"To Phaedrus, this backlight from the conflict between
the Sophists and the Cosmologists adds an entirely
new dimension to the Dialogues of Plato." — Robert M. Pirsig
"It’s all in Plato, all in Plato;
bless me, what do they
teach them at these schools?”
— C. S. Lewis in
The Narnia Chronicles
Compare and Contrast — Plato's Diamond.
The previous post, on a Joyce symposium in
Utrecht on June 15-20, 2014, suggests a review
of this journal in June 2014. From June 21
of that year —
"Without the possibility that
an origin can be lost, forgotten,
or alienated into what springs
forth from it, an origin could
not be an origin. The possibility
of inscription is thus a necessary
possibility, one that must always
be possible."
— Page 157 of The Tain of the Mirror:
Derrida and the Philosophy of Reflection ,
by Rodolphe Gasché, Harvard U. Press, 1986
Related art suggested by the above modal logic —
“The 2×2 matrix is commonly used in business strategy
as a representational tool to show conflicting concepts and
for decision making. This four-quadrant matrix diagram
is perfect to be used for business or marketing matrices
like BCG, SWOT, Ansoff, risk assessment…
Additionally, it will also be suitable to illustrate 4 ideas or
concepts.” [Link on “illustrate” added.]
See also a Log24 search for “Resplendent.”
Note the resemblance to Plato’s Diamond.
Click the Pritchard passage above for an interactive version.
The previous post’s search for Turing + Dyson yielded a
quotation from Kierkegaard on possibility and necessity.
Further details —
See also . . .
is a TCM special at 8 PM ET this evening.
A snow-globe phrase from April 28 —
Bauble, Babel . . . Bubble —
The "bubble" cited above —
For more metaphysical accounting, see
The Church of Synchronology.
See also yesterday’s Archimedes at Hiroshima and the
above 24 graphic permutations on All Souls’ Day 2010.
For some backstory, see Narrative Line (November 10, 2014).
From Ulysses , by James Joyce —
|
John Eglinton, frowning, said, waxing wroth: —Upon my word it makes my blood boil to hear anyone compare Aristotle with Plato. —Which of the two, Stephen asked, would have banished me from his commonwealth? |
Compare and contrast:
Fans of Plato might enjoy tales of Narnia, but fans of
James Joyce and Edgar Allan Poe might prefer
a tale by Michael Chabon from April 2001 about a
"doleful little corner of western Pennsylvania."
The title refers to the previous two posts.
Related literature —
Plato's Ghost: The Modernist Transformation of Mathematics
(Princeton University Press, 2008) and . . .
Plato's diamond-in-a-matrix:
Today’s New York Times on a character in a 1978 film —
“Cluelessly upbeat and charmingly idiotic.”
Related material from a post Saturday —
Coda —
See as well this journal on the above date — Sept. 24, 2015.
(The title is from yesterday morning's Graphical Interfaces.)
Thacker reportedly died on Monday, June 12, 2017.
This journal on that date —
Thacker retired from Microsoft in February.
For example, Plato's diamond as an object to be transformed —
Versions of the transformed object —
See also The 4×4 Relativity Problem in this journal.
Or: Philosophy for Jews
From a New Yorker weblog post dated Dec. 6, 2012 —
"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."
Socrates and the slave boy discussed a rather elementary "truth
about geometry" — A diamond inscribed in a square has area 2
(and side the square root of 2) if the square itself has area 4
(and side 2).
Consider that not-particularly-deep structure from the Meno dialogue
in the light of the following…
The following analysis of the Meno diagram from yesterday's
post "The Embedding" contradicts the Lévi-Strauss dictum on
the impossibility of going beyond a simple binary opposition.
(The Chinese word taiji denotes the fundamental concept in
Chinese philosophy that such a going-beyond is both useful
and possible.)
The matrix at left below represents the feminine yin principle
and the diamond at right represents the masculine yang .
From a post of Sept. 22,
"Binary Opposition Illustrated" —
A symbol of the unity of yin and yang —
Related material:
A much more sophisticated approach to the "deep structure" of the
Meno diagram —
Slowness is sometimes in the eye of the beholder.
