Tuesday, July 31, 2012
"The universe, then, is less intimation
than cipher: a mask rather than a revelation
in the romantic sense. Does love meet with love?
Do we receive but what we give? The answer is
surely a paradox, the paradox that there are
Platonic universals beyond, but that the glass
is too dark to see them. Is there a light beyond
the glass, or is it a mirror only to the self?
The Platonic cave is even darker than Plato
made it, for it introduces the echo, and so
leaves us back in the world of men, which does
not carry total meaning, is just
a story of events."
Comments Off on Logo
Monday, July 30, 2012
Related material:
Frank J. Prial on the late singer Tony Martin—
— and, on Jan. 1, 2005, on beverage marketing:
Every picture tells a story.
Happy birthday to Hilary Swank.
Comments Off on Logos
(Continued)
A Necessary Truth—
James Singer, "A Theorem in Finite Projective Geometry
and Some Applications to Number Theory," Transactions
of the American Mathematical Society 43 (1938), 377-385.
A Contingent Truth—
Singer Tony Martin reportedly died Friday evening, July 27, 2012.
In his memory, some references to a "Singer 7-Cycle."
See also this journal 7 years prior to Martin's death.
Comments Off on Geometry and Death
(Continued)
Eric M. Friedlander, President of the
American Mathematical Society (AMS),
in the March 2011 AMS Notices —
"I think the best thing the AMS does by far is the Notices .
It could easily be in all doctors’ and dentists’ offices."
Notices : "Really?"
Friedlander: "It could be."
Related material from this journal:
“Is it safe?"
— Annals of Art Education:
Geometry and Death
Comments Off on Something to Read
"There is no question about what arithmetic is for
or why it is supported. Society cannot proceed
without it. Addition, subtraction, multiplication,
division, percentages: though not all citizens can
deal fluently with all of them, we make the
assumption that they can when necessary.
Those who cannot are sometimes at a disadvantage.
Algebra, though, is another matter."
— Underwood Dudley in the Notices of the
American Mathematical Society, May 2010:
"What Is Mathematics For?"
A less nuanced remark from the American
Mathematical Society (AMS) today—
"The answer to the recent Op-Ed piece
in The New York Times entitled
'Is Algebra Necessary?'
is resoundingly YES!"
— Eric Friedlander, AMS president
* A review of philosophical terminology—
"The distinction between necessary truth
and contingent truth is a version of Leibniz 's
distinction between truths of reason and truths
of fact. A necessary truth must be true and
could not be false, whatever way the world is.
It is true in itself. A contingent truth, on the other
hand, depends upon the empirical world and might
have been false had the world been different."
— The Blackwell Dictionary of Western Philosophy
Comments Off on Unnecessary* Truth?
Sunday, July 29, 2012
(Continued)
The three parts of the figure in today's earlier post "Defining Form"—
— share the same vector-space structure:
0 |
c |
d |
c + d |
a |
a + c |
a + d |
a + c + d |
b |
b + c |
b + d |
b + c + d |
a + b |
a + b + c |
a + b + d |
a + b +
c + d |
(This vector-space a b c d diagram is from Chapter 11 of
Sphere Packings, Lattices and Groups , by John Horton
Conway and N. J. A. Sloane, first published by Springer
in 1988.)
The fact that any 4×4 array embodies such a structure was implicit in
the diamond theorem (February 1979). Any 4×4 array, regarded as
a model of the finite geometry AG(4, 2), may be called a Galois tesseract.
(So called because of the Galois geometry involved, and because the
16 cells of a 4×4 array with opposite edges identified have the same
adjacency pattern as the 16 vertices of a tesseract (see, for instance,
Coxeter's 1950 "Self-Dual Configurations and Regular Graphs," figures
5 and 6).)
A 1982 discussion of a more abstract form of AG(4, 2):
Source:
The above 1982 remarks by Brouwer may or may not have influenced
the drawing of the above 1988 Conway-Sloane diagram.
Comments Off on The Galois Tesseract
Background: Square-Triangle Theorem.
For a more literary approach, see "Defining Form" in this journal
and a bibliography from the University of Zaragoza.
Comments Off on Defining Form
Saturday, July 28, 2012
On painter Karl Benjamin of Claremont, California,
who reportedly died on Thursday—
He played them music
and everything was concentrated and timeless
and all were artists 'til the bell rang.
Another remark from Claremont—
"'Once upon a time' used to be a gateway to
a land that was inviting precisely because
it was timeless, like the stories it introduced
and their ageless lessons about the human condition."
– Dorothea Israel Wolfson,
Claremont Review of Books, Summer 2006
Benjamin was a professor emeritus at Pomona College.
Comments Off on Claremont Review
The end of the beginning of the London Games
suggests other games —
Shadows (July 14) —
A Game of Shadows — "You know my methods."
Related religious material —
The Feast of Saint Jude, 2011.
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Friday, July 27, 2012
Quoted in some remarks yesterday on geometry—
From posts linked to this morning—
The Source—
Comments Off on Olympics Special
Wikipedia on a magical ring—
Background— The Ring and the Stone, a story linked to here Wednesday.
"By then he was familiar with the work of the Vienna Actionists….
He once said that he had his first taste of the movement
when he heard the screams of his mother’s dental patients
from her office next door to the family’s apartment."
— Obituary of a Viennese artist who reportedly died Wednesday
"Is it safe?"
Comments Off on Raiders of the Lost Ring
Thursday, July 26, 2012
(Mathematics and Narrative, continued)
Narrative—
The Ring and The Stone from yesterday's post, and…
"In Medieval Jewish, Christian and Islamic legends,
the Seal of Solomon was a magical signet ring
said to have been possessed by King Solomon…."
— Wikipedia article, Seal of Solomon
Mathematics—
A fact related to the mathematical
"Solomon's seal" described above by Bell:
The reference to Edge is as follows—
[3] Edge, W. L., Quadrics over GF(2) and
their relevance for the cubic surface group,
Canadian J. Maths. 11 (1959) ….
(This reference relates Hirschfeld's remarks
quoted above to the 64-point affine space
illustrated below (via the associated
63-point projective space PG (5, 2)).
As for the narrative's Stone…
Comments Off on Solomon’s Seal
Wednesday, July 25, 2012
Tuesday, July 24, 2012
(Continued from July 22)
Manhattan, July 22, 2012 — "Once upon a time, in a quiet corner
of the Middle East, there lived a shepherd named Gyges. Despite
the hardships in his life Gyges was relatively satisfied with his meager
existence. Then, one day, he found a ring buried in a nearby cave."
Read more…
Comments Off on Biograph
"I want you on the Swansea lathe today."
— Boss of the Christ figure in "The Machinist" (2004)
Related material in this journal—
Dylan Thomas and Modern Times—
Comments Off on Joker
IMDb trivia page on "The Machinist" (2004)—
"The time of 1:30 AM is significant throughout the movie.
Trevor often notices something out of the ordinary at this time.
During the 1 hour 30 minute mark in the movie,
the major plot twist is revealed."
As for the date 1/30… See Tolkien on telepathy.
