Log24

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.

Saturday, November 3, 2018

The Space Theory of Truth

Filed under: General — Tags: — m759 @ 10:00 PM

Earlier posts have discussed the "story theory of truth"
versus the "diamond theory of truth," as defined by 
Richard Trudeau in his 1987 book The Non-Euclidean Revolution.

In a New York Times  opinion piece for tomorrow's print edition,*
novelist Dara Horn touched on what might be called 
"the space theory of truth."

When they return to synagogue, mourners will be greeted
with more ancient words: “May God comfort you
among the mourners of Zion and Jerusalem.”
In that verse, the word used for God is hamakom 
literally, “the place.” May the place comfort you.

[Link added.]

The Source —

See Dara Horn in this  journal, as well as Makom.

* "A version of this article appears in print on ,
on Page A23 of the New York edition with the headline: 
American Jews Know This Story."

Friday, September 28, 2018

ART WARS Midrash

Filed under: General — m759 @ 9:00 AM

"When times are mysterious
Serious numbers
Will always be heard."
— Paul Simon,
"When Numbers Get Serious"

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

— H. S. M. Coxeter, introduction to Richard J. Trudeau's remarks
on the "story theory" of truth as opposed to the "diamond theory"
of truth in The Non-Euclidean Revolution  (1987)

The deaths of Roth and Grünbaum on September 14th,
The Feast of the Holy Cross, along with Douthat's column
today titled "Only the Truth Can Save Us Now," suggest a
review of

Elements of Number Theory, by Vinogradov .

Thursday, April 17, 2014

Thursday with the Nashes

Filed under: General,Geometry — m759 @ 3:00 PM

“For every kind of vampire, there is a kind of cross.” — Gravity’s Rainbow

“I don’t write exclusively on Jewish themes or about Jewish characters.
My collection of short stories, Strange Attractors , contained nine pieces,
five of which were, to some degree, Jewish, and this ratio has provided me
with a precise mathematical answer (for me, still the best kind of answer)
to the question of whether I am a Jewish writer. I am five-ninths a Jewish writer.”

— Rebecca Goldstein, “Against Logic

Midrashim for Rebecca: 

The Diamond Theory vs.  the Story Theory (of truth)

Story Theory and the Number of the Beast

The Palm Sunday post “Gray Space”

For those who prefer the diamond theory of truth,
a “precise mathematical” view of a Gray code —

IMAGE- Six-bit binary and Gray codes

For those who prefer the story theory of truth,
Thursday with the Nashes —

The actors who portrayed Mr. and Mrs. John Nash in
‘A Beautiful Mind’ now portray Mr. and Mrs. Noah…

IMAGE- At UMC.org, the actors who portrayed Mr. and Mrs. John Nash in 'A Beautiful Mind' now portray Mr. and Mrs. Noah.

Monday, October 21, 2013

Edifice Complex

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

New! Improved!

"Euclid's edifice loomed in my consciousness 
as a marvel among sciences, unique in its
clarity and unquestionable validity." 
—Richard J. Trudeau in
   The Non-Euclidean Revolution  (First published in 1986)

Readers of this journal will be aware that Springer's new page
advertising Trudeau's book, pictured above, is a bait-and-switch
operation. In the chapter advertised, Trudeau promotes what he
calls "the Diamond Theory of Truth" as a setup for his real goal,
which he calls "the Story Theory of Truth."

For an earlier use of the phrase "Diamond Theory" in
connection with geometry, see a publication from 1977.

Tuesday, June 18, 2013

Multispeech

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

(Continued)

For those who prefer Trudeau's
"Story Theory" of truth to his "Diamond Theory"

IMAGE- Janet Maslin's review of Max Barry's novel 'Lexicon'

Related material: Click images below for the original posts.

See as well the novel  "Lexicon" at Amazon.com 
and the word  "lexicon" in this journal.

Thursday, November 1, 2012

Theories of Truth

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

A review of two theories of truth described
by a clergyman, Richard J. Trudeau, in
The Non-Euclidean Revolution

The Story Theory of Truth:

"But, I asked, is there a difference
between fiction and nonfiction?
'Not much,' she said, shrugging."

New Yorker  profile of tesseract
     author Madeleine L'Engle

The Diamond Theory of Truth:

(Click image for some background.)

Spaces as Hypercubes

See also the links on a webpage at finitegeometry.org.

Wednesday, August 10, 2011

Objectivity

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

From math16.com

Quotations on Realism
and the Problem of Universals:

"It is said that the students of medieval Paris came to blows in the streets over the question of universals. The stakes are high, for at issue is our whole conception of our ability to describe the world truly or falsely, and the objectivity of any opinions we frame to ourselves. It is arguable that this is always the deepest, most profound problem of philosophy. It structures Plato's (realist) reaction to the sophists (nominalists). What is often called 'postmodernism' is really just nominalism, colourfully presented as the doctrine that there is nothing except texts. It is the variety of nominalism represented in many modern humanities, paralysing appeals to reason and truth."
— Simon Blackburn, Think, Oxford University Press, 1999, page 268

"You will all know that in the Middle Ages there were supposed to be various classes of angels…. these hierarchized celsitudes are but the last traces in a less philosophical age of the ideas which Plato taught his disciples existed in the spiritual world."
— Charles Williams, page 31, Chapter Two, "The Eidola and the Angeli," in The Place of the Lion (1933), reprinted in 1991 by Eerdmans Publishing

For Williams's discussion of Divine Universals (i.e., angels), see Chapter Eight of The Place of the Lion.