See this journal on Slow Art Day 2015.
Related material: Epistemic States in this journal.
"But what was supposed to be the source of a compound's
authority? Why, the same as that of all new religious movements:
direct access to the godhead, which in this case was Creativity."
— Tom Wolfe, From Bauhaus to Our House
"Creativity is not a matter of magical inspiration."
— Burger and Starbird, The 5 Elements of Effective Thinking (2012)
Video published on Oct 19, 2012
"In this fifth of five videos, mathematics professor
Michael Starbird talks about the fifth element
in his new book, The 5 Elements of Effective Thinking ,
co-authored with Williams College professor
Edward B. Burger."
For more on the Starbird manifesto, see Princeton University Press.
An excerpt —
See also a post for Abel's Birthday, 2011 —
Midnight in Oslo — and a four-elements image from
the Jan. 26, 2010, post Symbology —
An image related to the recent posts Sense and Sensibility:
A quote from yesterday's post The Eight:
A possible source for the above phrase about phenomena "carved at their joints":
See also the carving at the joints of Plato's diamond from the Meno :
Related material: Phaedrus on Kant as a diamond cutter
in Zen and the Art of Motorcycle Maintenance .
A search for "Dark Fields of the Republic,"
an F. Scott Fitzgerald phrase mentioned in
the previous post, yields a book by that title.
"When does a life bend toward freedom?
grasp its direction?"
— Adrienne Rich on page 275 of
Later Poems Selected and New: 1971-2012
The book's author, Adrienne Rich, died at 82 on
March 27, 2012. See that date in this journal.
See also the following:
|
The Diamond Cutters by Adrienne Rich (1955)
However legendary,
Now, you intelligence
Be serious, because
Be hard of heart, because
Be proud, when you have set |
The Mathematical Association of America (MAA)
newsmagazine Focus for December 2012/January 2013:
The Babylonian tablet on the cover illustrates the
"Mathematical Treasures" article.
A search for related material yields a Babylonian tablet
reproduced in a Brazilian weblog on July 4, 2012:
In that weblog on the same day, July 4, 2012,
another post quotes at length my Diamond Theory page,
starting with the following image from that page—
That Brazilian post recommends use of geometry together
with Tarot and astrology. I do not concur with this
recommendation, but still appreciate the mention.
… Or: A Funny Thing Happened
on the Way to the Embedding
This journal on the morning of Saturday, Dec. 8, 2012:
Marilyn Monroe and her music coach in 1954,
from last night's online New York Times :
" 'We were very close to making love; I don’t remember
the stage we were at, but I would say half-dressed,'
Mr. Schaefer recalled. He added: 'And all of a sudden
for some reason, Marilyn got these vibrations, and
we went over to the window….' " more »
"Mr. Schaefer died on Saturday at 87 at his home in
Fort Lauderdale, Fla. ….
He [had] coached Monroe through 'Diamonds Are
a Girl’s Best Friend,' her signature number in the
1953 movie 'Gentlemen Prefer Blondes' (he arranged
the music as well)…."
Perhaps on Saturday she returned the favor.
… 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 —
"First steps"? The mathematics underlying such patterns
was presented 35 years earlier, in Diamond Theory.
* See Gombrich-Douat in this journal.
Part I
Embedding the Stone (March 23, 2012) —
The Meno Embedding
Part II
ReverbNation.com — Lawrence Class —
A physics quote relayed at Peter Woit's weblog today—
"The relation between 4D N=4 SYM and the 6D (2, 0) theory
is just like that between Darth Vader and the Emperor.
You see Darth Vader and you think 'Isn’t he just great?
How can anyone be greater than that? No way.'
Then you meet the Emperor."
Some related material from this weblog—
(See Big Apple and Columbia Film Theory)
The Meno Embedding:
Some related material from the Web—
See also uses of the word triality in mathematics. For instance…
A discussion of triality by Edward Witten—
Triality is in some sense the last of the exceptional isomorphisms,
and the role of triality for n = 6 thus makes it plausible that n = 6
is the maximum dimension for superconformal symmetry,
though I will not give a proof here.