(Backstory: The Gospel According to Father Hardon )
Comments Off on Time and Date
(Continued)
Part I:
Christian Bale as a Spanish Christ-parody in "The Machinist" (2004)
Part II:
"The expression 'the devil is in the details'
is turned on its head in the exhibit 'The Sacred Made Real'
at Washington's National Gallery of Art…."
— Catholic News Service, 2010
Part III:
Tonight's New York Times obituaries
Part IV:
"My goodness, there must be a hole in this glass."
— Maria in "The Machinist" (2004)
Comments Off on A Reappearing Number
Monday, July 23, 2012
Comments Off on In Memoriam
For those who like puzzles—
What film's page at IMDb recommends
the following "also liked" choices?
The Interpreter (2005), Identity (2003), The Game (1997),
The Ghost Writer (2010), The Machinist (2004), The Number 23 (2007)
A similar puzzle: Related Books
Comments Off on 23 Puzzle
Comments Off on Manchurian Symphony
Sunday, July 22, 2012
For art collector Herbert Vogel,
who reportedly died today
Philip Kennicott in The Washington Post , July 3, 2009—
"The Vogels help allay deep cultural fears
within the art world— fears that art is elitist,
or some kind of confidence game,
or not a serious endeavor (a fear that has
dogged art since at least the time of Plato)."
Some related material from finitegeometry.org,
offered without comment—
Comments Off on Art Wars
"One ring to bring them all…"
— J. R. R. Tolkien, Catholic author
Today in History, July 22, by The Associated Press—
"In 1934, bank robber John Dillinger was shot to death
by federal agents outside Chicago's Biograph Theater,
where he had just seen the Clark Gable movie
'Manhattan Melodrama.'"
From a Manhattan Melodrama—
"Follow the Ring"
Piatigorsky died on Sunday, July 15. Notes in this journal from that date—
Backstory—
Comments Off on Biograph
Saturday, July 21, 2012
Colin Moynihan on the late Alexander Cockburn—
"His attachment to left-wing journalism— and controversy—
was forged very early on. His father, Claud Cockburn, while
covering the Spanish Civil War for The Daily Worker , joined
the Republican forces fighting the rebellion of Francisco
Franco. (Claud Cockburn, under a pseudonym, also wrote
novels, including Beat the Devil , which was made into a
film with Humphrey Bogart and which his son used as the
title of his column in The Nation .)"
A video linked to in this evening's earlier post suggests
an antidote to the film oeuvre of Guillermo del Toro—
in particular, to Pan's Labyrinth.
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For a leftist who wrote well—
Here's your ticket, pack your bags,
time for jumpin' overboard
Transportation is here
—Talking Heads lyric
Comments Off on Ticket
The New York Times online front page
update of 10:11 this morning provides
a sort of antidote to Saturday morning
cartoons.
The update's time suggests a check
of this journal's most recent post
with the date 10/11. It turns out
to be a meditation on art and
the speed of perception.
Related material:
A linked-to post, Twenty-Four.
Comments Off on Photo Opportunity
"A Saturday morning cartoon is the colloquial term
for the animated television programming that has
typically been scheduled on Saturday mornings
on the major American television networks from
the 1960s to the present…." —Wikipedia
Martin Gardner in the Notices of the
American Mathematical Society ,
June/July 2005:
“I did a column in Scientific American
on minimal art, and I reproduced one of
Ed Rinehart’s [sic ] black paintings.
Of course, it was just a solid square of
pure black.”
Click on picture for details.
For a cartoon graveyard—
Comments Off on Saturday Morning Cartoon
Friday, July 20, 2012
http://www.latimes.com/news/politics/
la-pn-romney-colorado-shooting-is-
unspeakable-tragedy-20120720,0,1226295.story
Romney: Colorado shooting is 'unspeakable tragedy'
By Seema Mehta
July 20, 2012, 11:15 a.m.
BOW, N.H.—Hours after a shooter killed a dozen people
in a Colorado cinema, Mitt Romney scrubbed a scheduled
campaign rally Friday and instead offered his somber
condolences and prayers to the victims and their
families.
“Our hearts break with the sadness of this unspeakable
tragedy. Ann and I join the president and first lady
and all Americans in offering our deepest condolences
to those whose lives were shattered in a few moments,
a few moments of evil in Colorado,” Romney told a few
hundred people gathered at a lumber yard here.
“I stand before you today not as a man running for
office but as a father and grandfather, a husband, an
American. This is a time for each of us to look into
our hearts and remember how much we love one another
and how much we love and how much we care for our great
country. There’s so much love and goodness in the heart
of America.”
Romney, wearing a navy blue suit and blue tie, spoke
for four minutes. The trademark campaign banners with
slogans such as “Believe in America” or “Obama’s Upside-
Down Economy” were gone, leaving a handful of American
flags as the backdrop. Before Romney spoke, Father
Christian Tutor, an Anglican Catholic priest, led a
prayer. ...
|
Caped Crusader
Comments Off on Speaking the Unspeakable
Comments Off on I Mean, Seriously…
Thursday, July 19, 2012
For those who prefer fiction:
"Many Dimensions (1931) — An evil antiquarian illegally purchases
the fabled Stone of Suleiman (Williams uses this Muslim form
rather than the more familiar King Solomon) from its Islamic guardian
in Baghdad and returns to England to discover not only that the Stone
can multiply itself infinitely without diminishing the original, but that it
also allows its possessor to transcend the barriers of space and time."
— Wikipedia article on the author Charles Williams
Comments Off on But Seriously…
A Passage to India… With Slides and Chanting
"Why art thou here,
Come from the farthest Steppe of India?"
— Midsummer Night's Dream
"After graduating, Mr. Franken headed for Harvard,
while Mr. Davis chose the University of the Pacific
in Stockton, Calif., because, he said, he had heard
that it had a foreign study program in India, where
he hoped to smoke opium. (They did, and he did.)"
— Obituary of Saturday Night Live writer Tom Davis
by Douglas Martin in this evening's online New York Times
"Frances Alenikoff, a dancer, choreographer and visual artist
whose performances often interwove movement with slides,
film, speaking, tape recordings and chant, died on June 23
in Southampton, N.Y. She was 91."
— Margalit Fox, online NY Times of July 8, 2012
Click for up-to-date context from the Times.
Comments Off on Midsummer Nightmare
Connoisseurs of hermeneutics will find that interpretations
of three of the above numbers are not hard to come by.
Consider, say, dates, post numbers in Log24, times, and so forth.
For the fourth number, 0131, try the following search:
http://www.m759.net/wordpress/?s=0131.
Comments Off on Un Coup de Dés
Wednesday, July 18, 2012
Comments Off on Joyce’s Nightmare
(Continued from Midsummer Eve)
"At times, bullshit can only be countered with superior bullshit."
— Norman Mailer, March 3, 1992, PBS transcript
"Just because it is a transition between incommensurables, the transition between competing paradigms cannot be made a step at a time, forced by logic and neutral experience. Like the gestalt switch, it must occur all at once (though not necessarily in an instant) or not at all."
