Log24

Saturday, September 29, 2012

This Just In

Filed under: General — Tags: — m759 @ 10:31 am

Update of 11:22 AM ET— A job for Mitt—

B17

Filed under: General — Tags: — m759 @ 9:00 am

The New York Times  on its print edition yesterday:

A version of this article appeared in print
on September 28, 2012, on page 
B17 
of the 
New York edition with the headline:
John Silber Dies at 86; Led Boston University.

The Times 's Robert D. McFadden wrote that
Silber was "a philosopher by training but
a fighter by instinct."  

That phrase was brought to mind today
by a Sept. 25 link in The Harvard Crimson
to Mumford & Sons singing "The Boxer"
in Providence on Transfiguration Day.

There was no Transfiguration Day post
in this journal. Here are parts of the posts
for the preceding and following days—

See also "The Count" from September 17.

Friday, September 28, 2012

Empty Chair at B.U.*

Filed under: General — Tags: , — m759 @ 8:00 pm

Below: A New York Times  "Fashion Week: Immerse Yourself" ad
with obituary of former Boston University president John Silber—
"a philosopher by training but a fighter by instinct"—

IMAGE- NY Times obit of former B.U. president with ad-- 'Fashion Week: Immerse Yourself.'

"I can't do that to myself ." — Clint Eastwood

* See a Sept. 1st CNN piece by Boston University
   religion scholar Stephen Prothero—
  "Give Me Bali's Empty Chair over Eastwood's"—

  See also Prothero in this journal.

Classic Nothing

Filed under: General — Tags: , — m759 @ 3:17 pm

Click to enlarge:

IMAGE- Harvard president Drew Faust sums up the work of Joan Didion

Geometretos*

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

MEDEIS AGEOMETRETOS EISITO

— Inscription at entrance to
     Plato's Academy, according to
     an elementary introduction to
     philosophy by James L. Christian 

For Irving Adler, who reportedly
died on September 22, 2012—

 

Background: See Sangaku in this journal.

See also the following, from a different  
elementary introduction, by Adler—
Giant Golden Book of Mathematics,
illustrated by Lowell Hess

.

   (Detail of Flickr photo)


* See Liddell and Scott.

Thursday, September 27, 2012

Kummer and the Cube

Filed under: General,Geometry — Tags: , , — m759 @ 7:11 pm

Denote the d-dimensional hypercube by  γd .

"… after coloring the sixty-four vertices of  γ6
alternately red and blue, we can say that
the sixteen pairs of opposite red vertices represent
the sixteen nodes of Kummer's surface, while
the sixteen pairs of opposite blue vertices
represent the sixteen tropes."

— From "Kummer's 16," section 12 of Coxeter's 1950
    "Self-dual Configurations and Regular Graphs"

Just as the 4×4 square represents the 4-dimensional
hypercube  γ4  over the two-element Galois field GF(2),
so the 4x4x4 cube represents the 6-dimensional
hypercube  γ6  over GF(2).

For religious interpretations, see
Nanavira Thera (Indian) and
I Ching  geometry (Chinese).

See also two professors in The New York Times
discussing images of the sacred in an op-ed piece
dated Sept. 26 (Yom Kippur).

Mathematics and Narrative (continued)

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

In diamond-narrative news today…

IMAGE- Pink Panther actor dies at 95

"Among the low points of his career was his performance
in the disastrous 1985 remake of “King Solomon’s Mines….”

— David Belcher in today's online New York Times

A Kenning for Thor’s Day

Filed under: General — Tags: , — m759 @ 1:23 am

"A kenning… is a circumlocution
used instead of an ordinary noun
in Old Norse, Old English and
later Icelandic poetry." — Wikipedia

Note the title of Tuesday's post High White in the Dark Fields.

Related material, in memory of a composer-lyricist 
who died Monday (NY Times ) or Tuesday (LA Times )—

"Somewhere there's heaven…"

April 9, 1962

Filed under: General — Tags: — m759 @ 1:01 am

IMAGE- Andy Williams sings 'Moon River' from 'Breakfast at Tiffany's' at the Academy Awards on April 9, 1962.

The "1961" Oscars ceremony shown above was for the films of 1961.
The ceremony itself was held on April 9, 1962.

For a different Tiffany, see Tuesday's Another Day.

Wednesday, September 26, 2012

Flow

Filed under: General — Tags: , , — m759 @ 12:00 pm
 
From French cinema—

Duelle

"a 'non-existent myth' of a battle between
goddesses of the sun and the moon
for a mysterious blue diamond
that has the power to make
mortals immortal and vice versa"

"Moon River, wider than a mile…"

The most damaging and obstructive
cluster of ideas you face as a writer
are nearly all related to the idea of “flow.”

Like “genius.”

And “sincerity.”

And “inspiration.”

Distrust these words.

They stand for cherished myths,
but myths nonetheless.

— Verlyn Klinkenborg, 
"Several Short Sentences About Writing"       

"All she had to do was kick off and flow."

The Gameplayers of Zan

"I'se so silly to be flowing but I no canna stay."

Finnegans Wake

Tuesday, September 25, 2012

High White in the Dark Fields

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

"High white noon"

— Phrase of Don DeLillo and Josefine Lyche

"Spellbinding visuals dwarf weak characters."

Fox News review of Snow White and the Huntsman

For some stronger characters, see Limitless , a 2011 film 
based on a 2001 novel by Alan Glynn, The Dark Fields .

See also St. Andrew's Day 2011 in this journal.

Another Day

Filed under: General,Geometry — m759 @ 11:01 am

Verlyn Klinkenborg in yesterday's online New York Times

"Even metaphors — the best ones anyway —
are literal-minded. But that’s a story for another day."