— "Conformal Field Theory in Four and Six Dimensions"
and a discussion by Peter J. Cameron—
There are exactly two non-isomorphic ways
to partition the 4-subsets of a 9-set
into nine copies of AG( 3,2).
Both admit 2-transitive groups.
— "The Klein Quadric and Triality"
Exercise: Is Witten's triality related to Cameron's?
(For some historical background, see the triality link from above
and Cameron's Klein Correspondence and Triality.)
Cameron applies his triality to the pure geometry of a 9-set.
For a 9-set viewed in the context of physics, see A Beginning—
|
From MIT Commencement Day, 2011— A symbol related to Apollo, to nine, and to "nothing"— A minimalist favicon—
This miniature 3×3 square— |
Happy April 1.
"Imbedding the God character in a holy book's very detailed narrative
and building an entire culture around this narrative
seems by itself to confer a kind of existence on Him."
— John Allen Paulos in the philosophy column "The Stone,"
New York Times online, Oct. 24, 2010
A related post from Log24 later that year—
Sunday, November 28, 2010
|
"Next come the crown of thorns and Jesus' agonized crawl across the stage,
bearing the weight of his own crucifix. And at last, after making
yet another entrance, Mr. Nolan strikes the pose immortalized
in centuries of art, clad in a demure loincloth, arms held out to his sides,
one leg artfully bent in front of the other, head hanging down
in tortured exhaustion. Gently spotlighted, he rises from the stage
as if by magic, while a giant cross, pulsing with hot gold lights,
descends from above to meet him. Mr. Lloyd Webber's churning guitar rock
hits a climactic note, and the audience erupts in excited applause."
— Charles Isherwood, review of "Jesus Christ Superstar" in today's New York Times
Other remarks on embedding —
Part I
Review of a new book on linguistics, embedding, and a South American tribe—
"Imagine a linguist from Mars lands on Earth to survey the planet's languages…."
— Chronicle of Higher Education , March 20, 2012
Part II
The Embedding , by Ian Watson (Review of a 1973 novel from Shakespeare's birthday, 2006)
From tonight's online New York Times —
John McCracken, Sculptor of Geometric Forms, Dies at 76
McCracken died in Manhattan on Friday, April 8.
From Christopher Knight in tonight's online LA Times —
… the works embody perceptual and philosophical conundrums. The colored planks stand on the floor like sculptures….
McCracken was bedeviled by Stanley Kubrick's famously obscure science-fiction epic, "2001: A Space Odyssey," with its iconic image of an ancient monolith floating in outer space. The 1968 blockbuster was released two years after the artist made his first plank.
"At the time, some people thought I had designed the monolith or that it had been derived from my work," he told art critic Frances Colpitt of the coincidence in a 1998 interview.
Two photos of McCracken's 1967 Black Plank seem relevant—
November 28, 2010 (Click to enlarge) —
December 28, 2010 (Click to enlarge) —
Material that an artist might view as related, if only synchronistically—
Two posts in this journal on the dates the photos were taken—
The Embedding on November 28 and Dry Bones on December 28.
The photos are of an exhibition titled "There is nothing to see here" at the
National Gallery of Art, October 30, 2010-April 24, 2011 —
For related nihilism from the National Gallery, see "Pictures of Nothing" in this journal.
Some less nihilistic illustrations—
A photo by one of the artists whose work is displayed above beside McCracken's—
"Accentuate the Positive."
— Clint Eastwood
The New York Times Magazine this morning on a seminar on film theory at Columbia University—
"When the seminar reconvened after the break, Schamus said, 'Let’s dive into the Meno,' a dialogue in which Plato and Socrates consider virtue. 'The heart of it is the mathematical proof.' He rose from his seat and went to the whiteboard, where he drew figures and scribbled numbers as he worked through the geometry. 'You can only get the proof visually,' he concluded, stepping back and gazing at it. Plato may be skeptical about the category of the visual, he said, but 'you are confronted with a visual proof that gets you back to the idea embedded in visuality.'"
