Log24

Saturday, January 9, 2021

The Jewel and the Stone

Filed under: General — m759 @ 2:15 PM

Update of 8:09 PM ET on Saturday, Jan. 9, 2021 —

Plato’s Diamond.

Monday, September 14, 2020

Socrates in the Marketplace

Filed under: General — Tags: — m759 @ 7:39 AM

Plato's diamond in Jowett's version of the Meno dialogue

Diamond Matrix slide template at presentationgo.com

“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.”

Tuesday, April 14, 2020

Invariance

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

Note the resemblance to Plato’s Diamond.

Click the Pritchard passage above for an interactive version.

Monday, July 15, 2019

Possibility and Necessity: Kierkegaard Meets Nietzsche

Filed under: General — Tags: — m759 @ 7:29 AM

The previous post’s search for Turing + Dyson yielded a
quotation from Kierkegaard on possibility and necessity.
Further details —

See also . . .

Nietzsche, 'law in becoming' and 'play in necessity'

Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

Monday, May 13, 2019

“The Eyes of Orson Welles”…

Filed under: General — m759 @ 7:49 PM

is a TCM special at 8 PM ET this evening.

A snow-globe phrase from April 28 —

Bauble, Babel . . . Bubble —

Images including Plato's diamond on a tombstone

The "bubble" cited above —

For more metaphysical accounting, see
The Church of Synchronology.

Friday, January 11, 2019

Permutations at Oslo

Filed under: General — Tags: , , — m759 @ 8:45 PM

Webpage at Oslo of Josefine Lyche, 'Plato's Diamond'

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).

Sunday, October 28, 2018

Commonwealth Tales, or “Lost in Physics”

Filed under: General — m759 @ 11:00 PM

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:

Plato's diamond in Jowett's version of the Meno dialogue

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."

Saturday, April 14, 2018

Immanentizing the Transcendence

Filed under: General — m759 @ 10:15 AM

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:

Plato's diamond in Jowett's version of the Meno dialogue

Monday, June 19, 2017

Final Club

Filed under: General — m759 @ 11:20 AM

Today’s New York Times  on a character in a 1978 film —

“Cluelessly upbeat and charmingly idiotic.”

Related material from a post Saturday —

Plato's Formula: A Hollywood version of Plato's diamond from the Meno dialogue

Director with Oscar

Coda —

See as well this  journal on the above date — Sept. 24, 2015.

Thursday, June 15, 2017

Early Personal Computer

Filed under: General — m759 @ 10:01 AM

(The title is from yesterday morning's Graphical Interfaces.)

Plato's diamond in Jowett's version of the Meno dialogue

Wednesday, June 14, 2017

Graphical Interfaces

Filed under: General — Tags: — m759 @ 10:52 AM

Thacker reportedly died on Monday, June 12, 2017.

This journal on that date —

Images including Plato's diamond on a tombstone

Thacker retired from Microsoft in February.

Monday, May 15, 2017

Appropriation at MoMA

Filed under: General,Geometry — m759 @ 1:14 PM

For example, Plato's diamond as an object to be transformed —

Plato's diamond in Jowett's version of the Meno dialogue

Versions of the transformed object —

See also The 4×4 Relativity Problem in this journal.

Tuesday, September 27, 2016

Chomsky and Lévi-Strauss in China

Filed under: General,Geometry — Tags: — m759 @ 7:31 AM

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 —

The larger cases —

The diamond theorem

Friday, July 29, 2016

Illustration

Filed under: General — m759 @ 11:09 AM

Jantz— The Mothers in Faust

Plato's Diamond embedded in The Matrix

See also Embedding the Stone (March 23, 2012).

Monday, June 15, 2015

Slow Art

Filed under: General — Tags: — m759 @ 2:03 PM

Slowness is sometimes in the eye of the beholder.

See this journal on Slow Art Day 2015.

Related material: Epistemic States in this journal.

Saturday, April 11, 2015

The Starbird Manifesto

"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 —

Logo for 'Elements of Finite Geometry'.

Tuesday, September 16, 2014

Where the Joints Are

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

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 :

Image-- Plato's diamond and a modern version from finite geometry

Related material: Phaedrus on Kant as a diamond cutter
in Zen and the Art of Motorcycle Maintenance .

Tuesday, July 8, 2014

Toward Freedom

Filed under: General — m759 @ 12:00 PM

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,
The stone is still a stone,
though it had once resisted
The weight of Africa,
The hammer-blows of time
That wear to bits of rubble
The mountain and the pebble–
But not this coldest one.

Now, you intelligence
So late dredged up from dark
Upon whose smoky walls
Bison took fumbling form
Or flint was edged on flint–
Now, careful arriviste,
Delineate at will
Incisions in the ice.