— Thomas Kuhn, The Structure of Scientific Revolutions , 1962, as quoted in The Enneagram of Paradigm Shifting
"In the spiritual traditions from which Jung borrowed the term, it is not the SYMMETRY of mandalas that is all-important, as Jung later led us to believe. It is their capacity to reveal the asymmetry that resides at the very heart of symmetry."
— The Enneagram as Mandala
I have little respect for Enneagram enthusiasts, but they do at times illustrate Mailer's maxim.
My own interests are in the purely mathematical properties of the number nine, as well as those of the next square, sixteen.
Those who prefer bullshit may investigate non-mathematical properties of sixteen by doing a Google image search on MBTI.
For bullshit involving nine, see (for instance) Einsatz in this journal.
For non-bullshit involving nine, sixteen, and "asymmetry that resides at the very heart of symmetry," see Monday's Mapping Problem continued. (The nine occurs there as the symmetric figures in the lower right nine-sixteenths of the triangular analogs diagram.)
For non-bullshit involving psychological and philosophical terminology, see James Hillman's Re-Visioning Psychology .
In particular, see Hillman's "An Excursion on Differences Between Soul and Spirit."
Comments Off on Incommensurables
Tuesday, July 17, 2012
I need a photo opportunity
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard
— Paul Simon
See also the name Romanova
and the name Anastasia.
Comments Off on For Black Widow
Comments Off on Putting the X in…
Monday, July 16, 2012
(Continued.)
Jaws for Frank
Part I: October 8, 2010
Part II: Noon Today
"The rest is the madness of art."
See also Patterns in the Carpets
and Saturday's Shadows.
Comments Off on Finishing Up at Noon
The New York Times online opinion today—
"Merit has been traditionally equated with intelligence, industriousness, educational attainment, creativity and competency. In a meritocracy, formal qualifications provide opportunity, position is no longer ascribed by birth, and rewards flow to those who excel.
The rise of meritocratic competition as the preeminent means of social stratification in America has been hailed as a welcome advance because it replaced a society dominated by an upper class dependent on inherited wealth and status. The transition to meritocracy has, however, had unintended consequences. In the business sector, particularly, other less benign qualities emerge as essential to meritocratic success: aggressiveness, ruthlessness, dominance-seeking, victimizing behavior, acquisitiveness and the disciplined pursuit of self-interest."
— Journalism professor Thomas B. Edsall discussing remarks last December by Mitt Romney
Note the subtle shift here from "merit" to "meritocracy." Romney used the former word, not the latter.
Note also this sentence, aimed particularly at meritocratic New York Times readers—
"In a meritocracy, formal qualifications provide opportunity… and rewards flow to those who excel."
Edsall lies. In a meritocracy, rewards flow to those who rubber-stamp "formal qualifications." See particularly Walter Kirn on meritocracy.
Edsall is pandering to Times readers. Romney was pandering to a different group—
Comments Off on Merit vs. Meritocracy
Another approach to the square-to-triangle
mapping problem (see also previous post)—
For the square model referred to in the above picture, see (for instance)
Coordinates for the 16 points in the triangular arrays
of the corresponding affine space may be deduced
from the patterns in the projective-hyperplanes array above.
This should solve the inverse problem of mapping,
in a natural way, the triangular array of 16 points
to the square array of 16 points.
Update of 9:35 AM ET July 16, 2012:
Note that the square model's 15 hyperplanes S
and the triangular model's 15 hyperplanes T —
— share the following vector-space structure —
0 |
c |
d |
c + d |
a |
a + c |
a + d |
a + c + d |
b |
b + c |
b + d |
b + c + d |
a + b |
a + b + c |
a + b + d |
a + b +
c + d |
(This vector-space a b c d diagram is from
Chapter 11 of Sphere Packings, Lattices
and Groups , by John Horton Conway and
N. J. A. Sloane, first published by Springer
in 1988.)
Comments Off on Mapping Problem continued
Sunday, July 15, 2012
A trial solution to the
square-to-triangle mapping problem—
Problem: Is there any good definition of "natural"
square-to-triangle mappings according to which
the above mapping is natural (or, for that matter,
un-natural)?
Comments Off on Mapping Problem
"A figurate number… is a number
that can be represented by
a regular geometrical arrangement
of equally spaced points."
— Eric W. Weisstein at Wolfram MathWorld
For example—
Call a convex polytope P an n-replica if P consists of n
mutually congruent polytopes similar to P packed together.
The square-triangle theorem (or lemma) says that
"Every triangle is an n-replica"
is true if and only if n is a square.
Equivalently,
The positive integer n is a square
if and only if every triangle is an n-replica.
(I.e., squares are triangular.)
This supplies the converse to the saying that
Triangles Are Square.
Comments Off on Squares Are Triangular
Saturday, July 14, 2012
For example—
A letter to the editor of the American Mathematical Monthly
from the June-July 1985 issue has—
… a "square-triangle" lemma:
(∀ t ∈ T , t is an n -replica )
if and only if n is a square.
[I.e., "Every triangle is an n -replica"
is true if and only if n is a square.]
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For definitions, see the 1985 letter in Triangles Are Square.
(The 1984 lemma discussed there has now, in response to an article
in Wolfram MathWorld, been renamed the square-triangle theorem .)
A search today for related material yielded the following—
"Suppose that one side of a triangle
has length n . Then it can be cut
into n 2 congruent triangles which
are similar to the original one and
whose corresponding sides to the
side of length n have lengths 1."
|
This was supplied, without attribution, as part of the official solution
to Problem 3 in the 17th Asian Pacific Mathematics Olympiad
from March 2005. Apparently it seemed obvious to the composer
of the problem. As the 1985 letter notes, it may be not quite obvious.
At any rate, it served in Problem 3 as a lemma , in the sense
described above by Wikipedia. See related remarks by Doron Zeilberger.
Comments Off on Lemma
A tribute to Richard D. Zanuck in the style of Tim Burton—
Part I
Part II
Part III
The above Zanuck interview on Dark Shadows
was published on Midsummer Eve, June 23, 2012.
Also from June 23, 2012—
Related material— Russell on Hardy.
Comments Off on Shadows
Friday, July 13, 2012
1940 —
2003 —
"… Conceptualism — suddenly art
could be nothing more than an idea,
a thought on a piece of paper
that played in your head."
— Michael Kimmelman,
"The Dia Generation,"
The New York Times Magazine ,
Sunday, April 6, 2003
Suddenly?
Comments Off on Suddenly
Thursday, July 12, 2012
An example of lines in a Galois space * —
The 35 lines in the 3-dimensional Galois projective space PG(3,2)—
(Click to enlarge.)
There are 15 different individual linear diagrams in the figure above.
These are the points of the Galois space PG(3,2). Each 3-set of linear diagrams
represents the structure of one of the 35 4×4 arrays and also represents a line
of the projective space.
The symmetry of the linear diagrams accounts for the symmetry of the
840 possible images in the kaleidoscope puzzle.
* For further details on the phrase "Galois space," see
Beniamino Segre's "On Galois Geometries," Proceedings of the
International Congress of Mathematicians, 1958 [Edinburgh].