Another day: May 18, 2010—

Part I: At Pomona College

"Writer-in-Residence Verlyn Klinkenborg '74
Writes Essay on Graduation for New York Times"
— Pomona College news item, May 18, 2010, by
   Laura Tiffany

Part II: In this journal



Note that the geometric diamond in the screenshot above
is not blue but black.

See also Pomona College under the topic Defining Form
in this journal.

Signs

Filed under: General — m759 @ 9:48 am

"And so the sentence ceases to be a sentence—
a verbal construct of a certain length, velocity and
rhythm with, at bottom, an unambiguous literal
meaning. It becomes a sign instead that telepathic
communication is about to commence."

— Verlyn Klinkenborg, "The Trouble With Intentions,"
     in The New York Times  last night at 9:30 PM ET

Other signs of the Times  (click to enlarge)—

Signs suggested by Klinkenborg's remarks—

Click the above image for further details.

Monday, September 24, 2012

Short Story

Filed under: General — Tags: — m759 @ 9:25 pm

Ad for the story—

JAWS  MEETS  MOSES:

IMAGE- NY Times front page- JAWS MEETS MOSES, or 'How Sharks Behave' and 'Reinventing Ethics'

The Story —

IMAGE- 'Ayn Sof,' title of a Log24 post on Jan. 7, 2011

Midbrow in Paris

Filed under: General — m759 @ 7:11 pm

"Middlebrow culture was killed in the late 50's and 60's,
and the mortal blows came from opposite directions.
The intellectuals launched assaults on what they took to be
middlebrow institutions, attacks that are so vicious
they take your breath away….

At the same time, pop culture changed."

David Brooks in The New York Times , June 16, 2005

"… but the fighter still remains" —Paul Simon

"James Joyce frequently presents climactic moments
of realization of life at the end of his stories; these
psychological revelations, called epiphanies, constitute
moments of heightened awareness which foment reflection
on the part of both the character and the readers, as well
as introduce an element of surprise."

The Telling and the Tale , by Gilda Pacheco Acuña
and Kari Meyers Skredsvig, Editorial Universidad
de Costa Rica
, 2006, page 11

For Scott and Ernest, from Julio —

"The novel wins by points and the short story by knockout."

Id.  (See also Feb. 8,  Beach Boy .)

Nice Job, Jimmy

Filed under: General — Tags: — m759 @ 9:29 am

"… and now thanks to Philo T. Farnsworth,
we have 'Here Comes Honey Boo Boo.'"

Jimmy Kimmel at last night's Emmy Awards

Related material—

Aldous Huxley in last evening's Log24 post—

"Embraced, the lovers desperately try
to fuse their insulated ecstasies into
a single self-transcendence…."

From an anonymous author at the website Kill Devil Hill

"This little story… has that climactic moment of
heightened awareness….  This is a moment where
two individuals become one, empowering them
to transcend the limitations of their own individual
frailty and society. It's an epiphany, an almost
divine spark. It is an experience when one plus one
don't equal two, but something far greater."

Kill Devil Hills also appears in a 1983 film

"Suppose it were possible to transfer
from one mind to another
the experience of another person."

Trailer for "Brainstorm" (1983),
     the last film of Natalie Wood

Sunday, September 23, 2012

Point Counterpoint

Filed under: General — Tags: — m759 @ 6:00 pm

"We live together, we act on, and react to, one another; but always and in all circumstances we are by ourselves. The martyrs go hand in hand into the arena; they are crucified alone. Embraced, the lovers desperately try to fuse their insulated ecstasies into a single self-transcendence; in vain. By its very nature every embodied spirit is doomed to suffer and enjoy in solitude. Sensations, feelings, insights, fancies – all these are private and, except through symbols and at second hand, incommunicable. We can pool information about experiences, but never the experiences themselves. From family to nation, every human group is a society of island universes. Most island universes are sufficiently like one another to permit of inferential understanding or even of mutual empathy or "feeling into." Thus, remembering our own bereavements and humiliations, we can condole with others in analogous circumstances, can put ourselves (always, of course, in a slightly Pickwickian sense) in their places. But in certain cases communication between universes is incomplete or even nonexistent. The mind is its own place, and the places inhabited by the insane and the exceptionally gifted are so different from the places where ordinary men and women live, that there is little or no common ground of memory to serve as a basis for understanding or fellow feeling. Words are uttered, but fail to enlighten. The things and events to which the symbols refer belong to mutually exclusive realms of experience."

The Doors of Perception

"Greet guests with a touch of glass."

The Perception of Doors

Plan 9 (continued)–

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

In Like Flynn

From the Wall Street Journal  site Friday evening—

ESSAY September 21, 2012, 9:10 p.m. ET

Are We Really Getting Smarter?

Americans’ IQ scores have risen steadily over the past century.
James R. Flynn examines why.

IMAGE- Raven's Progressive Matrices problem with ninth configuration a four-diamonds grid

No, thank you. I prefer the ninth configuration as is—

IMAGE- Four-diamonds grid, the ninth configuration in a Raven's Progressive Matrices problem

Why? See Josefine Lyche’s art installation “Grids, you say?

Her reference there to “High White Noon” is perhaps
related to the use of that phrase in this journal.

The phrase is from a 2010 novel by Don DeLillo.
See “Point Omega,” as well as Lyche’s “Omega Point,”
in this journal.