The Meno Embedding
See also Plato's Code and
Plato Thanks the Academy.
Hoax and Hype
Four Years Ago Today—
There is Plato's diamond—
and there is diamond theory—
… but there is no "Plato's Diamond Theory."
See, however, today's noon entry, "Plato's Code."
"You gotta be true to your code…" —Sinatra
"The present study is closely connected with a lecture* given by Prof. Ernst Cassirer at the Warburg Library whose subject was 'The Idea of the Beautiful in Plato's Dialogues'…. My investigation traces the historical destiny of the same concept…."
* See Cassirer's Eidos und Eidolon : Das Problem des Schönen und der Kunst in Platons Dialogen, in Vorträge der Bibliothek Warburg II, 1922/23 (pp. 1–27). Berlin and Leipzig, B.G. Teubner, 1924.
— Erwin Panofsky, Idea: A Concept in Art Theory, foreword to the first German edition, Hamburg, March 1924
On a figure from Plato's Meno—
The above figures illustrate Husserl's phrase "eidetic variation"—
a phrase based on Plato's use of eidos, a word
closely related to the word "idea" in Panofsky's title.
For remarks by Cassirer on the theory of groups, a part of
mathematics underlying the above diamond variations, see
his "The Concept of Group and the Theory of Perception."
Sketch of some further remarks—
The Waterfield question in the sketch above
is from his edition of Plato's Theaetetus
(Penguin Classics, 1987).
The "design theory" referred to in the sketch
is that of graphic design, which includes the design
of commercial logos. The Greek word logos
has more to do with mathematics and theology.
"If there is one thread of warning that runs
through this dialogue, from beginning to end,
it is that verbal formulations as such are
shot through with ambiguity."
— Rosemary Desjardins, The Rational Enterprise:
Logos in Plato's Theaetetus, SUNY Press, 1990
Related material—
Robert Stone,
"'That old Jew gave me this here.' Egan looked at the diamond. 'I ain't giving this to you, understand? The old man gave it to me for my boy. It's worth a whole lot of money– you can tell that just by looking– but it means something, I think. It's got a meaning, like.'
'Let's see,' Egan said, 'what would it mean?' He took hold of Pablo's hand cupping the stone and held his own hand under it. '"The jewel is in the lotus," perhaps that's what it means. The eternal in the temporal. The Boddhisattva declining nirvana out of compassion. Contemplating the ignorance of you and me, eh? That's a metaphor of our Buddhist friends.' Pablo's eyes glazed over. 'Holy shit,' he said. 'Santa Maria.' He stared at the diamond in his palm with passion." For further details, click on the diamond. |
Today's online Times on
the Saturday, Dec. 27,
death of an artist:
Mr. Wasserman wrote more than 75 scripts for television, the stage and the movies, including screenplays for 'The Vikings' (1958), a seafaring epic with Tony Curtis and Kirk Douglas, and 'A Walk With Love and Death' (1969), a John Huston film set in 14th-century Europe….
He feuded with… John Huston, who gave the lead female role in 'Walk' to his teenage daughter, Anjelica, against Mr. Wasserman's wishes. And he never attended ceremonies to receive the awards he won."
Accepting for Mr. Wasserman:
Mr. Graham's widow,
Anjelica Huston —
"Well…"
Frame Tales
From June 30 —
("Will this be on the test?")
Frame Tale One:
|
Summer Reading
Subtitle: |
Frame Tale Two:
Barry Sharples
on his version of the
Kaleidoscope Puzzle —
Background:
"A possible origin of this puzzle is found in a dialogue
between Socrates and Meno written by the Greek philosopher,
Plato, where a square is drawn inside a square such that
the blue square is twice the area of the yellow square.
Colouring the triangles produces a starting pattern
which is a one-diamond figure made up of four tiles
and there are 24 different possible arrangements."
"The king asked, in compensation for his toils during this strangest
of all the nights he had ever known, that the twenty-four riddle tales
told him by the specter, together with the story of the night itself,
should be made known over the whole earth
and remain eternally famous among men."