(Cambridge U. Press, 1960, 488-499.)
(Update of Jan. 5, 2013— This post has been added to finitegeometry.org.)
Comments Off on Galois Space
Wednesday, July 11, 2012
Tuesday, July 10, 2012
From this journal on June 19, 2012—
Walter Gropius on space—
"Was ist Raum, wie können wir ihn
erfassen und gestalten?"
Walter Gropius,
The Theory and
Organization of the
Bauhaus (1923)
A book published on the same date—
June 19, 2012:
"… what Chalmers called the convergence of coincidence—
a force majeure of unrelated events that shaped one's life,
that perhaps defined the concept of life itself.
He believed in the power of that force."
— The Cryptos Conundrum , by Chase Brandon
See also Chase Brandon in Sunday's Huffington Post .
"I wrote another book."
— Robert De Niro as Harlan Kane
Comments Off on Space Cadets
Comments Off on Euclid vs. Galois
Monday, July 9, 2012
A Story That Works
“There is the dark, eternally silent, unknown universe;
there are the friend-enemy minds shouting and whispering
their tales and always seeking the three miracles —
- that minds should really touch, or
- that the silent universe should speak, tell minds a story,
- or (perhaps the same thing) that there should be a story
that works, that is all hard facts, all reality, with
no illusions and no fantasy;
and lastly, there is lonely, story-telling, wonder-questing,
mortal me.”
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Dichtung ist Stiftung.
Comments Off on Taps for Fatso
Sunday, July 8, 2012
"That n 2 points fall naturally into a triangular array
is a not-quite-obvious fact which may have applications…
and seems worth stating more formally."
— Steven H. Cullinane, letter in the
American Mathematical Monthly 1985 June-July issue
If the ancient Greeks had not been distracted by
investigations of triangular (as opposed to square )
numbers, they might have done something with this fact.
A search for occurrences of the phrase
"n2 [i.e., n 2 ] congruent triangles"
indicates only fairly recent (i.e., later than 1984) results.*
Some related material, updated this morning—
This suggests a problem—
What mappings of a square array of n 2 points to
a triangular array of n 2 points are "natural"?
In the figure above, whether
the 322,560 natural permutations
of the square's 16 points
map in any natural way to
permutations of the triangle's 16 points
is not immediately apparent.
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* Update of July 15, 2012 (11:07 PM ET)—
Theorem on " rep-n 2 " (Golomb's terminology)
triangles from a 1982 book—
Comments Off on Not Quite Obvious
Saturday, July 7, 2012
"Euclid (Ancient Greek: Εὐκλείδης Eukleidēs), fl. 300 BC,
also known as Euclid of Alexandria, was a Greek
mathematician, often referred to as the 'Father of Geometry.'"
— Wikipedia
A Euclidean quartet (see today's previous post)—
Image by Alexander Soifer
See also a link from June 28, 2012, to a University Diaries post
discussing "a perfection of thought."
Perfect means, among other things, completed .
See, for instance, the life of another Alexandrian who reportedly
died on the above date—
"Gabriel Georges Nahas was born in Alexandria, Egypt, on
March 4, 1920…."
— This afternoon's online New York Times
Comments Off on Quartet
For remarks related by logic, see the square-triangle theorem.
For remarks related by synchronicity, see Log24 on
the above publication date, June 15, 2010.
According to Google (and Soifer's page xix), Soifer wants to captivate
young readers.
Whether young readers should be captivated is open to question.
"There is such a thing as a 4-set."
Update of 9:48 the same morning—
Amazon.com says Soifer's book was published not on June 15, but on
June 29 , 2010
(St. Peter's Day).
Comments Off on Étude
Thursday, July 5, 2012
A post suggested by an article on The Shard of London
in this morning's Wall Street Journal—
As for the "Personal Jesus" song that accompanies the above video tribute,
listen to Liam Neeson as the voice of Aslan in recent Narnia films
and consider the saying of C. S. Lewis that Aslan is not a tame lion.
Here Lewis may, if one likes, be regarded as the "inkling" of Heidegger
in last night's post—
Comments Off on Shard
Or: Night of Lunacy
From 9 PM Monday —
Note that the last line, together with the page number, forms
a sort of key—
The rest of the story—
For one reinterpretation of the page number 304, see a link—
Sermon— from Tuesday's post Diamond Speech.
The linked-to sermon itself has a link, based on a rereading
of 304 as 3/04, to a post of March 4, 2004, with…
WW and ZZ
as rendered by figures from the Kaleidoscope Puzzle—
.
Yesterday morning the same letter-combinations occurred
in a presentation at CERN of a newly discovered particle—
(Click for context.)
Since the particle under discussion may turn out to be the
God particle, it seems fitting to interpret WW and ZZ as part
of an imagined requiem High Mass.
Ron Howard, director of a film about CERN and the God particle,
may regard this imaginary Mass as performed for the late
Andy Griffith, who played Howard's father in a television series.
Others may prefer to regard the imaginary Mass as performed
for the late John E. Brooks, S. J., who served as president of
The College of the Holy Cross, Worcester, Mass., for 24 years.
Griffith died Tuesday. Brooks died Monday.
For some background on the Holy Cross, see posts of
Sept. 14 (Holy Cross Day) and Sept. 15, 2010—
-
Language Game,
-
Wittgenstein, 1935, and
-
Holy Cross Day Revisited.
For more lunacy, see…
Continue a search for thirty-three and three
— Katherine Neville, The Eight
Comments Off on Claves Regni Caelorum
Wednesday, July 4, 2012
For a White House daughter…
See Sweater and Light.
From this evening's Capitol Fourth—
She goes off with a great big bang
Boys I tell ya it's a beautiful thing
Related material— Big Bang in this journal—
Detective Cruz enters Planck's Constant Café in "The Big Bang."
Comments Off on Physical Poetry
Comments Off on Poetic Physics
A story in two parts —
Part I (April 1986) and Part II (June 2012).
Comments Off on Western Union
Tuesday, July 3, 2012
—Rhodes, I want you to get to know people like that.
I'd like to sort of take you under my wing and educate you.
—Shucks, General, I'm just a country boy.
Comments Off on Calling
"And when I think about the values
that are important to me today,
I think first about meritocracy."
— Robert Diamond, Colby College '73, now
Chair of the Colby College Board of Trustees, in a
commencement address on Sunday, May 25, 2008
Other remarks on that Sunday —
Related material from Colby—
See also an MAA report on Gouvea from June 6, 2012.
Comments Off on Diamond Speech
Monday, July 2, 2012
Heidegger, "Hölderlin and the Essence of Poetry,"
translated by Douglas Scott, in Existence and Being ,
Regnery, 1949, pp. 291-316—
See also Hexagram 36.
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Images from a Google search suggested by
last night's post Coming to Meet, by the recent
film "Archie's Final Project," and by a Thursday,
June 28, 2012, Times Higher Education piece,
"Raiders of the Lost Archives"—
Log24, December 8, 2008 —
"Let the fingers do the research."