"People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only 'truths' strictly worthy of the name. Such truths I will call 'diamonds'; they are highly desirable but hard to find….The happy metaphor is Morris Kline's in Mathematics in Western Culture (Oxford, 1953), p. 430."
— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987, pages 114 and 117

"A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the 'Story Theory' of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.' The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes…. My own viewpoint is the Story Theory…. I concluded long ago that each enterprise contains only stories (which the scientists call 'models of reality'). I had started by hunting diamonds; I did find dazzlingly beautiful jewels, but always of human manufacture."
— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987, pages 256 and 259

Trudeau's confusion seems to stem from the nominalism of W. V. Quine, which in turn stems from Quine's appalling ignorance of the nature of geometry. Quine thinks that the geometry of Euclid dealt with "an emphatically empirical subject matter" — "surfaces, curves, and points in real space." Quine says that Euclidean geometry lost "its old status of mathematics with a subject matter" when Einstein established that space itself, as defined by the paths of light, is non-Euclidean. Having totally misunderstood the nature of the subject, Quine concludes that after Einstein, geometry has become "uninterpreted mathematics," which is "devoid not only of empirical content but of all question of truth and falsity." (From Stimulus to Science, Harvard University Press, 1995, page 55)
— S. H. Cullinane, December 12, 2000

The correct statement of the relation between geometry and the physical universe is as follows:

"The contrast between pure and applied mathematics stands out most clearly, perhaps, in geometry. There is the science of pure geometry, in which there are many geometries: projective geometry, Euclidean geometry, non-Euclidean geometry, and so forth. Each of these geometries is a model, a pattern of ideas, and is to be judged by the interest and beauty of its particular pattern. It is a map or picture, the joint product of many hands, a partial and imperfect copy (yet exact so far as it extends) of a section of mathematical reality. But the point which is important to us now is this, that there is one thing at any rate of which pure geometries are not pictures, and that is the spatio-temporal reality of the physical world. It is obvious, surely, that they cannot be, since earthquakes and eclipses are not mathematical concepts."
— G. H. Hardy, section 23, A Mathematician's Apology, Cambridge University Press, 1940

The story of the diamond mine continues
(see Coordinated Steps and Organizing the Mine Workers)— 

From The Search for Invariants (June 20, 2011):

The conclusion of Maja Lovrenov's 
"The Role of Invariance in Cassirer’s Interpretation of the Theory of Relativity"—

"… physical theories prove to be theories of invariants
with regard to certain groups of transformations and
it is exactly the invariance that secures the objectivity
of a physical theory."

— SYNTHESIS PHILOSOPHICA 42 (2/2006), pp. 233–241

http://www.log24.com/log/pix11B/110810-MajaLovrenovBio.jpg

Related material from Sunday's New York Times  travel section—

"Exhibit A is certainly Ljubljana…."

Tuesday, March 16, 2010

Variations on a Theme

Filed under: General — Tags: — m759 @ 2:29 PM

Today's previous entry was "Gameplayers of the Academy."

More on this theme–

David Corfield in the March 2010
European Mathematical Society newsletter

    "Staying on the theme of games, the mathematician
Alexandre Borovik* once told me he thinks of mathematics
as a Massively-Multiplayer Online Role-Playing Game. If
so, it would show up very clearly the difference between
internal and external viewpoints. Inside the game people
are asking each other whether they were right about
something they encountered in it– 'When you entered
the dungeon did you see that dragon in the fireplace or
did I imagine it?' But someone observing them from the
outside wants to shout: 'You’re not dealing with anything
real. You’ve just got a silly virtual reality helmet on.' External
nominalists say the same thing, if more politely, to
mathematical practitioners. But in an important way the
analogy breaks down. Even if the players interact with
the game to change its functioning in unforeseen ways,
there were the original programmers who set the bounds
for what is possible by the choices they made. When they
release the next version of the game they will have made
changes to allow new things to happen. In the case of
mathematics, it’s the players themselves who make these
choices. There’s no further layer outside.
    What can we do then instead to pin down internal reality?"

*See previous references to Borovik in this journal.

Related material:

The Diamond Theory vs. the Story Theory of Truth,

Infantilizing the Audience, and

It's Still the Same Old Story…God of War III

Thursday, February 18, 2010

Theories: An Outline

Filed under: General,Geometry — Tags: , — m759 @ 10:31 AM

Truth, Geometry, Algebra

The following notes are related to A Simple Reflection Group of Order 168.

1. According to H.S.M. Coxeter and Richard J. Trudeau

“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?’.”

— Coxeter, 1987, introduction to Trudeau’s The Non-Euclidean Revolution

1.1 Trudeau’s Diamond Theory of Truth

1.2 Trudeau’s Story Theory of Truth

2. According to Alexandre Borovik and Steven H. Cullinane

2.1 Coxeter Theory according to Borovik

2.1.1 The Geometry–

Mirror Systems in Coxeter Theory

2.1.2 The Algebra–

Coxeter Languages in Coxeter Theory

2.2 Diamond Theory according to Cullinane

2.2.1 The Geometry–

Examples: Eightfold Cube and Solomon’s Cube

2.2.2 The Algebra–

Examples: Cullinane and (rather indirectly related) Gerhard Grams

Summary of the story thus far:

Diamond theory and Coxeter theory are to some extent analogous– both deal with reflection groups and both have a visual (i.e., geometric) side and a verbal (i.e., algebraic) side.  Coxeter theory is of course highly developed on both sides. Diamond theory is, on the geometric side, currently restricted to examples in at most three Euclidean (and six binary) dimensions. On the algebraic side, it is woefully underdeveloped. For material related to the algebraic side, search the Web for generators+relations+”characteristic two” (or “2“) and for generators+relations+”GF(2)”. (This last search is the source of the Grams reference in 2.2.2 above.)