Frame Tale Three:
"The quad gospellers may own the targum
but any of the Zingari shoolerim may pick a peck
of kindlings yet from the sack of auld hensyne."
The following poem of Emily Dickinson is quoted here in memory of John Watson Foster Dulles, a scholar of Brazilian history who died at 95 on June 23. He was the eldest son of Secretary of State John Foster Dulles, a nephew of Director of Central Intelligence Allen Dulles, brother of Roman Catholic Cardinal Avery Dulles, and a grandson of Presbyterian minister Allen Macy Dulles, author of The True Church.
| I asked no other thing, No other was denied. I offered Being for it; The mighty merchant smiled. Brazil? He twirled a button, Without a glance my way: "But, madam, is there nothing else That we can show to-day?" |
"He twirled a button…."
The above figure
of Plato (see 3/22)
was suggested by
Lacan's diamond
(losange or poinçon)
as a symbol —
according to Frida Saal —
of Derrida's différance —
which is, in turn,
"that which enables and
results from Being itself"
— according to
Professor John Lye
“… he triumphed again with The Goldberg Variations. Mr Jay, assisted by Goldberg, a concentration camp survivor, is rehearsing a montage of biblical scenes in Jerusalem. It is inspired satire, laced with Jewish and Christian polemics, sparkling wit and dazzlingly simple effects. For Golgotha a stagehand brings on three crosses. ‘Just two,’ says Jay. ‘The boy is bringing his own.’ Tabori often claimed that the joke was the most perfect literary form.”
Log24 on
the date of
Tabori’s death:
Click on image
for variations
on the theme.
George Tabori
“BERLIN (AP) — Hungarian-born playwright and director George Tabori, a legend in Germany’s postwar theater world whose avant-garde works confronted anti-Semitism, died Monday [July 23, 2007]. He was 93.
Tabori, who as recently as three years ago dreamed of returning to stage to play the title role in Shakespeare’s ‘King Lear,’ died in his apartment near the theater, the Berliner Ensemble said Tuesday, noting that friends and family had accompanied him through his final days. No cause of death was given.
Born into a Jewish family in Budapest on May 24, 1914, Tabori fled in 1936 to London, where he started working for the British Broadcasting Corp., and became a British citizen. His father, and other members of his family, were killed at Auschwitz.
Tabori moved to Hollywood in the 1950s, where he worked as a scriptwriter, most notably co-writing the script for Alfred Hitchcock’s 1953 film, ‘I Confess.’
He moved to Germany in the 1970s and launched a theater career that spanned from acting to directing to writing. He used sharp wit and humor in his plays to examine the relationship between Germany and the Jews, as well as attack anti-Semitism.
Among his best-known works are ‘Mein Kampf,’ set in the Viennese hostel where Adolf Hitler lived from 1910-1913, and the ‘Goldberg Variations,’ both dark farces that poke fun at the Nazis.”
From Year of Jewish Culture:
“The year 2006 marks the 100th anniversary of the establishment of the Jewish Museum in Prague.”
From the related page Programme (October-December):
“Divadlo v Dlouhé
George Tabori: GOLDBERGOVSKÉ VARIACE / THE GOLDBERG VARIATIONS, 19 October, 7 p.m. A comedy on creation and martyrdom.”
|
From Log24 on the date of 
The above is from Variable Resolution 4–k Meshes: Concepts and Applications (pdf), by Luiz Velho and Jonas Gomes. See also Symmetry Framed |
|
Theme (Plato, Meno)
Click on “variations” above |
Theme
(Plato, Meno)
Click on picture for details.
“A diamond jubilance
beyond the fire,
That gives its power
to the wild-ringed eye”
— Wallace Stevens,
“The Owl in the Sarcophagus”
In 1946, Robert Graves published “King Jesus, an historical novel based on the theory and Graves’ own historical conjecture that Jesus was, in fact, the rightful heir to the Israelite throne… written while he was researching and developing his ideas for The White Goddess.”
In 1948, C. S. Lewis finished the first draft of The Lion, The Witch, and The Wardrobe, a novel in which one of the main characters is “the White Witch.”
In 1948, Robert Graves published The White Goddess.