The Wall Street Journal  author above, James R. Flynn (born in 1934),
“is famous for his discovery of the Flynn effect, the continued
year-after-year increase of IQ scores in all parts of the world.”
Wikipedia

His son Eugene Victor Flynn is a mathematician, co-author
of the following chapter on the Kummer surface— 

For use of the Kummer surface in Buddhist metaphysics, see last night’s
post “Occupy Space (continued)” and the letters of Nanavira Thera from the
late 1950s at nanavira.blogspot.com.

These letters, together with Lyche’s use of the phrase “high white noon,”
suggest a further quotation

You know that it would be untrue
You know that I would be a liar
If I was to say to you
Girl, we couldn’t get much higher

See also the Kummer surface at the web page Configurations and Squares.

Saturday, September 22, 2012

Occupy Space

Filed under: General — Tags: , , — m759 @ 11:00 pm

(Continued)

"The word 'space' has, as you suggest, a large number of different meanings."

Nanavira Thera in [Early Letters. 136] 10.xii.1958

From that same letter (links added to relevant Wikipedia articles)—

Space (ākāsa) is undoubtedly used in the Suttas
to mean 'what/where the four mahābhūtas are not',
or example, the cavities in the body are called ākāsa
M.62—Vol. I, p. 423). This, clearly, is the everyday
'space' we all experience—roughly, 'What I can move
bout in', the empty part of the world. 'What you can't
ouch.' It is the 'space' of what Miss Lounsberry has so
appily described as 'the visible world of our five
senses'. I think you agree with this. And, of course, if
this is the only meaning of the word that we are
going to use, my 'superposition of several spaces' is
disqualified. So let us say 'superposition of several
extendednesses'. But when all these
extendednesses have been superposed, we get
'space'—i.e. our normal space-containing visible
world 'of the five senses'. But now there is another
point. Ākāsa is the negative of the four mahābhūtas,
certainly, but of the four mahābhūtas understood
in the same everyday sense—namely, solids (the
solid parts of the body, hair, nails, teeth, etc.),
liquids (urine, blood, etc.), heat and processes
(digestion) and motion or wind (N.B. not 'air').
These four, together with space, are the normal
furniture of our visible world 'of the five senses',
and it is undoubtedly thus that they are intended
in many Suttas. But there is, for example, a Sutta
(I am not sure where) in which the Ven. Sariputta
Thera is said to be able to see a pile of logs
successively as paṭhavi, āpo, tejo, and vāyo; and
it is evident that we are not on the same level.
On the everyday level a log of wood is solid and
therefore pathavi (like a bone), and certainly not
āpo, tejo, or vāyo. I said in my last letter that I
think that, in this second sense—i.e. as present in,
or constitutive of, any object (i.e. = rupa)—they
are structural and strictly parallel to nama and can
be defined exactly in terms of the Kummer
triangle. But on this fundamental level ākāsa has
no place at all, at least in the sense of our normal
everyday space. If, however, we take it as equivalent
to extendedness then it would be a given arbitrary
content—defining one sense out of many—of which
the four mahābhūtas (in the fundamental sense) are
the structure. In this sense (but only in this sense—
and it is probably an illegitimate sense of ākāsa)
the four mahābhūtas are the structure of space
(or spatial things). Quite legitimately, however, we
can say that the four mahābhūtas are the structure
of extended things—or of coloured things, or of smells,
or of tastes, and so on. We can leave the scientists'
space (full of right angles and without reference to the
things in it) to the scientists. 'Space' (= ākāsa) is the
space or emptiness of the world we live in; and this,
when analyzed, is found to depend on a complex
superposition of different extendednesses (because
all these extendednesses define the visible world
'of the five senses'—which will include, notably,
tangible objects—and this world 'of the five
senses' is the four mahābhūtas [everyday space]
and ākāsa).

Your second letter seems to suggest that the space
of the world we live in—the set of patterns
(superimposed) in which “we” are—is scientific space.
This I quite disagree with—if you do suggest it—,
since scientific space is a pure abstraction, never
experienced by anybody, whereas the superimposed
set of patterns is exactly what I experience—the set
is different for each one of us—, but in all of these
sets 'space' is infinite and undifferentiable, since it is,
by definition, in each set, 'what the four mahābhūtas
are not'. 

A simpler metaphysical system along the same lines—

The theory, he had explained, was that the persona
was a four-dimensional figure, a tessaract in space,
the elementals Fire, Earth, Air, and Water permutating
and pervolving upon themselves, making a cruciform
(in three-space projection) figure of equal lines and
ninety degree angles.

The Gameplayers of Zan ,
a 1977 novel by M. A. Foster

"I am glad you have discovered that the situation is comical:
 ever since studying Kummer I have been, with some difficulty,
 refraining from making that remark."

— Nanavira Thera, [Early Letters, 131] 17.vii.1958

Hook

Filed under: General — Tags: — m759 @ 1:20 pm

( Or: Occupy Space The Prequel  )

From this journal last year on November 19 and 18—

IMAGE- 'It frequently happens that the object offers a hook to the projection....' --Jung, with Natalie Wood in 'Brainstorm'

Friday, September 21, 2012

Trouble with the Curve

Filed under: General — Tags: , — m759 @ 7:00 pm

The Harvard Crimson  on last night's Ig Nobel Prize ceremony:

"The theme of the evening was 'The Universe,' a catchword
that had the audience cheering any time it was mentioned
throughout the night. Throughout the ceremony, a mini opera
entitled 'The Intelligent Designer and the Universe'* premiered
in four acts.

The opera’s final line was “This is how the Universe decays
into insanity.”