Friday, April 10, 2009

Friday April 10, 2009

Filed under: General,Geometry — m759 @ 8:00 AM

Pilate Goes
to Kindergarten

“There is a pleasantly discursive
 treatment of Pontius Pilate’s
unanswered question
‘What is truth?’.”

— H. S. M. Coxeter, 1987,
introduction to Trudeau’s
 remarks on the “Story Theory
 of truth as opposed to the
Diamond Theory” of truth in
 The Non-Euclidean Revolution

Consider the following question in a paper cited by V. S. Varadarajan:

E. G. Beltrametti, “Can a finite geometry describe physical space-time?” Universita degli studi di Perugia, Atti del convegno di geometria combinatoria e sue applicazioni, Perugia 1971, 57–62.

Simplifying:

“Can a finite geometry describe physical space?”

Simplifying further:

“Yes. VideThe Eightfold Cube.'”

Froebel's 'Third Gift' to kindergarteners: the 2x2x2 cube

Tuesday, March 17, 2009

Tuesday March 17, 2009

Filed under: General,Geometry — m759 @ 11:07 AM
Deep Structures

The traditional 'Square of Opposition'

The Square of Oppositon
at Stanford Encylopedia of Philosophy


The Square of Opposition diagram in its earliest known form

The Square of Opposition
in its original form

"The diagram above is from a ninth century manuscript of Apuleius' commentary on Aristotle's Perihermaneias, probably one of the oldest surviving pictures of the square."

Edward Buckner at The Logic Museum

From the webpage "Semiotics for Beginners: Paradigmatic Analysis," by Daniel Chandler:
 

The Semiotic Square of Greimas

The Semiotic Square

"The structuralist semiotician Algirdas Greimas introduced the semiotic square (which he adapted from the 'logical square' of scholastic philosophy) as a means of analysing paired concepts more fully (Greimas 1987,* xiv, 49). The semiotic square is intended to map the logical conjunctions and disjunctions relating key semantic features in a text. Fredric Jameson notes that 'the entire mechanism… is capable of generating at least ten conceivable positions out of a rudimentary binary opposition' (in Greimas 1987,* xiv). Whilst this suggests that the possibilities for signification in a semiotic system are richer than the either/or of binary logic, but that [sic] they are nevertheless subject to 'semiotic constraints' – 'deep structures' providing basic axes of signification."

* Greimas, Algirdas (1987): On Meaning: Selected Writings in Semiotic Theory (trans. Paul J Perron & Frank H Collins). London: Frances Pinter

Another version of the semiotic square:
 

Rosalind Krauss's version of the semiotic square, which she calls the Klein group

Krauss says that her figure "is, of course, a Klein Group."

Here is a more explicit figure representing the Klein group:

The Klein Four-Group, illustration by Steven H. Cullinane

There is also the logical
    diamond of opposition

The Diamond of Opposition (figure from Wikipedia)

A semiotic (as opposed to logical)
diamond has been used to illustrate
remarks by Fredric Jameson,
 a Marxist literary theorist:

"Introduction to Algirdas Greimas, Module on the Semiotic Square," by Dino Felluga at Purdue University–

The semiotic square has proven to be an influential concept not only in narrative theory but in the ideological criticism of Fredric Jameson, who uses the square as "a virtual map of conceptual closure, or better still, of the closure of ideology itself" ("Foreword"* xv). (For more on Jameson, see the [Purdue University] Jameson module on ideology.)

Greimas' schema is useful since it illustrates the full complexity of any given semantic term (seme). Greimas points out that any given seme entails its opposite or "contrary." "Life" (s1) for example is understood in relation to its contrary, "death" (s2). Rather than rest at this simple binary opposition (S), however, Greimas points out that the opposition, "life" and "death," suggests what Greimas terms a contradictory pair (-S), i.e., "not-life" (-s1) and "not-death" (-s2). We would therefore be left with the following semiotic square (Fig. 1):

A semiotic 'diamond of opposition'

As Jameson explains in the Foreword to Greimas' On Meaning, "-s1 and -s2"—which in this example are taken up by "not-death" and "not-life"—"are the simple negatives of the two dominant terms, but include far more than either: thus 'nonwhite' includes more than 'black,' 'nonmale' more than 'female'" (xiv); in our example, not-life would include more than merely death and not-death more than life.

* Jameson, Fredric. "Foreword." On Meaning: Selected Writings in Semiotic Theory. By Algirdas Greimas. Trans. Paul J. Perron and Frank H. Collins. Minneapolis: U of Minnesota P, 1976.

"The Game in the Ship cannot be approached as a job, a vocation, a career, or a recreation. To the contrary, it is Life and Death itself at work there. In the Inner Game, we call the Game Dhum Welur, the Mind of God."

The Gameplayers of Zan, by M.A. Foster

"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon,
 Gravity's Rainbow

Crosses used by semioticians
to baffle their opponents
are illustrated above.

Some other kinds of crosses,
and another kind of opponent:

Monday, July 11, 2005

Logos
for St. Benedict's Day

Click on either of the logos below for religious meditations– on the left, a Jewish meditation from the Conference of Catholic Bishops; on the right, an Aryan meditation from Stormfront.org.

Logo of Conference of Catholic Bishops     Logo of Stormfront website

Both logos represent different embodiments of the "story theory" of truth, as opposed to the "diamond theory" of truth.  Both logos claim, in their own ways, to represent the eternal Logos of the Christian religion.  I personally prefer the "diamond theory" of truth, represented by the logo below.