In 1949, Robert Graves published Seven Days in New Crete [also titled Watch the North Wind Rise], “a novel about a social distopia in which Goddess worship is (once again?) the dominant religion.”
Lewis died on November 22, 1963, the day John F. Kennedy was killed.
Related material:
Log24, December 10, 2005
Graves died on December 7 (Pearl Harbor Day), 1985.
Related material:
Log24, December 7, 2005, and
Log24, December 11, 2005
Jesus died, some say, on April 7 in the year 30 A.D.
Related material:
Art Wars, April 7, 2003:
Geometry and Conceptual Art,Eight is a Gate, and
Plato’s Diamond
— Motto of
Plato’s Academy
“How much story do you want?”
— George Balanchine
The previous entry dealt with a transformation
of the diamond figure from Plato’s Meno
into a visual proof of the Pythagorean theorem:
For the mathematics dealing with
this sort of transformation, see
The Diamond 16 Puzzle and Diamond Theory.
For Jung’s 7/26 Birthday:
A Logocentric Meditation
Leftist academics are trying to pull a fast one again. An essay in the most prominent American mathematical publication tries to disguise a leftist attack on Christian theology as harmless philosophical woolgathering.
In a review of Vladimir Tasic’s Mathematics and the Roots of Postmodern Thought, the reviewer, Michael Harris, is being less than candid when he discusses Derrida’s use of “logocentrism”:
“Derrida uses the term ‘logocentrism’… as ‘the metaphysics of phonetic writing’….”
— Notices of the American Mathematical Society, August 2003, page 792
We find a rather different version of logocentrism in Tasic’s own Sept. 24, 2001, lecture “Poststructuralism and Deconstruction: A Mathematical History,” which is “an abridged version of some arguments” in Tasic’s book on mathematics and postmodernism:
“Derrida apparently also employs certain ideas of formalist mathematics in his critique of idealist metaphysics: for example, he is on record saying that ‘the effective progress of mathematical notation goes along with the deconstruction of metaphysics.’
Derrida’s position is rather subtle. I think it can be interpreted as a valiant sublation of two completely opposed schools in mathematical philosophy. For this reason it is not possible to reduce it to a readily available philosophy of mathematics. One could perhaps say that Derrida continues and critically reworks Heidegger’s attempt to ‘deconstruct’ traditional metaphysics, and that his method is more ‘mathematical’ than Heidegger’s because he has at his disposal the entire pseudo-mathematical tradition of structuralist thought. He has himself implied in an interview given to Julia Kristeva that mathematics could be used to challenge ‘logocentric theology,’ and hence it does not seem unreasonable to try looking for the mathematical roots of his philosophy.”
The unsuspecting reader would not know from Harris’s review that Derrida’s main concern is not mathematics, but theology. His ‘deconstruction of metaphysics’ is actually an attack on Christian theology.
From “Derrida and Deconstruction,” by David Arneson, a University of Manitoba professor and writer on literary theory:
“Logocentrism: ‘In the beginning was the word.’ Logocentrism is the belief that knowledge is rooted in a primeval language (now lost) given by God to humans. God (or some other transcendental signifier: the Idea, the Great Spirit, the Self, etc.) acts a foundation for all our thought, language and action. He is the truth whose manifestation is the world.”
Some further background, putting my July 23 entry on Lévi-Strauss and structuralism in the proper context:
Part I. The Roots of Structuralism
“Literary science had to have a firm theoretical basis…”
Part II. Structuralism/Poststructuralism
“Most [structuralists] insist, as Levi-Strauss does, that structures are universal, therefore timeless.”
Part III. Structuralism and
Jung’s Archetypes
Jung’s “theories, like those of Cassirer and Lévi-Strauss, command for myth a central cultural position, unassailable by reductive intellectual methods or procedures.”
And so we are back to logocentrism, with the Logos — God in the form of story, myth, or archetype — in the “central cultural position.”