* An opera "about an insane wealthy man who bequeaths his
  fortune to have someone design a beautiful dress for the
  universe." —Mark Pratt, Associated Press

In related news…

"Most mysteries begin in confusion and end in certainty;
Pynchon likes to change this trajectory, so that what begins
a mystery ends as pure chaos. (Well aware how frustrating
some readers find this, Pynchon sets up a running gag in
Inherent Vice  about a class action suit brought against MGM
by audiences who don't like the way its stories end.)"

— Sarah Churchwell in The Guardian , Sunday, July 26, 2009

History

Filed under: General — m759 @ 9:48 am

Where Entertainment is God continues…

Excerpts from "Today in History,"
by The Associated Press,
for Friday, September 21, 2012

Today's Birthdays:
Poet-songwriter Leonard Cohen is 78.
Producer Jerry Bruckheimer is 69.
Author Stephen King is 65.
Actor-comedian Bill Murray is 62.

Thought for Today: "The crisis of yesterday
is the joke of tomorrow." — H.G. Wells, English author
(born this day in 1866, died 1946).

And the joke of yesterday?

Related material:
http://en.wikipedia.org/wiki/Al-Qiyama

Thursday, September 20, 2012

Immersion

Filed under: General — Tags: , , — m759 @ 9:29 am

      Part of a New York Times  banner ad last night—

IMAGE- 'Fashion Week: Immerse Yourself'

     (Fashion week dates 2012 — 
     New York Sept. 6-13, London Sept. 14-18,
     Milan Sept. 19-25, Paris Sept. 25-Oct. 3.)

     Some related prose suggested by a link in
     last night's Log24 post

The theory, he had explained, was that the persona
was a four-dimensional figure, a tessaract in space,
the elementals Fire, Earth, Air, and Water permutating
and pervolving upon themselves, making a cruciform
(in three-space projection) figure of equal lines and
ninety degree angles.

The Gameplayers of Zan , a novel by M. A. Foster

IMAGE- Immersion in a fictional vision of resurrection within a tesseract

      See also, if you can find a copy, Jeff Riggenbach's 
      "Science Fiction as Will and Idea," Riverside Quarterly 
       Vol. 5, No. 3 (whole number 19, August 1972, ed. by
       Leland Sapiro et al.), 168-177.

      Some background—
      Tuesday's Simple Skill and 4D Ambassador,
      as well as Now What? from May 23, 2012.

Wednesday, September 19, 2012

Game

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

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

 — The Gameplayers of Zan

"When Death tells a story
 you really have to listen."

The Book Thief , cover

Art Wars (continued)

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

Today's previous post, "For Odin's Day," discussed 
a mathematical object, the tesseract, from a strictly
narrative point of view.

In honor of George Balanchine, Odin might yield the
floor this evening to Apollo.

From a piece in today's online New York Times  titled
"How a God Finds Art (the Abridged Version)"—

"… the newness at the heart of this story,
in which art is happening for the first time…."

Some related art

IMAGE- Figure from Plato's Meno in version by Benjamin Jowett, Master of Balliol College, Oxford

and, more recently

This more recent figure is from Ian Stewart's 1996 revision 
of a 1941 classic, What Is Mathematics? , by Richard Courant
and Herbert Robbins.

Apollo might discuss with Socrates how the confused slave boy
of Plato's Meno  would react to Stewart's remark that

"The number of copies required to double an
 object's size depends on its dimension."

Apollo might also note an application of Socrates' Meno  diagram
to the tesseract of this afternoon's Odin post

.

For Odin’s Day*

Filed under: General — m759 @ 12:00 pm

(Mathematics and Narrative, continued)

"My dad has a great expression,"
Steve Sabol told USA TODAY Sports
last year. "He always says, 'Tell me
a fact, and I'll learn. Tell me the truth,
and I believe. But tell me a story,
and it will live in my heart forever.' "

Fact—

Sabol died yesterday.

Truth—

An art gallery in Oslo is exhibiting a tesseract.

Story—

The Jewel of Odin's Treasure Room

(Click to enlarge.)

* I.e., Wednesday. For some apt Nordic spirit,
   see Odin's Day 2012 Trailer.

Tuesday, September 18, 2012

4D Ambassador

Filed under: General — Tags: — m759 @ 1:00 pm

IMAGE- '4D Ambassador (Hypercube), 2012' by Josefine Lyche at The Boiler Room Gallery in Oslo

Simple Skill

Filed under: General — Tags: — m759 @ 10:18 am

But with good Will
To show our simple skill…

( Continued from Midsummer Eve, 1993 )

The "Black Diamond" search from Holy Cross Day 
leads to Talk Amongst Yourselves, which in turn
leads to PyrE in the Book, with Alfred Bester's
version of "Will and Idea."

This phrase may be regarded as a version of 
Schopenhauer's "Will and Representation."

Related material—

"Schopenhauer's notion of the will comes from the Kantian thing-in-itself, which Kant believed to be the fundamental reality behind the representation that provided the matter of perception, but lacked form. Kant believed that space, time, causation, and many other similar phenomena belonged properly to the form imposed on the world by the human mind in order to create the representation, and these factors were absent from the thing-in-itself. Schopenhauer pointed out that anything outside of time and space could not be differentiated, so the thing-in-itself must be one and all things that exist, including human beings, must be part of this fundamental unity. Our inner-experience must be a manifestation of the noumenal realm and the will is the inner kernel* of every being. All knowledge gained of objects is seen as self-referential, as we recognize the same will in other things as is inside us." —Wikipedia

* "Die Schrecken des Todes beruhen großentheils auf dem falschen Schein, daß jetzt das Ich verschwinde, und die Welt bleibe, Vielmehr aber ist das Gegentheil wahr: die Welt verschwindet; hingegen der innerste Kern des Ich, der Träger und Hervorbringer jenes Subjekts, in dessen Vorstellung allein die Welt ihr Daseyn hatte, beharrt." 