Illustration of the 2x2 case of the diamond theorem

See also the previous entry
(below) and the entries
  of 7/11, 2003.
 

Sunday, July 10, 2005

Mathematics
and Narrative

 
Click on the title
for a narrative about

Nikolaos K. Artemiadis

Nikolaos K. Artemiadis,
 (co-) author of

Artemiadis's 'History of Mathematics,' published by the American Mathematical Society
 

From Artemiadis's website:
1986: Elected Regular Member
of the Academy of Athens
1999: Vice President
of the Academy of Athens
2000: President
of the Academy of Athens
Seal of the American Mathematical Society with picture of Plato's Academy

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

— Remark attributed to Plato

Friday, January 30, 2009

Friday January 30, 2009

Filed under: General,Geometry — m759 @ 11:07 AM
Two-Part Invention

This journal on
October 8, 2008,
at noon:

“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?'”

— H. S. M. Coxeter, introduction to Richard J. Trudeau’s remarks on the “story theory” of truth as opposed to the “diamond theory” of truth in The Non-Euclidean Revolution

Trudeau’s 1987 book uses the phrase “diamond theory” to denote the philosophical theory, common since Plato and Euclid, that there exist truths (which Trudeau calls “diamonds”) that are certain and eternal– for instance, the truth in Euclidean geometry that the sum of a triangle’s angles is 180 degrees.

Insidehighered.com on
the same day, October 8, 2008,
at 12:45 PM EDT

“Future readers may consider Updike our era’s Mozart; Mozart was once written off as a too-prolific composer of ‘charming nothings,’ and some speak of Updike that way.”

— Comment by BPJ

“Birthday, death-day–
 what day is not both?”
John Updike

Updike died on January 27.
On the same date,
Mozart was born.

Requiem

Mr. Best entered,
tall, young, mild, light.
He bore in his hand
with grace a notebook,
new, large, clean, bright.

— James Joyce, Ulysses,
Shakespeare and Company,
Paris, 1922, page 178

Related material:

Dec. 5, 2004 and

Inscribed carpenter's square

Jan. 27-29, 2009

Wednesday, October 8, 2008

Wednesday October 8, 2008

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

Serious Numbers

A Yom Kippur
Meditation

"When times are mysterious
Serious numbers
Will always be heard."
— Paul Simon,
"When Numbers Get Serious"

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

— H. S. M. Coxeter, introduction to Richard J. Trudeau's remarks on the "story theory" of truth as opposed to the "diamond theory" of truth in The Non-Euclidean Revolution

Trudeau's 1987 book uses the phrase "diamond theory" to denote the philosophical theory, common since Plato and Euclid, that there exist truths (which Trudeau calls "diamonds") that are certain and eternal– for instance, the truth in Euclidean geometry that the sum of a triangle's angles is 180 degrees. As the excerpt below shows, Trudeau prefers what he calls the "story theory" of truth–

"There are no diamonds. People make up stories about what they experience. Stories that catch on are called 'true.'"

(By the way, the phrase "diamond theory" was used earlier, in 1976, as the title of a monograph on geometry of which Coxeter was aware.)

Richard J. Trudeau on the 'Story Theory' of truth

Excerpt from
The Non-Euclidean Revolution

What does this have to do with numbers?

Pilate's skeptical tone suggests he may have shared a certain confusion about geometric truth with thinkers like Trudeau and the slave boy in Plato's Meno. Truth in a different part of mathematics– elementary arithmetic– is perhaps more easily understood, although even there, the existence of what might be called "non-Euclidean number theory"– i.e., arithmetic over finite fields, in which 1+1 can equal zero– might prove baffling to thinkers like Trudeau.

Trudeau's book exhibits, though it does not discuss, a less confusing use of numbers– to mark the location of pages. For some philosophical background on this version of numerical truth that may be of interest to devotees of the Semitic religions on this evening's High Holiday, see Zen and Language Games.

For uses of numbers that are more confusing, see– for instance– the new website The Daily Beast and the old website Story Theory and the Number of the Beast.

Tuesday, April 25, 2006

Tuesday April 25, 2006

Filed under: General,Geometry — m759 @ 3:09 PM

“There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
‘What is truth?'”

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

A Serious Position

“‘Teitelbaum,’ in German,
is ‘date palm.'”
Generations, Jan. 2003   

“In Hasidism, a mystical brand
of Orthodox Judaism, the grand rabbi
is revered as a kinglike link to God….”

Today’s New York Times obituary
of Rabbi Moses Teitelbaum,
who died on April 24, 2006
(Easter Monday in the
Orthodox Church
)

From Nextbook.org, “a gateway to Jewish literature, culture, and ideas”:

NEW BOOKS: 02.16.05
Proofs and Paradoxes
Alfred Teitelbaum changed his name to Tarski in the early 20s, the same time he changed religions, but when the Germans invaded his native Poland, the mathematician was in California, where he remained. His “great achievement was his audacious assault on the notion of truth,” says Martin Davis, focusing on the semantics and syntax of scientific language. Alfred Tarski: Life and Logic, co-written by a former student, Solomon Feferman, offers “remarkably intimate information,” such as abusive teaching and “extensive amorous involvements.”

From Wikipedia, an unsigned story:

“In 1923 Alfred Teitelbaum and his brother Wacław changed their surnames to Tarski, a name they invented because it sounded very Polish, was simple to spell and pronounce, and was unused. (Years later, he met another Alfred Tarski in northern California.) The Tarski brothers also converted to Roman Catholicism, the national religion of the Poles. Alfred did so, even though he was an avowed atheist, because he was about to finish his Ph.D. and correctly anticipated that it would be difficult for a Jew to obtain a serious position in the new Polish university system.”