What does all this have to do with mathematics? See
“the Klein group (much beloved of Structuralists)”
Another Michael Harris Essay, Note 47 –
“From Krauss’s article I learned that the Klein group is also called the Piaget group.”
and Jung on Quaternity:
Beyond the Fringe –
“…there is no denying the fact that [analytical] psychology, like an illegitimate child of the spirit,
leads an esoteric, special existence beyond the fringe of what is generally acknowledged to be the academic world.”
What attitude should mathematicians have towards all this?
Towards postmodern French
atheist literary/art theorists –
Mathematicians should adopt the attitude toward “the demimonde of chic academic theorizing” expressed in Roger Kimball’s essay, Feeling Sorry for Rosalind Krauss.
Towards logocentric German
Christian literary/art theorists –
Mathematicians should, of course, adopt a posture of humble respect, tugging their forelocks and admitting their ignorance of Christian theology. They should then, if sincere in their desire to honestly learn something about logocentric philosophy, begin by consulting the website
The Quest for the Fiction of an Absolute.
For a better known, if similarly disrespected, “illegitimate child of the spirit,” see my July 22 entry.
Elementary,
My Dear Gropius
“What is space, how can it be understood and given a form?”
— Walter Gropius
    |
Stoicheia,” Elements, is the title of
Euclid’s treatise on geometry.
Stoicheia is apparently also related to a Greek verb meaning “march” or “walk.”
According to a website on St. Paul’s phrase “ta stoicheia tou kosmou,” which might be translated
“… the verbal form of the root stoicheo was used to mean, ‘to be in a line,’ ‘to march in rank and file.’ … The general meaning of the noun form (stoicheion) was ‘what belongs to a series.’ “
As noted in my previous entry, St. Paul used a form of stoicheo to say “let us also walk (stoichomen) by the Spirit.” (Galatians 5:25) The lunatic ravings* of Saul of Tarsus aside, the concepts of walking, of a spirit, and of elements may be combined if we imagine the ghost of Gropius strolling with the ghosts of Plato, Aristotle, and Euclid, and posing his question about space. Their reply might be along the following lines:
Combining stoicheia with a peripatetic peripateia (i.e., Aristotelian plot twist), we have the following diagram of Aristotle’s four stoicheia (elements),
which in turn is related, by the “Plato’s diamond” figure in the monograph Diamond Theory, to the Stoicheia, or Elements, of Euclid.
Quod erat demonstrandum.
* A phrase in memory of the Paulist Norman J. O’Connor, the “jazz priest” who died on St. Peter’s day, Sunday, June 29, 2003. Paulists are not, of course, entirely mad; the classic The Other Side of Silence: A Guide to Christian Meditation, by the Episcopal priest Morton Kelsey, was published by the Paulist Press.
Its cover (above), a different version of the four-elements theme, emphasizes the important Jungian concept of quaternity. Jung is perhaps the best guide to the bizarre world of Christian symbolism. It is perhaps ironic, although just, that the Paulist Fathers should distribute a picture of “ta stoicheia tou kosmou,” the concept that St. Paul himself railed against.
The above book by Kelsey should not be confused with another The Other Side of Silence, a work on gay history, although confusion would be understandable in light of recent ecclesiastical revelations.
Let us pray that if there is a heaven, Father O’Connor encounters there his fellow music enthusiast Cole Porter rather than the obnoxious Saul of Tarsus.
Orwell’s question, according to
an admirer of leftist Noam Chomsky:
“When so much of the BS is right out in the open,
why is it that we know so little about it?
Why don’t we see what’s right in front of our eyes?”
 Oscar |
Lying, Truth-Telling, and the Social Order |
 Michael Moore |
“First of all, I’d like to thank the Academy….”
— Quotation attributed to Plato
The New Yorker of March 31, 2003, discusses leftist academic Noam Chomsky. The online edition provides a web page listing pro-Chomsky links.
Chomsky’s influence is based in part on the popularity of his half-baked theories on linguistics, starting in the 1950’s with “deep structure” and “transformational,” or “generative,” grammar.
Chomsky has abandoned many of his previous ideas and currently touts what he calls The Minimalist Program.