Be serious, because
The stone may have contempt
For too-familiar hands,
And because all you do
Loses or gains by this:
Respect the adversary,
Meet it with tools refined,
And thereby set your price.

Be hard of heart, because
the stone must leave your hand.
Although you liberate
Pure and expensive fires
Fit to enamor Shebas,
Keep your desire apart.
Love only what you do,
And not what you have done.

Be proud, when you have set
The final spoke of flame
In that prismatic wheel,
And nothing’s left this day
Except to see the sun
Shine on the false and the true,
And know that Africa
will yield you more to do.

Wednesday, January 16, 2013

Treasure Hunt

Filed under: General,Geometry — Tags: — m759 @ 3:17 PM

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—

IMAGE- Plato's Diamond

That Brazilian post recommends use of geometry together
with Tarot and astrology. I do not concur with this 
recommendation, but still appreciate the mention.

Thursday, December 13, 2012

Vibrations

Filed under: General,Geometry — m759 @ 11:18 AM

 Or:  A Funny Thing Happened
     on the Way to the Embedding

This journal on the morning of Saturday, Dec. 8, 2012:

Plato's Diamond embedded in The Matrix

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.

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

Plato's Diamond embedded in The Matrix

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.

Thursday, December 6, 2012

The Embedding

Filed under: General — m759 @ 6:29 PM

Part I

Embedding the Stone (March 23, 2012) —

The Meno Embedding

Plato's Diamond embedded in The Matrix

Part II

ReverbNation.com — Lawrence Class —

Sunday, April 1, 2012

The Palpatine Dimension

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

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."

— Arkani-Hamed

Some related material from this  weblog—

(See Big Apple and Columbia Film Theory)

http://www.log24.com/log/pix12/120108-Space_Time_Penrose_Hawking.jpg

The Meno Embedding:

Plato's Diamond embedded in The Matrix

Some related material from the Web—

IMAGE- The Penrose diamond and the Klein quadric

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—

IMAGE- Generic 3x3 square as favicon

This miniature 3×3 square— http://log24.com/log/pix11A/110518-3x3favicon.ico — may, if one likes,
be viewed as the "nothing" present at the Creation. 
See Feb. 19, 2011, and Jim Holt on physics.

Happy April 1.

Friday, March 23, 2012

Embedding the Stone

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

"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

The Embedding

 — m759 @ 6:00 AM

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

Plato's Diamond embedded in The Matrix

See also Plato's Code and
 Plato Thanks the Academy.

"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)

Sunday, April 10, 2011

Bedeviled

Filed under: General — Tags: — m759 @ 10:30 PM

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)

http://www.log24.com/log/pix11/110410-McCrackenPlank1967400w.jpg

December 28, 2010 (Click to enlarge)

http://www.log24.com/log/pix11/110410-McCracken-NatGallery-NothingToSeeHere-400w.jpg

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 —

Click to enlarge.

http://www.log24.com/log/pix11/110410-NothingToSee-400w.jpg

For related nihilism from the National Gallery, see "Pictures of Nothing" in this journal.

Some less nihilistic illustrations—

The Meno  Embedding

Plato's Diamond embedded in The Matrix

A photo by one of the artists whose work is displayed above beside McCracken's—

http://www.log24.com/log/pix11/110410-Sugimoto-AndoChurch.jpg

"Accentuate the Positive."
 — Clint Eastwood

Monday, November 29, 2010

On Time

Filed under: General — m759 @ 5:45 AM

and under budget —

The Tiffany Case

http://www.log24.com/log/pix10B/101129-TheTiffanyCase.jpg

See also Sunday morning’s pictures

Plato's Diamond embedded in The Matrix

The sound of singing grows louder.

Sunday, November 28, 2010

The Embedding

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

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

Plato's Diamond embedded in The Matrix

See also Plato's Code and
 Plato Thanks the Academy.

Thursday, July 1, 2010

Darkness at Seven

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

Hoax and Hype 
Four Years Ago Today—

Image-- Fanfiction-- Harry Potter and Plato's Diamond

There is Plato's diamond—

Image-- Plato's Diamond

and there is diamond theory

Google Search result for '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

Saturday, June 26, 2010

Plato’s Logos

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

“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

IMAGE- Plato's diamond and finite geometry

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—

http://www.log24.com/log/pix10A/100626-Theories.jpg

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—

(Click to enlarge.)

http://www.log24.com/log/pix10A/100626-CrossOnSocratesSm.gif

Tuesday, June 8, 2010

From Plato to Finite Geometry

Filed under: General,Geometry — m759 @ 12:30 PM

A supplement to yesterday's post on variation of an eidos

Image-- Plato's diamond and a modern version from finite geometry

Enlarge.