The image “http://www.log24.com/log/pix06/060425-Tarski.jpg” cannot be displayed, because it contains errors.

Alfred Tarski

The image “http://www.log24.com/log/pix06/060424-Crimson2.jpg” cannot be displayed, because it contains errors.

See also
 
The Crimson Passion.

Sunday, November 20, 2005

Sunday November 20, 2005

Filed under: General,Geometry — m759 @ 4:04 PM
An Exercise
of Power

Johnny Cash:
“And behold,
a white horse.”

The image “http://www.log24.com/log/pix05B/051120-SpringerLogo9.gif” cannot be displayed, because it contains errors.
Adapted from
illustration below:

The image “http://www.log24.com/log/pix05B/051120-NonEuclideanRev.jpg” cannot be displayed, because it contains errors.

“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?'”

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

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

Richard J. Trudeau in
The Non-Euclidean Revolution

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

— Jim Holt in The New Yorker.

(Click on the box below.)

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

Exercise of Power:

Show that a white horse–

A Singer 7-Cycle

a figure not unlike the
symbol of the mathematics
publisher Springer–
is traced, within a naturally
arranged rectangular array of
polynomials, by the powers of x
modulo a polynomial
irreducible over a Galois field.

This horse, or chess knight–
“Springer,” in German–
plays a role in Diamond Theory
(a phrase used in finite geometry
in 1976, some years before its use
by Trudeau in the above book).

Related material

On this date:

 In 1490, The White Knight
 (Tirant lo Blanc The image “http://www.log24.com/images/asterisk8.gif” cannot be displayed, because it contains errors. )–
 a major influence on Cervantes–
was published, and in 1910

The image “http://www.log24.com/log/pix05B/051120-Caballo1.jpg” cannot be displayed, because it contains errors.

the Mexican Revolution began.

Illustration:
Zapata by Diego Rivera,
Museum of Modern Art,
New York

The image “http://www.log24.com/images/asterisk8.gif” cannot be displayed, because it contains errors. Description from Amazon.com

“First published in the Catalan language in Valencia in 1490…. Reviewing the first modern Spanish translation in 1969 (Franco had ruthlessly suppressed the Catalan language and literature), Mario Vargas Llosa hailed the epic’s author as ‘the first of that lineage of God-supplanters– Fielding, Balzac, Dickens, Flaubert, Tolstoy, Joyce, Faulkner– who try to create in their novels an all-encompassing reality.'”

Wednesday, September 28, 2005

Wednesday September 28, 2005

Filed under: General,Geometry — m759 @ 4:26 AM
Mathematical Narrative,
continued:

There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
“What is truth?”

— H. S. M. Coxeter, introduction to
Richard J. Trudeau’s
The Non-Euclidean Revolution

“People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only ‘truths’ strictly worthy of the name. Such truths I will call ‘diamonds’; they are highly desirable but hard to find….The happy metaphor is Morris Kline’s in Mathematics in Western Culture (Oxford, 1953), p. 430.”

— Richard J. Trudeau,
   The Non-Euclidean Revolution,
   Birkhauser Boston,
   1987, pages 114 and 117

“A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the ‘Story Theory’ of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called ‘true.’ The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes…. My own viewpoint is the Story Theory…. I concluded long ago that each enterprise contains only stories (which the scientists call ‘models of reality’). I had started by hunting diamonds; I did find dazzlingly beautiful jewels, but always of human manufacture.”

  — Richard J. Trudeau,
     The Non-Euclidean Revolution,
     Birkhauser Boston,
     1987, pages 256 and 259

An example of
the story theory of truth:

The image “http://www.log24.com/log/pix05B/050925-Proof1.jpg”  cannot be displayed, because it contains errors.

Actress Gwyneth Paltrow (“Proof”) was apparently born on either Sept. 27, 1972, or Sept. 28, 1972.   Google searches yield  “about 193” results for the 27th and “about 610” for the 28th.

Those who believe in the “story theory” of truth may therefore want to wish her a happy birthday today.  Those who do not may prefer the contents of yesterday’s entry, from Paltrow’s other birthday.

Friday, August 19, 2005

Friday August 19, 2005

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

Mathematics and Narrative
continued

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

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

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

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

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

Richard J. Trudeau in The Non-Euclidean Revolution

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

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

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

* Many stripes

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

 

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

Monday, July 11, 2005

Monday July 11, 2005

Filed under: General — m759 @ 12:00 AM
Logos
for St. Benedict’s Day

Click on either of the logos below for religious meditations — on the left, a Jewish meditation from the Conference of Catholic Bishops; on the right, an Aryan meditation from Stormfront.org.

     

Both logos represent different embodiments of the “story theory” of truth, as opposed to the “diamond theory” of truth.  Both logos claim, in their own ways, to represent the eternal Logos of the Christian religion.  I personally prefer the “diamond theory” of truth, represented by the logo below.

See also the previous entry
and the entries of 7/11, 2003.

Thursday, May 26, 2005

Thursday May 26, 2005

Filed under: General,Geometry — m759 @ 4:23 PM
Drama of the Diagonal
“The beautiful in mathematics
resides in contradiction.
Incommensurability, logoi alogoi, was
the first splendor in mathematics.”
— Simone Weil, Oeuvres Choisies,
éd. Quarto
, Gallimard, 1999, p. 100

Logos Alogos
by S. H. Cullinane

“To a mathematician, mathematical entities have their own existence, they habitate spaces created by their intention.  They do things, things happen to them, they relate to one another.  We can imagine on their behalf all sorts of stories, providing they don’t contradict what we know of them.  The drama of the diagonal, of the square…

— Dennis Guedj, abstract of “The Drama of Mathematics,” a talk to be given this July at the Mykonos conference on mathematics and narrative.