— Archive Raiders
Comments Off on Hexagram 44 Revisited
Sunday, July 1, 2012
This evening's online New York Times—
Doris Sams, Pro Baseball Star, Dies at 85
By RICHARD GOLDSTEIN
Published: July 1, 2012
Doris Sams, who pitched a perfect game and set a single-season home run record in the women’s professional baseball world of the 1940s and 50s that inspired the movie “A League of Their Own,” died Thursday in Knoxville, Tenn. She was 85. more>>
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"High summer holds the earth."
— James Agee, quoted in a post by University Diaries
linked to here on Thursday.
See also For Taylor and Country Strong.
* A phrase from the quoted Agee poem
Comments Off on Shining Night*
Hexagram 44:
Coming to Meet
"This hexagram indicates a situation in which
the principle of darkness, after having been eliminated,
furtively and unexpectedly obtrudes again from within
and below. Of its own accord the female principle
comes to meet the male. It is an unfavourable and
dangerous situation, and we must understand and
promptly prevent the possible consequences.
The hexagram is linked with the fifth month
[June-July], because at the summer solstice
the principle of darkness gradually becomes
ascendant again."
— Richard Wilhelm
To counteract the principle of darkness—
The Uploading (Friday— St. Peter's Day, 2012),
Thor's Light Bulb Joke, and …
.
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Saturday, June 30, 2012
The New York Times this evening—
Horacio Coppola, Evocative
Argentine Photographer,
Dies at 105
By DENISE GRADY
Published: June 30, 2012
Horacio Coppola, whose black-and-white photographs of the cafes, side streets and neon-lit boulevards of Buenos Aires in the 1930s, and of ordinary objects like a typewriter and a doll, introduced avant-garde photography to Argentina, died on June 18 in Buenos Aires. He was 105. more >>
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Related story—
Coppola photographed the new Obelisk of Buenos Aires in 1936.
"Where the Obelisco stands, a church dedicated to St. Nicholas
of Bari [or of Myra] was previously demolished."
Related images—
Wikipedia image
"And if you should survive to a hundred and five,
look at all you'll derive …" —Sinatra
Comments Off on Santa vs. the Obelisk
"… to snare the spirits of mankind in nets of magic"
— The aim of the artist, according to Thomas Wolfe
Related entertainment—
High-minded— Many Dimensions .
Not so high-minded— The Cosmic Cube .
Comments Off on Snares
Friday, June 29, 2012
A non-Lyche* gate—
Part of the Andrew Amesbury series Archway to Highgate.
* See Lyche gate in this journal.
Happy feast of Saints Peter and Paul.
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Click image for some context. See also tonight's previous
post and Cliffs of Moher in this journal.
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It Must Be Abstract
It Must Change
It Must Give Pleasure
— Parts of a poem by Wallace Stevens
“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”
– Thomas Wolfe, Of Time and the River
Of Time and the River and the Frogs —
* This post's title refers to the above uploading date— Jan. 26, 2008.
Comments Off on The Uploading (continued)*
Thursday, June 28, 2012
Wednesday, June 27, 2012
Comments Off on Architectural Memorial
Tuesday, June 26, 2012
Last night's post on The Trinity of Max Black and the use of
the term "eightfold" by the Mathematical Sciences Research Institute
at Berkeley suggest a review of an image from Sept. 22, 2011—
The triskele detail above echoes a Buddhist symbol found,
for instance, on the Internet in an ad for meditation supplies—
Related remarks—
http://www.spencerart.ku.edu/about/dialogue/fdpt.shtml—
Mary Dusenbury (Radcliffe '64)—
"… I think a textile, like any work of art, holds a tremendous amount of information— technical, material, historical, social, philosophical— but beyond that, many works of art are very beautiful and they speak to us on many layers— our intellect, our heart, our emotions. I've been going to museums since I was a very small child, thinking about what I saw, and going back to discover new things, to see pieces that spoke very deeply to me, to look at them again, and to find more and more meaning relevant to me in different ways and at different times of my life. …
… I think I would suggest to people that first of all they just look. Linger by pieces they find intriguing and beautiful, and look deeply. Then, if something interests them, we have tried to put a little information around the galleries to give a bit of history, a bit of context, for each piece. But the most important is just to look very deeply."
http://en.wikipedia.org/wiki/Nikaya_Buddhism—
According to Robert Thurman, the term "Nikāya Buddhism" was coined by Professor Masatoshi Nagatomi of Harvard University, as a way to avoid the usage of the term Hinayana.[12] "Nikaya Buddhism" is thus an attempt to find a more neutral way of referring to Buddhists who follow one of the early Buddhist schools, and their practice.
12. The Emptiness That is Compassion:
An Essay on Buddhist Ethics, Robert A. F. Thurman, 1980
[Religious Traditions , Vol. 4 No. 2, Oct.-Nov. 1981, pp. 11-34]
http://dsal.uchicago.edu/cgi-bin/philologic/getobject.pl?c.2:1:6.pali—
Nikāya [Sk. nikāya, ni+kāya]
collection ("body") assemblage, class, group
http://en.wiktionary.org/wiki/नि—
Sanskrit etymology for नि (ni)
Prefix
नि (ni)
http://www.rigpawiki.org/index.php?title=Kaya—
Kaya (Skt. kāya ; སྐུ་, Tib. ku ; Wyl. sku ) —
the Sanskrit word kaya literally means ‘body’
but can also signify dimension, field or basis.
སྐུ། (Wyl. sku ) n. Pron.: ku
• structure, existentiality, founding stratum ▷HVG KBEU
• gestalt ▷HVG LD
Note that The Trinity of Max Black is a picture of a set—
i.e., of an "assemblage, class, group."
Note also the reference above to the word "gestalt."
"Was ist Raum, wie können wir ihn
erfassen und gestalten?"
— Walter Gropius
Comments Off on Looking Deeply
A companion to tonight’s earlier post, “Bright Black“—
Above: Leonard Bernstein conducts the Mahler Ninth ending.
Wikipedia—
The work was premiered on June 26, 1912,
at the Vienna Festival by the Vienna Philharmonic Orchestra ….
Related material—
The above video was uploaded on January 19th, 2008.
Comments Off on The Uploading (continued)
“‘In the dictionary next to [the] word “bright,” you should see Paula’s picture,’ he said. ‘She was super smart, with a sparkling wit. … She had a beautiful sense of style and color.'”
— Elinor J. Brecher in The Miami Herald on June 8, quoting Palm Beach Post writer John Lantigua on the late art historian Paula Hays Harper
This journal on the date of her death—
For some simpleminded commentary, see László Lovász on the cube space.
Some less simpleminded commentary—
“Was ist Raum, wie können wir ihn
erfassen und gestalten?”
Walter Gropius,
The Theory and
Organization of the
Bauhaus (1923)
Comments Off on Bright Black
Monday, June 25, 2012
Remarks on Wallace Stevens's poem "Notes toward a Supreme Fiction"
from Michael Bryson—
The question of the eighth canto, "What am I to believe?", leads the way back from the heightened mysticism of the previous cantos toward a renewed consideration of the particular, the immanent, the local. Men and birds are considered in their activities, in their "Mere repetitions," and these repetitions (as well the repeating figures, the men and birds themselves) are each considered as "A thing final in itself and, therefore, good: / One of the vast repetitions final in / Themselves and, therefore, good". The poem comes to a Nietzschean affirmation of recurrence with its "merely going round is a final good," and its suggestion that the "man-hero" is "he that of repetition is most master".