Monday, December 29, 2008

Monday December 29, 2008

Filed under: General — Tags: — m759 @ 12:21 PM
The Gift
 

Plato's Diamond

Robert Stone,
A Flag for Sunrise:

"'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.

 

Related narratives:

Today's online Times on
the Saturday, Dec. 27,
death of an artist:

Robert Graham obituary, NY Times, 12/29/08

"Dale Wasserman… the playwright responsible for two Broadway hits of the 1960s, 'One Flew Over the Cuckoo’s Nest' and 'Man of La Mancha,' died on Sunday [December 21, 2008] at his home in Paradise Valley, Ariz., near Phoenix….

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

Anjelica Huston and Jack Nicholson

"Well…"

Monday, November 10, 2008

Monday November 10, 2008

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

Frame Tales

From June 30

("Will this be on the test?")

Frame Tale One:

Summer Reading

The King and the Corpse: Tales of the Soul's Conquest of Evil

Subtitle:
Tales of the Soul's
Conquest of Evil

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.

Plato's Diamond

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."

Twenty-four Variations on a Theme of Plato

The King and the Corpse  —

"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:

Finnegans Wake

"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."

Saturday, June 28, 2008

Saturday June 28, 2008

Filed under: General — Tags: — m759 @ 12:00 PM
The God Factor

NY Lottery June 23, 2008: Mid-day 322, Evening 000


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…."

Plato's diamond figure from the 'Meno'

The above figure
of Plato
(see 3/22)
was suggested by
Lacan's diamond
Lacan's lozenge - said by some to symbolize Derrida's 'differance'
(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

I prefer Plato and Dulles
to Lacan and Lye.
 

Saturday, July 28, 2007

Saturday July 28, 2007

Filed under: General,Geometry — m759 @ 6:15 AM
The Third Cross


The Guardian, July 26,
on the late playwright
 George Tabori:

“… 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.”

Related material:

Log24 on
the date of
Tabori’s death
:

Harry Potter and Plato's Diamond
 
Click on image
for variations
 on the theme.

Wednesday, July 25, 2007

Wednesday July 25, 2007

Filed under: General,Geometry — m759 @ 9:00 AM
The Comedy of
George Tabori

George Tabori

From AP “Obituaries in the News”–
Filed with The New York Times
at 11:16 p.m. ET July 24, 2007–

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.”

Variations on
Birth and Death

From Log24 on the date of
the Prague production of the
Tabori “Goldberg Variations,”
an illustration in honor of
Sir Thomas Browne, who
was born, and died,
on that date:

Laves tiling

The above is from
Variable Resolution 4–k Meshes:
Concepts and Applications
(pdf),
by Luiz Velho and Jonas Gomes.

See also Symmetry Framed
and The Garden of Cyrus.

Variations on
the Afterlife

 From Log24
on the date of
Tabori’s death:

Theme

(Plato, Meno)

Plato's Diamond colored

and Variations:

Diamond Theory cover, 1976

Click on “variations” above
for some material on
the “Goldberg Variations”
of Johann Sebastian Bach.

 

Monday, July 23, 2007

Monday July 23, 2007

Filed under: General,Geometry — Tags: — m759 @ 7:59 AM
 
Today’s Birthday:
Daniel Radcliffe
(“Harry Potter”)

Harry Potter and the Philosopher's Stone DVD

Theme

(Plato, Meno)

Plato's Diamond colored

and Variations:

Diamond Theory cover, 1976
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”

Friday, December 16, 2005

Friday December 16, 2005

Filed under: General,Geometry — m759 @ 2:00 PM
Jesus vs. the Goddess:
A Brief Chronology

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

The image “http://www.log24.com/log/pix05B/051216-PlatoDiamond.gif” cannot be displayed, because it contains errors.

Plato’s Diamond

The image “http://www.log24.com/log/pix05B/051216-Motto.jpg” cannot be displayed, because it contains errors.

— Motto of
Plato’s Academy

“Plato is wary of all forms of rapture other than reason’s. He is most deeply leery of, because himself so susceptible to, the literary imagination. He speaks of it as a kind of holy madness or intoxication and goes on to link it to Eros, another derangement that joins us, but very dangerously, with the gods.”
 
Rebecca Goldstein in
    The New York Times,
    three years ago today
    (December 16, 2002) 
 
“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

“How much story do you want?”
— George Balanchine

Thursday, May 26, 2005

Thursday May 26, 2005

Filed under: General,Geometry — m759 @ 4:00 AM
The Changing

The previous entry dealt with a transformation
of the diamond figure from Plato’s Meno
into a visual proof of the Pythagorean theorem:

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

Here is a transformation of Plato’s diamond
into the “gyronny” pattern of heraldry:

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

The image “http://www.log24.com/theory/images/DiamondChanging2.jpg” cannot be displayed, because it contains errors.