For some background on Chomsky’s recent linguistic notions, see the expository essay “Syntactic Theory,” by Elly van Gelderen of the Arizona State University English Department. Van Gelderen lists her leftist political agenda on her “Other Interests” page. Her department may serve as an example of how leftists have converted many English departments in American universities to propaganda factories.
Some attacks on Chomsky’s scholarship:
Forty-four Reasons Why the Chomskians Are Mistaken
Chomsky’s (Mis)Understanding of Human Thinking
Anatomy of a Revolution… Chomsky in 1962
…Linguistic Theory: The Rationality of Noam Chomsky
Some attacks on Chomsky’s propaganda:
Destructive Generation excerpt
Partners in Hate: Noam Chomsky and the Holocaust Deniers
Chomsky and Plato’s Diamond
Like another purveyor of leftist nonsense, Jacques Derrida, Chomsky is fond of citing Plato as a precedent. In particular, what Chomsky calls “Plato’s problem” is discussed in Plato’s Meno. For a look at the diamond figure that plays a central role in that dialogue, see Diamond Theory. For an excellent overview of related material in Plato, see Theory of Forms.
ART WARS:
From The New Yorker, issue of March 17, 2003, Clive James on Aldous Huxley:
“The Perennial Philosophy, his 1945 book compounding all the positive thoughts of West and East into a tutti-frutti of moral uplift, was the equivalent, in its day, of It Takes a Village: there was nothing in it to object to, and that, of course, was the objection.”
For a cultural artifact that is less questionably perennial, see Huxley’s story “Young Archimedes.”
Plato, Pythagoras, and
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From the New Yorker Contributors page for St. Patrick’s Day, 2003:
“Clive James (Books, p. 143) has a new collection, As of This Writing: The Essential Essays, 1968-2002, which will be published in June.”
See also my entry “The Boys from Uruguay” and the later entry “Lichtung!” on the Deutsche Schule Montevideo in Uruguay.
Birthdate of Hermann Weyl
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Result of a Google search.
Category: Science > Math > Algebra > Group Theory
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Weyl, H.: Symmetry. |
Sponsored Link Symmetry Puzzle |
Quotation from Weyl’s Symmetry:
“Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect.”
In honor of Princeton University, of Sylvia Nasar (see entries of Nov, 6), of the Presbyterian Church (see entry of Nov. 8), and of Professor Weyl (whose work partly inspired the website Diamond Theory), this site’s background music is now Pink Floyd’s
You Crazy Diamond.” |
Updates of Friday, November 15, 2002:
In order to clarify the meaning of “Shine” and “Crazy” in the above, consult the following —
To accompany this detailed exegesis of Pink Floyd, click here for a reading by Marlon Brando.
For a related educational experience, see pages 126-127 of The Book of Sequels, by Henry Beard, Christopher Cerf, Sarah Durkee, and Sean Kelly (Random House paperback, 1990).
Speaking of sequels, be on the lookout for Annie Dillard’s sequel to Teaching a Stone to Talk, titled Teaching a Brick to Sing.
Evariste Galois and
The Rock That Changed Things
An article in the current New York Review of Books (dated Sept. 26) on Ursula K. Le Guin prompted me to search the Web this evening for information on a short story of hers I remembered liking. I found the following in the journal of mathematician Peter Berman:
I agree that the story is elegant (from a mathematician, a high compliment), so searched Berman’s pages further, finding this:
between The French Mathematician (a novel about Galois) and Harry Potter and the Sorcerer’s Stone.
My own version of the Philosopher’s Stone (the phrase used instead of “Sorcerer’s Stone” in the British editions of Harry Potter) appears in my profile picture at top left; see also the picture of Plato’s diamond figure in my main math website. The mathematics of finite (or “Galois”) fields plays a role in the underlying theory of this figure’s hidden symmetries. Since the perception of color plays a large role in the Le Guin story and since my version of Plato’s diamond is obtained by coloring Plato’s version, this particular “rock that changes things” might, I hope, inspire Berman to extend his table to include Le Guin’s tale as well.
Even the mosaic theme is appropriate, this being the holiest of the Mosaic holy days.
Dr. Berman, G’mar Chatimah Tova.
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