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Or the woman-hero…
From a Log24 post on June 1, 2004—
“A tongue-in-cheek comment by programmers is worth thinking about: ‘Sometimes you have a programming problem and it seems like the best solution is to use regular expressions; now you have two problems.’ Regular expressions are amazingly powerful and deeply expressive. That is the very reason writing them is just as error-prone as writing any other complex programming code.”
– David Mertz, Learning to Use Regular Expressions
Happy birthday to the late Willard Van Orman Quine.
Comments Off on Repetition
The New York Times this morning reports the death
last Tuesday (June 19, 2012) in Boston
of Gerhard Kallman, a Brutalist architect
born in Berlin in 1915.
Some Log24 images from the date of his death—
The above view shows the south side of Kirkland Street (at Quincy).
A more appealing architectural image, from the other side
of Kirkland Street—
Comments Off on Design (continued)
Sunday, June 24, 2012
"What summer reading needs to be is purposeful."
— New York Times opinion column today
One of a set of posts titled "Summer Reading"
in this journal in 2007—
(Click for the original post)
It was only in retrospect
that the silliness
became profound.
— Review of
Faust in Copenhagen
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Saturday, June 23, 2012
"Ayant été conduit par des recherches particulières
à considérer les solutions incommensurables, je suis
parvenu à quelques résultats que je crois nouveaux."
— Évariste Galois, "Sur la Théorie des Nombres"
Soon to be a major motion picture!
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"The Double-Cross System, or XX System, was a World War II
anti-espionage and deception operation of the British military
intelligence arm, MI5. Nazi agents in Britain… were captured,
turned themselves in or simply announced themselves and were
then used by the British to broadcast mainly disinformation to
their Nazi controllers." —Wikipedia
The XX —
The Double Cross of Fritz Leiber—
Source: Rudolf Koch, The Book of Signs
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Friday, June 22, 2012
The New York Times today—
"Reality and our perception of it are incommensurate…."
The above New York Times Wire item from 3:35 PM ET today
mentions two topics touched on in today's earlier Log24 post
Bowling in Diagon Alley— magic (implied by the title) and
incommensurability. The connection in that post
between the two topics is the diagonal of a square.
The wire item shows one detail from a Times illustration
of the linked article— a blindfolded woman.
Another detail from the same illustration—
Hands-on Wand Work
See also remarks on Magic in this journal and on Harry Potter.
I dislike both topics.
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Josefine Lyche bowling (Facebook, June 12, 2012)
"Where Does Math Come From?"
A professor of philosophy in 1984 on Socrates's geometric proof in Plato's Meno dialogue—
"These recondite issues matter because theories about mathematics have had a big place in Western philosophy. All kinds of outlandish doctrines have tried to explain the nature of mathematical knowledge. Socrates set the ball rolling…."
— Ian Hacking in The New York Review of Books , Feb. 16, 1984
The same professor introducing a new edition of Kuhn's Structure of Scientific Revolutions—
"Paradigms Regained" (Los Angeles Review of Books , April 18, 2012)—
"That is the structure of scientific revolutions: normal science with a paradigm and a dedication to solving puzzles; followed by serious anomalies, which lead to a crisis; and finally resolution of the crisis by a new paradigm. Another famous word does not occur in the section titles: incommensurability. This is the idea that, in the course of a revolution and paradigm shift, the new ideas and assertions cannot be strictly compared to the old ones."
The Meno proof involves inscribing diagonals in squares. It is therefore related, albeit indirectly, to the classic Greek discovery that the diagonals of a square are incommensurable with its sides. Hence the following discussion of incommensurability seems relevant.
See also von Fritz and incommensurability in The New York Times (March 8, 2011).
For mathematical remarks related to the 10-dot triangular array of von Fritz, diagonals, and bowling, see this journal on Nov. 8, 2011— "Stoned."
Comments Off on Bowling in Diagon Alley
Thursday, June 21, 2012
In memory of art historian John Golding,
whose obituary appeared (finally) in
today’s online Telegraph—
“His most recent book, Paths to the Absolute (based on
his 1997 series of AW Mellon lectures in the Fine Arts
delivered at the National Gallery of Art, Washington DC),
addressed seven abstract artists — Mondrian, Kazimir
Malevich, Kandinsky, Pollock, Barnett Newman, Rothko
and Clyfford Still — and argued that abstract art was
not simply decorative but ‘heavily imbued with meaning
[and] with content’. The book won the Mitchell Prize for
the History of Art in 2002.”
Commentary on Golding’s obituary suggested by
this evening’s 4-digit New York Lottery number,
1051—
Post 1051 in this journal, together with a post from
April 1, 2012 found in a search for the digits 1051
in Log24. That search may serve as a review.
* A phrase from Gravity’s Rainbow
Comments Off on A Kind of Cross*
From Tony Rothman's review of a 2006 book by
Siobhan Roberts—
"The most engaging aspect of the book is its
chronicle of the war between geometry and algebra,
which pits Coxeter, geometry's David, against
Nicolas Bourbaki, algebra's Goliath."
The conclusion of Rothman's review—
"There is a lesson here."
Related material: a search for Galois geometry .
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In memory of actor Richard Lynch, 76, who was found
dead at his California home on Tuesday, June 19, 2012
Lynch's last role was apparently as the Reverend John Hawthorne
in the upcoming film The Lords of Salem .
(For a post on some related theological territory, see this journal
on the date Lynch's body was found.)
Wikipedia on the Salem film—
Lords of Salem is the third film from Haunted Films,*
the first two being Paranormal Activity and Insidious .
For other tales of paranormal activity, see the Bible.
For a post in this journal from the Insidious release date,
see Mathematics Awareness Month (April 1, 2011).
See, too, related discussions of Finnegans Wake by
James S. Atherton in The Books at the Wake—
Pages 146-147 and 199-200.
* At IMDb, Haunted Movies. See also Blumhouse Productions.
Comments Off on Lynch’s Wake
Wednesday, June 20, 2012
For those who prefer a cinematic approach…
"I was alone, I took a ride…"
— Sound track of the 2010 film Steve Jobs on Flash
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A quote from The Oxford Murders ,
a novel by Guillermo Martinez—
"Anyone can follow the path once it’s been marked out.
But there is of course an earlier moment of illumination,
what you called the knight’s move. Only a few people,
sometimes only one person in many centuries,
manage to see the correct first step in the darkness.”
“A good try,” said Seldom.
Comments Off on Discouraging Words
Tuesday, June 19, 2012
In memory of Victor Spinetti, who died today—
"Oh wow, oh wow, oh wow."
— Courtesy of Steve Jobs and Aldous Huxley—
Comments Off on Last Words
The New York Times online front page last night—
"Microsoft introduced its own tablet computer,
called Surface, illustrating the pressure
Apple's success has put on it to marry
software and hardware more tightly."