For the mathematics dealing with
this sort of transformation, see
The Diamond 16 Puzzle and Diamond Theory.

Friday, July 25, 2003

Friday July 25, 2003

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

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

Plato’s Diamond,

Rosalind Krauss on Art –

“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.

Saturday, July 5, 2003

Saturday July 5, 2003

Filed under: General,Geometry — m759 @ 7:21 PM

Elementary,
My Dear Gropius

“What is space, how can it be understood and given a form?”
— Walter Gropius

Stoicheia:

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 Elements of the Cosmos,

“… 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.

Monday, March 24, 2003

Monday March 24, 2003

Filed under: General — m759 @ 12:52 PM

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
Deep Chomsky:
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:

The Emperor’s New Linguistics

The New Grammarians’ Funeral

Beyond Chomsky

Could Chomsky Be Wrong? 

Forty-four Reasons Why the Chomskians Are Mistaken

Call for Papers, Chomsky 2003

Chomsky’s (Mis)Understanding of Human Thinking

Anatomy of a Revolution… Chomsky in 1962

…Linguistic Theory: The Rationality of Noam Chomsky

A Bibliography

Some attacks on Chomsky’s propaganda:

LeftWatch.com Chomsky page

Destructive Generation excerpt

The Sick Mind of Noam Chomsky

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.

Thursday, March 13, 2003

Thursday March 13, 2003

Filed under: General — m759 @ 4:44 PM

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
the diamond figure

Plato’s Diamond in the Meno
Plato as a precursor of Gerard Manley Hopkins’s “immortal diamond.” An illustration shows the ur-diamond figure.

Plato’s Diamond Revisited
Ivars Peterson’s Nov. 27, 2000 column “Square of the Hypotenuse” which discusses the diamond figure as used by Pythagoras (perhaps) and Plato. Other references to the use of Plato’s diamond in the proof of the Pythagorean theorem:

Huxley:

“… and he proceeded to prove the theorem of Pythagoras — not in Euclid’s way, but by the simpler and more satisfying method which was, in all probability, employed by Pythagoras himself….
‘You see,’ he said, ‘it seemed to me so beautiful….’
I nodded. ‘Yes, it’s very beautiful,’ I said — ‘it’s very beautiful indeed.'”
— Aldous Huxley, “Young Archimedes,” in Collected Short Stories, Harper, 1957, pp. 246 – 247

Heath:

Sir Thomas L. Heath, in his commentary on Euclid I.47, asks how Pythagoreans discovered the Pythagorean theorem and the irrationality of the diagonal of a unit square. His answer? Plato’s diamond.
(See Heath, Sir Thomas Little (1861-1940),
The thirteen books of Euclid’s Elements translated from the text of Heiberg with introduction and commentary. Three volumes. University Press, Cambridge, 1908. Second edition: University Press, Cambridge, 1925. Reprint: Dover Publications, New York, 1956.

Other sites on the alleged
“diamond” proof of Pythagoras

Colorful diagrams at Cut-the-Knot

Illustrated legend of the diamond proof

Babylonian version of the diamond proof

For further details of Huxley’s story, see

The Practice of Mathematics,

Part I, by Robert P. Langlands, from a lecture series at the Institute for Advanced Study, Princeton.

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.

Saturday, November 9, 2002

Saturday November 9, 2002

Filed under: General,Geometry — m759 @ 4:44 AM

Birthdate of Hermann Weyl

Weyl


Plato’s Diamond

Result of a Google search.

Category:  Science > Math > Algebra > Group Theory 

Weyl, H.: Symmetry.
Description of the book Symmetry by Weyl, H., published by Princeton University Press. pup.princeton.edu/titles/
865.html – 7k – Nov. 8, 2002

Sponsored Link

Symmetry Puzzle
New free online puzzle illustrates
the mathematics of symmetry.
m759.freeservers.com/puzzle.
html

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


“Shine On, 
   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 Talktitled Teaching a Brick to Sing.

Sunday, September 15, 2002

Sunday September 15, 2002

Filed under: General,Geometry — m759 @ 11:07 PM

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:

  • A Fisherman of the Inland Sea, Ursula K. Le Guin, 1994:
    A book of short stories. Good, entertaining. I especially liked “The Rock That Changed Things.” This story is set in a highly stratified society, one split between elite and enslaved populations. In this community, the most important art form is a type of mosaic made from rocks, whose patterns are read and interpreted by scholars from the elite group. The main character is a slave woman who discovers new patterns in the mosaics. The story is slightly over-the-top but elegant all the same.

I agree that the story is elegant (from a mathematician, a high compliment), so searched Berman’s pages further, finding this:

A table of parallels

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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