— Schopenhauer, Die Welt als Wille und Vorstellung , Kapitel 41

Added Nov. 16, 2012, a translation by E. F. J. Payne—

"The terrors of death rest for the most part on the false illusion that then the I or ego vanishes, and the world remains. But rather is the opposite true, namely that the world vanishes; on the other hand, the innermost kernel of the ego endures, the bearer and producer of that subject in whose representation alone the world had its existence."

THE WORLD AS WILL AND REPRESENTATION

by Arthur Schopenhauer
Translated from the German by E. F. J. Payne
In two volumes
© 1969 Dover Publications, Inc.
© 1958 by The Falcon's Wing Press

Volume Two: Supplements to the Fourth Book, 
XLI. On Death and Its Relation to the Indestructibility of Our Inner Nature

Monday, September 17, 2012

The Count

Filed under: General — Tags: , — m759 @ 11:01 pm
 

… I saw a shadow
sliding around the ropes
to get at me. The referee
moved it back, and then
went over and picked up the count.
"One!" The fog was clearing.

I rose to a knee,
and at "nine" to my feet.

— Louis Simpson, "The Appointment"

Simpson reportedly died on Holy Cross Day.

That day in this journal—

IMAGE- Log24 posts 'Please Mister Please' and 'Plan 9'

Pattern Conception

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

( Continued from yesterday's post FLT )

Context Part I —

"In 1957, George Miller initiated a research programme at Harvard University to investigate rule-learning, in situations where participants are exposed to stimuli generated by rules, but are not told about those rules. The research program was designed to understand how, given exposure to some finite subset of stimuli, a participant could 'induce' a set of rules that would allow them to recognize novel members of the broader set. The stimuli in question could be meaningless strings of letters, spoken syllables or other sounds, or structured images. Conceived broadly, the project was a seminal first attempt to understand how observers, exposed to a set of stimuli, could come up with a set of principles, patterns, rules or hypotheses that generalized over their observations. Such abstract principles, patterns, rules or hypotheses then allow the observer to recognize not just the previously seen stimuli, but a wide range of other stimuli consistent with them. Miller termed this approach 'pattern conception ' (as opposed to 'pattern perception'), because the abstract patterns in question were too abstract to be 'truly perceptual.'….

…. the 'grammatical rules' in such a system are drawn from the discipline of formal language theory  (FLT)…."

— W. Tecumseh Fitch, Angela D. Friederici, and Peter Hagoort, "Pattern Perception and Computational Complexity: Introduction to the Special Issue," Phil. Trans. R. Soc. B  (2012) 367, 1925-1932 

Context Part II —

IMAGE- Wikipedia article 'Formal language'

Context Part III —

A four-color theorem describes the mathematics of
general  structures, not just symbol-strings, formed from
four kinds of things— for instance, from the four elements
of the finite Galois field GF(4), or the four bases of DNA.

Context Part IV —

A quotation from William P. Thurston, a mathematician
who died on Aug. 21, 2012—

"It may sound almost circular to say that
what mathematicians are accomplishing
is to advance human understanding of mathematics.
I will not try to resolve this
by discussing what mathematics is,
because it would take us far afield.
Mathematicians generally feel that they know
what mathematics is, but find it difficult
to give a good direct definition.
It is interesting to try. For me,
'the theory of formal patterns'
has come the closest, but to discuss this
would be a whole essay in itself."

Related material from a literate source—

"So we moved, and they, in a formal pattern"

Formal Patterns—

Not formal language theory  but rather
finite projective geometry  provides a graphic grammar
of abstract design

IMAGE- Harvard Crimson ad, Easter Sunday, 2008: 'Finite projective geometry as a graphic grammar of abstract design'

See also, elsewhere in this journal,
Crimson Easter Egg and Formal Pattern.

Sunday, September 16, 2012

FLT

Filed under: General,Geometry — Tags: , , — m759 @ 8:28 pm

The "FLT" of the above title is not Fermat's Last Theorem,
but Formal Language Theory (see image below).

In memory of George A. Miller, Harvard cognitive psychologist, who
reportedly died at 92 on July 22, 2012, the first page of a tribute
published  shortly before his death

IMAGE- Design and Formal Language Theory

The complete introduction is available online. It ends by saying—

"In conclusion, the research discussed in this issue
breathes new life into a set of issues that were raised,
but never resolved, by Miller 60 years ago…."

Related material: Symmetry and Hierarchy (a post of 9/11), and
Notes on Groups and Geometry, 1978-1986 .

Happy Rosh Hashanah.

Sermon

Filed under: General — m759 @ 11:00 am

"I'm 18."

— Spoken by a very beautiful girl
      in the summer of 1991

"Work on what has been spoiled [ Decay ]."

Hexagram 18

IMAGE- Matchbook with monogram ROT from 'North by Northwest'

Click image for some background.

Master Class

Filed under: General — Tags: , — m759 @ 4:00 am

Wikipedia (links added)—

"Hubbard coined Dianetics  from the Greek stems dia ,
meaning through, and nous , meaning mind."

Log24 on August 30

"The snow kept falling on the world,
big white flakes like white gloves."

— Frederick Seidel, "House Master,"
poem in The New Yorker  of Sept. 3, 2012

Detail of Aug. 30 illustration, with added arrow—

IMAGE- Detail of large 'Search for the Lost Tesseract' image with Amy Adams, Richard Zanuck, 'snowflake' structure, and white gloves

  The part of the illustration at upper right is from a post of
  Friday, July 13th, 2012, on the death of producer Richard Zanuck.