Commentary—
Google Maps image
Related material—
"Was ist Raum, wie können wir ihn
erfassen und gestalten?"
Walter Gropius,
The Theory and
Organization of the
Bauhaus (1923)
Update of Feb. 3, 2013:
See also The Perception of Doors in this journal.
Comments Off on Design
Monday, June 18, 2012
"Poetry is an illumination of a surface…."
— Wallace Stevens
Some poetic remarks related to a different surface, Klein's Quartic—
This link between the Klein map κ and the Mathieu group M24
is a source of great delight to the author. Both objects were
found in the 1870s, but no connection between them was
known. Indeed, the class of maximal subgroups of M24
isomorphic to the simple group of order 168 (often known,
especially to geometers, as the Klein group; see Baker [8])
remained undiscovered until the 1960s. That generators for
the group can be read off so easily from the map is
immensely pleasing.
— R. T. Curtis, Symmetric Generation of Groups ,
Cambridge University Press, 2007, page 39
Other poetic remarks related to the simple group of order 168—
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Sunday, June 17, 2012
A Google search today yielded no results
for the phrase "congruent group actions."
Places where this phrase might prove useful include—
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Saturday, June 16, 2012
In memory of William S. Knowles, chiral chemist, who died last Wednesday (June 13, 2012)—
Detail from the Harvard Divinity School 1910 bookplate in yesterday morning's post—
"ANDOVER–HARVARD THEOLOGICAL LIBRARY"
Detail from Knowles's obituary in this morning's New York Times—
William Standish Knowles was born in Taunton, Mass., on June 1, 1917. He graduated a year early from the Berkshire School, a boarding school in western Massachusetts, and was admitted to Harvard. But after being strongly advised that he was not socially mature enough for college, he did a second senior year of high school at another boarding school, Phillips Academy in Andover, N.H.
Dr. Knowles graduated from Harvard with a bachelor’s degree in chemistry in 1939….
"This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them."
— Hermann Weyl, The Classical Groups, Princeton University Press, 1946, p. 16
From Pilate Goes to Kindergarten—
The six congruent quaternion actions illustrated above are based on the following coordinatization of the eightfold cube—
Problem: Is there a different coordinatization
that yields greater symmetry in the pictures of
quaternion group actions?
A paper written in a somewhat similar spirit—
"Chiral Tetrahedrons as Unitary Quaternions"—
ABSTRACT: Chiral tetrahedral molecules can be dealt [with] under the standard of quaternionic algebra. Specifically, non-commutativity of quaternions is a feature directly related to the chirality of molecules….
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Friday, June 15, 2012
In memory of Paul Sussman, author of archaeological
mystery novels about Egypt—
Sussman's last novel, not yet published, was
The Labyrinth of Osiris .
Sussman, 45, reportedly died suddenly on May 31, 2012.
A perhaps relevant thought—
"A world of made
is not a world of born— pity poor flesh
and trees, poor stars and stones, but never this
fine specimen of hypermagical
ultraomnipotence."
– e. e. cummings, 1944
Comments Off on Elements
Thursday, June 14, 2012
The Fog of Law continues…
Egypt's highest court
declares parliament invalid
By the CNN Wire Staff
updated 11:36 AM EDT, Thu June 14, 2012
* See State of a Nation (Alicia Keys's birthday, 2012)
Comments Off on For Alicia*
Notes on Groups and Geometry, 1978-1986,
is now available at the Internet Archive.
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Wednesday, June 13, 2012
The new June/July issue of the AMS Notices
on a recent Paris exhibit of art and mathematics—
Mathématiques, un dépaysement soudain
Exhibit at the Fondation Cartier, Paris
October 21, 2011–March 18, 2012
… maybe walking
into the room was supposed to evoke the kind of
dépaysement for which the exhibition is named
(the word dépaysement refers to the sometimes
disturbing feeling one gets when stepping outside
of one’s usual reference points). I was with
my six-year-old daughter, who quickly gravitated
toward the colorful magnetic tiles on the wall that
visitors could try to fit together. She spent a good
half hour there, eventually joining forces with a
couple of young university students. I would come
and check on her every once in a while and heard
some interesting discussions about whether or not
it was worth looking for patterns to help guide the
placing of the tiles. The fifteen-year age difference
didn’t seem to bother anyone.
The tiles display was one of the two installations
here that offered the visitor a genuine chance to
engage in mathematical activity, to think about
pattern and structure while satisfying an aesthetic
urge to make things fit and grow….
— Nathalie Sinclair
The Notices included no pictures with this review.
A search to find out what sort of tiles were meant
led, quite indirectly, to the following—
The search indicated it is unlikely that these Truchet tiles
were the ones on exhibit.
Nevertheless, the date of the above French weblog post,
1 May 2011, is not without interest in the context of
today's previous post. (That post was written well before
I had seen the new AMS Notices issue online.)
Comments Off on State of the Art
A book first published in hardcover in 1974—
For more-recent discussions of religious social phenomena,
see Laurie Goodstein and David V. Mason.
Comments Off on Turn, Turn, Turn
Tuesday, June 12, 2012
Background— August 30, 2006—
The Seventh Symbol:
In the 2006 post, the above seventh symbol 110000 was
interpreted as the I Ching hexagram with topmost and
next-to-top lines solid, not broken— Hexagram 20, View .
In a different interpretation, 110000 is the binary for the decimal
number 48— representing the I Ching's Hexagram 48, The Well .
“… Max Black, the Cornell philosopher, and
others have pointed out how ‘perhaps every science
must start with metaphor and end with algebra, and
perhaps without the metaphor there would never
have been any algebra’ ….”
– Max Black, Models and Metaphors,
Cornell U. Press, 1962, page 242, as quoted
in Dramas, Fields, and Metaphors,
by Victor Witter Turner, Cornell U. Press,
paperback, 1975, page 25
The algebra is certainly clearer than either I Ching
metaphor, but is in some respects less interesting.
For a post that combines both the above I Ching
metaphors, View and Well , see Dec. 14, 2007.
In memory of scholar Elinor Ostrom,
who died today—
"Time for you to see the field."
— Bagger Vance
Comments Off on Meet Max Black (continued)
Background: Geometry of the Dance (May 9)
and Midnight in Oslo (May 10).
Peter Pesic has described the action of the
symmetric group S4 on a tetrahedron as a dance—
Compare and contrast:
The following figure may be seen as a tetrahedron,
viewed from above—
See also Masterman and Child’s Play.
Comments Off on Dance Theology
Monday, June 11, 2012
"What we need is… a third way
between the longstanding models
of war and peace. Movement in
this direction is already under way."
— Yale Law professor John Fabian Witt,
"The Legal Fog Between War and Peace"
Tolstoy he ain't.
Witt's remarks appeared yesterday
evening (between 8 and 9 PM EDT)
in the online New York Times .
For related "third way" material, see
yesterday's 7 PM EDT post in this journal.