For the drama of the diagonal of the square, see

Saturday, March 12, 2005

Saturday March 12, 2005

Filed under: General,Geometry — m759 @ 5:09 AM
Three Eleanors

Continued from March 10:

For some children…

The image “http://www.log24.com/log/pix05/050310-Burton.jpg” cannot be displayed, because it contains errors.

It takes three Eleanors.

The image “http://www.log24.com/log/pix05/050310-Eleanors.jpg” cannot be displayed, because it contains errors.
1             2              3

For Alice, a beautiful child

who died in London
on Tuesday
at 72:

The image “http://www.log24.com/log/pix05/050312-Form.jpg” cannot be displayed, because it contains errors.

Today’s New York Times says that
Alice, the author of Fairy Tale,
was a
“passionately traditional Catholic.”

For related material, see
Immortal Diamond:
O’Hara, Hopkins, and Joyce
.

See also the conflict between Trudeau’s
  diamond theoryand
story theory
of truth
,

and Suzanne Keen‘s article from the
Catholic publication Commonweal:

Getting to Truth by Lying.

Friday, October 10, 2003

Friday October 10, 2003

Filed under: General — m759 @ 1:35 AM

The West Wing’s
Story Line

From USATODAY.com, Oct. 9, 2003:

News analysis by Judy Keen, USA TODAY

Posted 10/9/2003 9:40 PM 
Updated 10/9/2003 9:42 PM

WASHINGTON — President Bush’s fierce defense Thursday of the war with Iraq was part of an effort to regain control of the debate over the wisdom of the conflict….

Bush’s insistence that the United States “won’t run from a challenge” in Iraq was a sign that he and his top aides are doing what they always do when they’re in trouble. They attempt to recapture equilibrium by confronting critics and trying to control the story line.

See also the “story theory of truth”
versus the “diamond theory of truth.”

Saturday, August 9, 2003

Saturday August 9, 2003

Filed under: General — m759 @ 12:07 PM

Beware of…
Jews Peddling Stories:

An episode in the ongoing saga of the conflict between the "story theory of truth" and the "diamond theory of truth."

The following set of pictures summarizes some reflections on truth and reality suggested by the August 9, 2003, New York Times obituary of writer William Woolfolk, who died on July 20, 2003.

Woolfolk was the author of The Sex Goddess and was involved in the production of the comic book series The Spirit (see below).

The central strategy of the three Semitic religions — Judaism, Christianity, and Islam — is to pretend that we are all characters in a story whose author is God.  This strategy suggests the following Trinity, based on the work of William Woolfolk (The Sex Goddess and The Spirit) and Steven Spielberg ("Catch Me If You Can").  Like other Semitic tales, the story of this Trinity should not be taken too seriously.

 

William Woolfolk
Woolfolk as
a Jewish God

The Sex Goddess
Woolfolk's Story

 

Martin Sheen in Catch Me If You Can
The Father as
a Lutheran God

 

Amy Adams in Catch Me If You Can
The Father's
Story

DiCaprio as a doctor
The Son

DiCaprio and Adams
The Son's Story

Amy Adams, star of Catch Me If You Can
The Holy
Spirit

The Spirit, 1942
The Holy
Spirit's Story

 

A Confession of Faith:

Theology Based On the Film
"Catch Me If You Can":

The Son to God the Lutheran Father:

"I'm nothing really, just a kid in love with your daughter."

This is taken from a review of "Catch Me If You Can" by Thomas S. Hibbs.

For some philosophical background to this confession, see Hibbs's book

Shows About Nothing:
Nihilism in Popular Culture
from The Exorcist to Seinfeld
.

By the way, today is the anniversary of the dropping on Nagasaki
of a made-in-USA Weapon of Mass Destruction, a plutonium bomb
affectionately named Fat Man.

Fat Man was a sequel to an earlier Jewish story,

Trinity.

Friday, July 11, 2003

Friday July 11, 2003

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

Links for St. Benedict

Today is the feast of St. Benedict.

Here is a link from the left:

The Trial of Depleted Uranium,
by Saint Philip Berrigan

Here is a link from the right:

On a Preview of “The Passion,”
a film by Saint Mel Gibson

Both Berrigan and Gibson are devout  Catholics.  (I use the present tense for Berrigan, though he is dead, since, as a saint, he is not very dead.)  Both are worthy of respect, and should be listened to carefully, even though the religion they espouse is that of Hitler and Torquemada.

Logos 

For more details, see sites related to the above links…. Click on either of the logos below — on the left, a Jewish meditation from the Conference of Catholic Bishops; on the right, an Aryan meditation from Stormfront.org.

     

Both logos represent different embodiments of the “story theory” of truth, as opposed to the “diamond theory” of truth.  Both logos claim, in their own ways, to represent the eternal Logos of the Christian religion.  I personally prefer the “diamond theory” of truth, represented by the logo below.

Saturday, June 14, 2003

Saturday June 14, 2003

Filed under: General,Geometry — m759 @ 5:00 PM

Indiana Jones
and the Hidden Coffer

In memory of Bernard Williams,

Oxford philosopher, who died Tuesday, June 10, 2003. 

