews" ?

As jesting Pilate seems to have realized, whenever Jews (or, for that matter, Christians) tell stories, issues of truth may arise.  Such issues, as shown by current events in that damned Semitic Hell-on-Earth that used to be referred to as "the Holy Land," can be of life-and-death importance.

Scene from
The Passion

The Roman soldiers may have fashioned a physical crown of thorns, but the Jews are quite capable of fashioning a very uncomfortable crown of, as Gopnik says, "ideas."

Here is an example.

"Ernst Hans Josef Gombrich, who as an author went by the name E. H. Gombrich, was born in Vienna in 1909….

The Gombrich family was Jewish, but his parents felt this had no particular relevance. In later years Mr. Gombrich said that whether someone was Jewish or not was a preoccupation for the Gestapo."

— Michael Kimmelman's obituary for Gombrich in the New York Times. Kimmelman is chief art critic for the New York Times and author of the Times's Aug. 15 Varnedoe obituary.

The web page Understanding cited above contains a link to

Pilate, Truth, and Friday the Thirteenth,

a page combining some religious remarks with a quotation of an extremely patronizing and superficial reference to my own work (and, in passing, to Truchet/Douat patterns).

This reference, and the above-quoted remark by Gombrich, constitute my own modest claim to what the Jew Gopnik jokingly calls a "thorny crown of ideas."

To me it is no joke.

This partly accounts for the rather strained quality of the attempt at humor in a web page I put together yesterday in response to Varnedoe's obituary:

Fahne Hoch, Macbeth!

Another reason for the strained quality is my being struck by the synchronicity of reading Varnedoe's obituary shortly after I had done a journal entry related to the death in July of an earlier Museum of Modern Art curator.  Like Robert A. Heinlein, I think the God of the Jews is a lousy deity and an even worse father figure.  I do, however, believe in synchronicity.

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