Comments Off on The Fog of Law
Sunday, June 10, 2012
Lee Marvin in the 1983 film Gorky Park
For related material, see yesterday's post on Nietzsche's
Birth of Tragedy and a May 27, 2010, post— Masks .
The link to the Masks post was suggested by four things:
- Tonight's Tony Awards
- A speech dated May 27, 2010 (the Masks date)—
"Russia— Getting It Right the First Time"
- The name of the organization on whose website
the speech appears— Tertium Datur
- Tertium Datur in this journal—
* The title is in memory of business writer Mike Hammer.
Comments Off on Outside the Box*
Saturday, June 9, 2012
Jim Holt in tomorrow’s New York Times—
“Allow me to quote Nietzsche
(although I know that will be considered
by some to be in bad taste):
‘As the circle of science grows larger,
it touches paradox at more places.'”
A possible source for this misquotation—
Harvard University Press—
A more accurate quotation—
Anyone who has ever experienced the pleasure of Socratic insight and felt how, spreading in ever-widening circles, it seeks to embrace the whole world of appearances, will never again find any stimulus toward existence more violent than the craving to complete this conquest and to weave the net impenetrably tight. To one who feels that way, the Platonic Socrates will appear as the teacher of an altogether new form of “Greek cheerfulness” and blissful affirmation of existence that seeks to discharge itself in actions— most often in maieutic and educational influences on noble youths, with a view to eventually producing a genius.
But science, spurred by its powerful illusion, speeds irresistibly towards its limits where its optimism, concealed in the essence of logic, suffers shipwreck. For the periphery of the circle of science has an infinite number of points; and while there is no telling how this circle could ever be surveyed completely, noble and gifted men nevertheless reach, e’er half their time and inevitably, such boundary points on the periphery from which one gazes into what defies illumination. When they see to their horror how logic coils up at these boundaries and finally bites its own tail— suddenly the new form of insight breaks through, tragic insight which, merely to be endured, needs art as a protection and remedy.
— Friedrich Nietzsche, The Birth of Tragedy , translated by Walter Kaufmann (Modern Library)
Comments Off on Misquoting Nietzsche
From a transcript of the Charlize Theron film
"The Astronaut's Wife"—
Schoolchildren —
"Down came the rain,
and washed the spider out,
out came the sun,
and dried up all the rain,
and the itsy-bitsy spider
climbed up the spout again."
See also The Patterning Windows.
Comments Off on Literary Symbolism
Friday, June 8, 2012
Comments Off on For Ravenna
A remark from the prepared text of Salman Khan,
who spoke at the MIT commencement today—
"I always tell people that MIT is the closest
thing to being Hogwarts— Harry Potter’s
wizarding school— in real life."
A detail from one computer's view of
the webcast of the commencement—
Time elapsed (from the start
of the browser's window, not
from the start of the webcast)
This suggests a look at the date 11/27—
Click on St. Patrick's for further details.
* See June 6, 2007.
Comments Off on For Cullinane College*
In memory of Arthur P. Stern, a link to Feb. 23, 2010.
Related material— Not Quite Nothing.
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For some background, see "Cartoon Graveyard" and "Many Dimensions."
Comments Off on Cartoon Graveyard
Thursday, June 7, 2012
Click image for some background.
Comments Off on Trinity Riddle
"Time for you to see the field." —Bagger Vance
This post was suggested by a link from a post
in this journal seven years ago yesterday—
“Is the language of thought
any more than a dream?“
— Rimbaud
Yes.
Comments Off on The Field
Wednesday, June 6, 2012
Suggested by the previous posts "Venus Winks" and "Ray Bradbury, 1920-2012"—
And then, of course, the biggest crime of all was that she had come here only five years ago from Earth, and she remembered the sun and the way the sun was and the sky was when she was four in Ohio. And they, they had been on Venus all their lives, and they had been only two years old when last the sun came out and had long since forgotten the color and heat of it and the way it really was. But Margot remembered.
"It's like a penny," she said once, eyes closed.
"No it's not!" the children cried.
"It's like a fire," she said, "in the stove."
"You're lying, you don't remember!" cried the children.
But she remembered and stood quietly apart from all of them and watched the patterning windows.
— From the 1954 Ray Bradbury story "All Summer in a Day"
Comments Off on The Patterning Windows
Comments Off on Ray Bradbury, 1920-2012
Tuesday, June 5, 2012
… and Money Talks—
This morning's post Chinese Epiphany discussed interpretations of Chinese
stock market numbers. A followup is shown above.
Here 12:12, the time of the New York Times market quotes pictured,
may be interpreted as 12/12, Sinatra's birthday. The percentage
numbers +0.07 and +0.11 are, of course, lucky for gamblers.
The percentage number -0.01 is perhaps less lucky, but for whom?
Comments Off on Venus Winks…
References here yesterday to Epiphany
and to Chinese logic suggest two observations—
First, a political interpretation of the number "64.89"
from Monday's Shanghai stock market index
yielded the date 6/4 in 1989—
Second, an interpretation of 64.89 as the number 64 in 1989
(on the Feast of the Epiphany, January 6)—
Note of January 6, 1989 showing
the 64 hexagrams in the von Franz style
No connection of the number 64 with the date 6/4 is implied.
Comments Off on Chinese Epiphany
Monday, June 4, 2012
"… Western academic philosophy will likely come to appear
utterly parochial in the coming years if it does not find a way
to approach non-Western traditions that is much more rigorous
and respectful than the tokenism that reigns at present."
— Justin E. H. Smith in the New York Times philosophy
column "The Stone" yesterday
For example—
Selected Bibliography on Ancient Chinese Logic
Comments Off on Rigor and Respect
Some background for this morning's post:
Margaret Masterman's Language, Cohesion and Form .
(See the morning post's footnote.)
Update of 12:25 PM EDT June 4, 2012—
See also "The Epiphany Philosophers" in the online
New York Times , a brief article dated September 19, 2008.
Jungians might enjoy a synchronistic note—
"Toward the Light," a brief post from this journal
on that same date.
Comments Off on Brightness at Noon (continued)
Yesterday's post Child's Play displayed a cube formed
by a Hasse diagram of the 8 subsets of a 3-set.*
This suggests a review of a post from last January—
* See a comment on yesterday's post relating it to earlier,
very similar, remarks by Margaret Masterman.
I was unaware yesterday that those remarks exist.
Comments Off on Cube to Tesseract
Sunday, June 3, 2012
(Continued)
“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”
– Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art , Cornell U. Press, 1975
Related material—
The Trinity Cube
Saturday, June 2, 2012
In memory of Sir Andrew Huxley, OM, who died on May 30, 2012
C. P. Snow on G. H. Hardy at Trinity College, Cambridge—
He played his games and indulged his eccentricities.
He was living in some of the best intellectual company
in the world— G. E. Moore, Whitehead, Bertrand Russell,
Trevelyan, the high Trinity society which was shortly to
find its artistic complement in Bloomsbury. (Hardy himself
had links with Bloomsbury, both of personal friendship
and of sympathy.)
See also "Max Black" + Trinity in this journal.
Comments Off on High Society
Comments Off on Snow White vs. Pitch Black
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