  "Pay no attention to the shadow behind the curtain."

9/16

Filed under: General — m759 @ 2:01 am

Today's date suggests a review of
Incommensurables, a post of July 18, 2012.

Saturday, September 15, 2012

Jeremiad

Filed under: General — m759 @ 9:00 am

IMAGE- 'God goes Hollywood,' by Jeremiah Cullinane

Click for further details.

Some context—

Friday, September 14, 2012

Plan 9

Filed under: General — m759 @ 4:30 pm

(ContinuedA Meditation for Holy Cross Day )

Black Diamond in this journal
versus
Black Diamond at Harvard

IMAGE- The Harvard Crimson on the new Black Diamond investment club for students

Please Mister Please

Filed under: General — m759 @ 7:01 am

Quotations for a Memorial

"There is a body  on the cross in my church."

"Please Mister please, don't play B-17."

Thursday, September 13, 2012

Backstory

Filed under: General — m759 @ 2:00 am

Yesterday's online Los Angeles Times  
on a film that inspired recent protests in Cairo—

The film… was shown on June 23
to an audience of less than 10
at a theater on Hollywood Boulevard,
a source familiar with the screening said….
The screening was at The Vine Theater,
which rents itself out for private screenings,
said one person involved in the theater.

An image from this journal on that same day, June 23

IMAGE- Rudolf Koch's version of the 'double cross' symbol

    Source: Rudolf KochThe Book of Signs

For some background on the symbol, see Damnation Morning.

See also Don Henley's Hollywood hymn "Garden of Allah."

Update of 8 PM Sept. 13, 2012—

Other sources give the film's screening date not as June 23,
2012, but rather as June 30, 2012. (BBC News, LAWEEKLY blogs)

The following post from this journal on that  date may or
may not have some religious relevance.

Saturday, June 30, 2012

Snares

Filed under: Uncategorized — m759 @ 7:20 PM

"… 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 .

Wednesday, September 12, 2012

Class Act

Filed under: General — m759 @ 5:31 pm

Once in love with Amy

IMAGE- Harvard Class of 2016 arrives

Later…

IMAGE- 'Romney Goes the Full D'Souza,' with picture of D'Souza film '2016'

Review

Filed under: General — m759 @ 1:44 pm

A review of Max Bialystock's new smash hit,
"The Empty Chair"—

"Record-breaking!"

Where Madness Lies

Filed under: General — m759 @ 5:24 am

IMAGE- NYT obituaries-- psychiatrist Thomas Szasz and Broadway director Albert Marre-- with Stravinsky/Balanchine ad

    "Who knows where madness lies?" —Man of La Mancha

    "Hum a few bars and I'll fake it." —Stravinsky

Tuesday, September 11, 2012

Symmetry and Hierarchy

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

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

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

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

Monday, September 10, 2012

O for Origin

Filed under: General — m759 @ 6:00 pm

IMAGE- Roger O. Thornhill's monogrammed 'ROT' matchbook in 'North by Northwest'

Stanley Cavell on the film North by Northwest

"The 'nothing,' or naught, in the ROT monogram equally appropriately stands for origin, so its simultaneous meaning is that the actor is the origin of the character and also the origin of what becomes of himself or herself on film. The further thought that the human self as such is both an origin and a nothing is a bit of Cartesianism that is conceivably not called for in the context of this film."

Cavell on Film , SUNY Press, 2005, pp. 44-45

For another central O, see Four Gods in this journal.

The film's mistaken-identity plot involves a fictional character named Kaplan. For a real Kaplan, see a 2001 New Yorker  piece.

For a related catchphrase, see Kaplan Boo.

Sunday, September 9, 2012

Grid Compass

Filed under: General — Tags: — m759 @ 10:31 pm

IMAGE- Grid Systems designer of 'Grid Compass,' first laptop, dies at 69.

Related material:  The Empty Chair Award.

For a different sort of grid compass, see February 3, 2011.

Decomposition Sermon

Filed under: General,Geometry — m759 @ 11:00 am

(Continued from Walpurgisnacht 2012)

Wikipedia article on functional decomposition

"Outside of purely mathematical considerations,
perhaps the greatest value of functional decomposition
is the insight it provides into the structure of the world."

Certainly this is true for the sort of decomposition
known as harmonic analysis .

It is not, however, true of my own decomposition theorem,
which deals only with structures made up of at most four
different sorts of elementary parts.

But my own approach has at least some poetic value.

See the four elements of the Greeks in (for instance)
Eliot's Four Quartets  and in Auden's For the Time Being .

Saturday, September 8, 2012

Meritocracy

Filed under: General — Tags: — m759 @ 6:00 pm

(Continued)

"… the modern meritocracy dates only to the 1930s,
when Harvard President James Bryant Conant
directed his admissions staff to find a measure of
ability to supplement the old boys’ network. They
settled on the exam we know as the SAT."

— "Tyranny of Merit," by Samuel Goldman,
       a book review dated August 21, 2012

SAT

Filed under: General — Tags: — m759 @ 1:01 pm

The producer of the films "Gandhi," "City of Joy," 
and "The Legend of Bagger Vance"
reportedly died on Thursday, Sept. 6, 2012.

Film producer Jake Eberts is shown
on the set of "City of Joy" in 1991. 
(David Appleby photo, Los Angeles Times ,
with the Sanskrit word SAT added)

Thursday, September 6, 2012

Decomp Revisited

Filed under: General — m759 @ 1:11 pm

Frogs:

"Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time."