“…in… Truth and Truthfulness [September, 2002], he sought to speak plainly, and took on the post-modern, politically correct notion that truth is merely relative…”

— Christopher Lehmann-Haupt

“People have always longed for truths about the world — not logical truths, for all their utility; or even probable truths, without which daily life would be impossible; but informative, certain truths, the only ‘truths’ strictly worthy of the name. Such truths I will call ‘diamonds’; they are highly desirable but hard to find….

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

— Richard J. Trudeau, The Non-Euclidean Revolution, Birkhauser Boston, 1987

Today is the feast day of Saint Jorge Luis Borges (b. Buenos Aires, August 24, 1899 – d. Geneva, June 14, 1986).

From Borges’s “The Aleph“:

“The Faithful who gather at the mosque of Amr, in Cairo, are acquainted with the fact that the entire universe lies inside one of the stone pillars that ring its central court…. The mosque dates from the seventh century; the pillars come from other temples of pre-Islamic religions…. Does this Aleph exist in the heart of a stone?”

(“Los fieles que concurren a la mezquita de Amr, en el Cairo, saben muy bien que el universo está en el interior de una de las columnas de piedra que rodean el patio central…. la mezquita data del siglo VII; las columnas proceden de otros templos de religiones anteislámicas…. ¿Existe ese Aleph en lo íntimo de una piedra?”)

From The Hunchback of Notre Dame:

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

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

See also the figures obtained by coloring and permuting parts of the above religious symbol.

Lena Olin and Harrison Ford
in “Hollywood Homicide

Monday, April 28, 2003

Monday April 28, 2003

Filed under: General,Geometry — Tags: — m759 @ 12:07 AM

ART WARS:

Toward Eternity

April is Poetry Month, according to the Academy of American Poets.  It is also Mathematics Awareness Month, funded by the National Security Agency; this year's theme is "Mathematics and Art."

Some previous journal entries for this month seem to be summarized by Emily Dickinson's remarks:

"Because I could not stop for Death–
He kindly stopped for me–
The Carriage held but just Ourselves–
And Immortality.

………………………
Since then–'tis Centuries–and yet
Feels shorter than the Day
I first surmised the Horses' Heads
Were toward Eternity– "

 

Consider the following journal entries from April 7, 2003:
 

Math Awareness Month

April is Math Awareness Month.
This year's theme is "mathematics and art."


 

An Offer He Couldn't Refuse

Today's birthday:  Francis Ford Coppola is 64.

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


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

 

From a website titled simply Sinatra:

"Then came From Here to Eternity. Sinatra lobbied hard for the role, practically getting on his knees to secure the role of the street smart punk G.I. Maggio. He sensed this was a role that could revive his career, and his instincts were right. There are lots of stories about how Columbia Studio head Harry Cohn was convinced to give the role to Sinatra, the most famous of which is expanded upon in the horse's head sequence in The Godfather. Maybe no one will know the truth about that. The one truth we do know is that the feisty New Jersey actor won the Academy Award as Best Supporting Actor for his work in From Here to Eternity. It was no looking back from then on."

From a note on geometry of April 28, 1985:

 
The "horse's head" figure above is from a note I wrote on this date 18 years ago.  The following journal entry from April 4, 2003, gives some details:
 

The Eight

Today, the fourth day of the fourth month, plays an important part in Katherine Neville's The Eight.  Let us honor this work, perhaps the greatest bad novel of the twentieth century, by reflecting on some properties of the number eight.  Consider eight rectangular cells arranged in an array of four rows and two columns.  Let us label these cells with coordinates, then apply a permutation.

 


 Decimal 
labeling

 
Binary
labeling


Algebraic
labeling


Permutation
labeling

 

The resulting set of arrows that indicate the movement of cells in a permutation (known as a Singer 7-cycle) outlines rather neatly, in view of the chess theme of The Eight, a knight.  This makes as much sense as anything in Neville's fiction, and has the merit of being based on fact.  It also, albeit rather crudely, illustrates the "Mathematics and Art" theme of this year's Mathematics Awareness Month.

The visual appearance of the "knight" permutation is less important than the fact that it leads to a construction (due to R. T. Curtis) of the Mathieu group M24 (via the Curtis Miracle Octad Generator), which in turn leads logically to the Monster group and to related "moonshine" investigations in the theory of modular functions.   See also "Pieces of Eight," by Robert L. Griess.

Monday, April 7, 2003

Monday April 7, 2003

Filed under: General,Geometry — Tags: — m759 @ 1:17 PM

An Offer He Couldn't Refuse

Today's birthday:  Francis Ford Coppola is 64.

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


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

 

From a website titled simply Sinatra:

"Then came From Here to Eternity. Sinatra lobbied hard for the role, practically getting on his knees to secure the role of the street smart punk G.I. Maggio. He sensed this was a role that could revive his career, and his instincts were right. There are lots of stories about how Columbia Studio head Harry Cohn was convinced to give the role to Sinatra, the most famous of which is expanded upon in the horse's head sequence in The Godfather. Maybe no one will know the truth about that. The one truth we do know is that the feisty New Jersey actor won the Academy Award as Best Supporting Actor for his work in From Here to Eternity. It was no looking back from then on."

From a note on geometry of April 28, 1985:


 

Monday, December 16, 2002

Monday December 16, 2002

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

Rebecca Goldstein
at Heaven’s Gate

This entry is in gratitude for Rebecca Goldstein’s
excellent essay
in The New York Times of December 16, 2002.