— Freeman Dyson (See July 22, 2011)

A Rhetorical Question:

Robert Osserman in 2004

"The past decade has been an exciting one in the world of mathematics and a fabulous one (in the literal sense) for mathematicians, who saw themselves transformed from the frogs of fairy tales— regarded with a who-would-want-to-kiss-that aversion, when they were noticed at all— into fascinating royalty, portrayed on stage and screen….

Who bestowed the magic kiss on the mathematical frog?"

A Rhetorical Answer:

http://www.log24.com/log/pix11C/111130-SunshineCleaning.jpg

Above: Amy Adams in "Sunshine Cleaning"

Related material:

Glory Road (continued)

Filed under: General,Geometry — m759 @ 7:59 am

"In ancient Greece, 9 was the number of the Muses,
patron goddesses of the arts. They were the daughters
of Mnemosyne ('memory'), the source
of imagination, which in turn is the carrier of archetypal,
elementary ideas to artistic realization in the field
of space-time. The number 9, that is to say, relates
traditionally to the Great Goddess of Many Names
(Devi, Inanna, Ishtar, Astarte, Artemis, Venus, etc.),
as matrix of the cosmic process, whether in the
macrocosm or in a microcosmic field of manifestation."

— Joseph Campbell in The Inner Reaches of Outer Space ,
      first published in 1986

From Robert A. Heinlein’s Glory Road  (1963):

Her face turned thoughtful. “Would you like to call me ‘Ettarre’?”

“Is that one of your names?”

“It is much like one of them, allowing for different spelling and accent.  Or it could be ‘Esther’ just as closely.  Or ‘Aster.’  Or even ‘Estrellita.’ “

” ‘Aster,’ ” I repeated. “Star. Lucky Star!”

Wednesday, September 5, 2012

Plan 9

Filed under: General — Tags: — m759 @ 9:00 am

(Continued from Up to Date, Aug. 28.)

Voyager 1 Story
By Amy Hubbard in the Los Angeles Times

September 4, 2012, 3:11 p.m. [PDT]

How long does it take to fly to the edge of
the solar system? At least 35 years. 
Voyager 1 is there now….

Related material—

IMAGE- Amy Hubbard in an Aug. 31, 2012, tweet- 'Dinga dong ding, Blue Moon.'

IMAGE- Joseph Campbell, 'The Inner Reaches of Outer Space,' meditation on the number nine, the Goddess, and the Angelus

      Dinga dong ding.

Tuesday, September 4, 2012

Dialogue

Filed under: General — m759 @ 5:31 pm

Quis custodiet?

Res ipsa loquitur.

But seriously…

Filed under: General — m759 @ 7:59 am

This post is continued from May 12, 2011.

See also another journal's post on that date
as well as some related posts here.

First we take Manhattan….

Up for Grabs

Filed under: General — Tags: — m759 @ 6:29 am

Deep background:  One Night in Bangkok.

IMAGE- Daily Beast headline: election is 'Up for Grabs'- Google News 6:06 AM EDT

See also…

The words she knows,
the tune she hums.

Monday, September 3, 2012

High Anxiety

Filed under: General — m759 @ 11:30 pm

IDEAS OF REFERENCE Department

New York Times  online front page, 11 PM EDT today—

IMAGE- NY Times, 'Music of the Upset Mind'

NOTE: 

The above Times  teaser on
"my obsessive-compulsive brain"
does not  refer to the initials "O.C.D."
in this morning's Log24 post "Hashtag E."
The source of those initials was not
"Obsessive-Compulsive Disorder," but
rather the phrase "Our Class, Dear" 
in a Sept. 3, 2012, New Yorker  poem —

IMAGE- Poem on Harvard in the 1950s

See also an August 30 post for Amy Adams.

Strategy

Filed under: General — m759 @ 11:02 pm

IMAGE- California Democratic chairman says GOP uses 'Big Lie' strategy.

Some background: 

The "big lie" strategy was originally described
by the National Socialists not as their own,
but  as the strategy of their enemies .

Hashtag E

Filed under: General — m759 @ 5:48 am

For Kristen

Hilary Swank in 'Million Dollar Baby'

O.C.D.          

Sunday, September 2, 2012

Washington Times

Filed under: General — m759 @ 8:16 pm

IMAGE- Washington Times founder died at 92 Sunday afternoon, Sept. 2, 2012, at about 12:54 PM EDT (Monday morning, 1:54 AM, Seoul time)

The Word in the Desert

Filed under: General — Tags: — m759 @ 3:09 am

(Continued)

For Trotsky's Birthday (Old Style), 2009—

IMAGE- Two Log24 posts, on Rosalind Krauss and on the occult, from Oct. 25, 2009

Related material:

IMAGE- Video- On the road to the U2 Rose Bowl concert of Oct. 25, 2009- 'Quest for the U2 Joshua Tree + Zabriskie'

IMAGE- NY Times Sept. 1, 2012, online obituary for Alexander Saxton, who died by his own hand on Aug. 20, 2012

(Click for further details.)

See also St. Stephen's Day, 2011.

Saturday, September 1, 2012

College of the Desert

Filed under: General — Tags: — m759 @ 6:08 am

(Continued from 6:08 AM EDT yesterday and the day before)

"Richard Elster was seventy-three, I was less than half his age. He’d invited me to join him here, old house, under-furnished, somewhere south of nowhere in the Sonoran Desert or maybe it was the Mojave Desert or another desert altogether.* Not a long visit, he’d said."

— Don DeLillo, Point Omega

IMAGE- Detail of John Ritter's NY Times illustration for Geoff Dyer's review of 'Point Omega,' plus link to Twitter beneath illustration

Maybe it was the desert near Twentynine Palms.