She talks about the perennial conflict between two theories of truth that Richard Trudeau called the “story theory” and the “diamond theory.” My entry of December 13, 2002, “Rhyme Scheme,” links the word “real” to an article in the Stanford Encyclopedia of Philosophy that contains the following:

“According to a platonist about arithmetic, the truth of the sentence ‘7 is prime’ entails the existence of an abstract object, the number 7. This object is abstract because it has no spatial or temporal location, and is causally inert. A platonic realist about arithmetic will say that the number 7 exists and instantiates the property of being prime independently of anyone’s beliefs, linguistic practices, conceptual schemes, and so on. A certain kind of nominalist rejects the existence claim which the platonic realist makes: there are no abstract objects, so sentences such as ‘7 is prime’ are false…”

This discussion of “sevenness,” along with the discussion of “eightness” in my December 14, 2002, note on Bach, suggest that I supply a transcription of a note in my paper journal from 2001 that deals with these matters.

From a paper journal note of October 5, 2001:

The 2001 Silver Cup Award
for Realism in Mathematics
goes to…
Glynis Johns, star of
The Sword and the Rose,
Shake Hands with the Devil, and
No Highway in the Sky.

Glynis Johns is 78 today.

“Seven is heaven,
Eight is a gate.”
— from
Dealing with Memory Changes
as You Grow Older
,
by Kathleen Gose and Gloria Levi

“There is no highway in the sky.”
— Quotation attributed to Albert Einstein.
(See
Gotthard Günther’s website
“Achilles and the Tortoise, Part 2”.)

“Don’t give up until you
Drink from the silver cup
And ride that highway in the sky.”
America, 1974

See also page 78 of
Realism in Mathematics
(on Gödel’s Platonism)
by Penelope Maddy,
Clarendon Press, Oxford, 1990
(reprinted, 2000).

Added 12/17/02: See also
the portrait of Rebecca Goldstein in
Hadassah Magazine
 Volume
78
Number 10
(June/July 1997).

For more on the Jewish propensity to
assign mystical significance to numbers, see
Rabbi Zwerin’s Kol Nidre Sermon.

For the significance of “seven” in Judaism, see
Zayin: The Woman of Valor.
For the significance of “eight” in Judaism, see
Chet: The Life Dynamic.

For the cabalistic significance of
“Seven is heaven, Eight is a gate,”
note that Zayin, Seven, signifies
“seven chambers of Paradise”
and that Chet, Eight, signifies
the “gateway to infinity.”

For the significance of the date 12.17, see
Tet: The Concealed Good.

Monday, November 25, 2002

Monday November 25, 2002

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

Swashbucklers and Misfits

There are two theories of truth, according to a a book on the history of geometry —

The “Story Theory” and the “Diamond Theory.” 

For those who prefer the story theory

From a review by Brian Hayes of A Beautiful Mind:

“Mathematical genius is rare enough. Cloaked in madness, or wrapped in serious eccentricity, it’s the stuff legends are made of.

There are brilliant and productive mathematicians who go to the office from nine to five, play tennis on the weekend, and worry about fixing the gearbox in the Volvo. Not many of them become the subjects of popular biographies. Instead we read about the great swashbucklers and misfits of mathematics, whose stories combine genius with high romance or eccentricity.”

Russell Crowe,
swashbuckler

Marilyn
Monroe,
misfit

Hollywood has recently given us a mathematical Russell Crowe.  For a somewhat tougher sell, Marilyn Monroe as a mathematician, see “Insignificance,” 1985: “Marilyn Monroe on her hands and knees explains the theory of relativity to Albert Einstein.”  

For a combination of misfit and swashbuckler in one Holy Name, see today’s earlier note, “The Artist’s Signature.”

See also my note of October 4, 2002, on Michelangelo, and the description of “the face of God” in this review.

Sunday, August 4, 2002

Sunday August 4, 2002

Filed under: General,Geometry — m759 @ 2:52 PM

The Story Theory of Truth

versus

The Diamond Theory of Truth

One year ago today, Lorenzo Music, the voice of Carlton the doorman on Rhoda, died.  His eulogy from Valerie Harper:

 “Valerie’s heart is breaking, but Rhoda is certain that Carlton the doorman is giving St. Peter at the gate a run for his money.”

Today’s birthday: Logician John Venn

Appearing for the story theory

Flannery O’Connor:

“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.”

Appearing for the diamond theory

Mary McCarthy and G. H. Hardy:

From the Hollywood Investigator:

 On October 18, 1979, Mary McCarthy said on PBS’s Dick Cavett Show: “Every word she writes is a lie, including ‘and’ and ‘the.'”

Don’t forget “a,” as in “a people is known” —

“Greek mathematics is permanent, more permanent even than Greek literature.  Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not.”

— G. H. Hardy in A Mathematician’s Apology

And a closing rebuttal from the story theory

Martin Heidegger and Dean Martin: 

Words of wisdom from Martin Heidegger, Catholic Nazi:

“The nature of art is poetry.  The nature of poetry, in turn, is the founding of truth…. In the work, truth is thrown toward… an historical group of men.”

Poetry, Language, Thought, page 75, translated by Albert Hofstadter, Harper & Row paperback, 1975

And from Dean Martin, avatar of anti-art :

That’s Amore:

– Artist: Dean Martin as sung on “Dean Martin’s Greatest Hits”
– Capitol 4XL-9389
– peak Billboard position # 2 in 1953
– from the movie “the Caddy” starring Dean, Jerry Lewis, and Donna Reed
– Words and Music by Harry Warren and Jack Brooks

(In Napoli where love is King, when boy meets girl, here’s what they say)

When the moon hits your eye like a big-a pizza pie,
That’s amore!
When the world seems to shine like you’ve had too much wine,
That’s amore!

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