IMAGE- Twentynine Palms in Geoff Dyer's review of 'Point Omega'

"Sometimes a wind comes before the rain
and sends birds sailing past the window,
spirit birds that ride the night,
stranger than dreams."

— Ending of Point Omega

* Update of Sept. 2, 2012— A different passage yields a more precise location.

Friday, August 31, 2012

Translation

Filed under: General — Tags: — m759 @ 6:08 am

"Translation in the direction
conceptual -> concrete and symbolic
is much easier than
translation in the reverse direction…."

The late William P. Thurston

(See also "Atlas to the Text," Harvard Crimson , March 8, 2011).

Related cinematic imagery

Conceptual  (thanks to Don DeLillo and The New York Times )—

IMAGE- NY Times headline 'A Wrinkle in Time' with 24 Hour Psycho and Point Omega scene

Concrete and symbolic (thanks to Amy Adams and Emily Blunt, as well as
Frederick Seidel in the September 3, 2012, New Yorker )

"Biddies still cleaned the student rooms."

IMAGE- Shower wall in 'Sunshine Cleaning'

Thursday, August 30, 2012

The Cruelest Month

Filed under: General — Tags: — m759 @ 6:08 am

Last night's 10 PM post linked to an April 7, 2012,
post that through a series of further links leads
to Columbia Film Theory .

For other film-related remarks, by a
Columbia alumnus,* see last night's post.

See also the 1.3 MB image from Aug. 16, the night 
of Elvis's Wrap Party. An excerpt from that image
stars Amy Adams—

Images, including the late Richard Zanuck

For Amy, from the current New Yorker

The Master

* N.O.C.D.

Wednesday, August 29, 2012

It’s 10 PM…

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

Do you know where your children are?

Continued from Plan 9 , a Log24 post of  9 PM Monday

See another weblog's April 7, 2012, post on
God and Horror Movies.

See also this  weblog's post on that date.

Hexagram 18

Filed under: General — Tags: — m759 @ 9:14 am

(Continued from June 14, 2007)

The late William P. Thurston on how mathematical knowledge may decay:

"There are several obvious mechanisms of decay. The experts in a subject retire and die, or simply move on to other subjects and forget. Mathematics is commonly explained and recorded in symbolic and concrete forms that are easy to communicate, rather than in conceptual forms that are easy to understand once communicated. Translation in the direction conceptual -> concrete and symbolic is much easier than translation in the reverse direction, and symbolic forms often replaces [sic ] the conceptual forms of understanding. And mathematical conventions and taken-for-granted knowledge change, so older texts may become hard to understand.

In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths [sic ] life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining — they depend very heavily on the community of mathematicians."

At mathoverflow.net, October 30, 2010.
     The discussion has been "closed as no longer relevant."
     For another Thurston quote of interest, see a more recent
     mathoverflow discussion "closed as not a real question."

Tuesday, August 28, 2012

Dark and Stormy

Filed under: General — Tags: , — m759 @ 10:31 pm

It  was a  dark and stormy night.

A Wrinkle in Time  (brought  up to date)

Up to Date

Filed under: General — Tags: , , — m759 @ 9:29 pm

"Plato's cave was brought up to date in 1978…."

— Keith Devlin in Mathematics: The Science of Patterns

Related material from yesterday: Touchy-Feely and Plan 9.

"Plan 9 deals with the resurrection of the dead.

IMAGE- Bill Murray explains Ed Wood's 'Plan 9 from Outer Space'

For a rather different approach to Plato, see three posts of August 16, 2012—

Hope and Pope

Filed under: General — Tags: , , — m759 @ 4:59 am

IMAGE- 'Hope of Heaven,' by John O'Hara, 1947 Avon paperback

Hope of Heaven , by John O'Hara
Avon paperback edition, 1947

   Heaven from all creatures hides the book of Fate,
All but the page prescribed, their present state:
From brutes what men, from men what spirits know:
Or who could suffer being here below?
The lamb thy riot dooms to bleed to-day,
Had he thy reason, would he skip and play?
Pleased to the last, he crops the flowery food,
And licks the hand just raised to shed his blood.
Oh, blindness to the future! kindly given,
That each may fill the circle, marked by Heaven:
Who sees with equal eye, as God of all,
A hero perish, or a sparrow fall,
Atoms or systems into ruin hurled,
And now a bubble burst, and now a world.
   Hope humbly, then; with trembling pinions soar;
Wait the great teacher Death; and God adore.
What future bliss, He gives not thee to know,
But gives that hope to be thy blessing now.
Hope springs eternal in the human breast:
Man never is, but always to be blest:
The soul, uneasy and confined from home,
Rests and expatiates in a life to come.

— Alexander Pope in An Essay on Man

Monday, August 27, 2012

Plan 9

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

(Continued)

IMAGE- 'The Ninth Configuration,' based on a novel by William Peter Blatty

See also "Or Only Die" and Corpus Hypercubus .

Touchy-Feely

Filed under: General — Tags: , , — m759 @ 5:24 am

A remark by the late William P. Thurston

Please note: I'm not advocating that
we turn mathematics into a touchy-feely subject.

Noted. But see this passage—

The Mathematical Experience , by Philip J. Davis and Reuben Hersh (1981), updated study edition, Springer, 2011—

From the section titled "Four-Dimensional Intuition," pages 445-446:

"At Brown University Thomas Banchoff, a mathematician, and Charles Strauss, a computer scientist, have made computer-generated motion pictures of a hypercube….

… at the Brown University Computing Center, Strauss gave me a demonstration of the interactive graphic system which made it possible to produce such a film….

… Strauss showed me how all these controls could be used to get various views of three-dimensional projections of a hypercube. I watched, and tried my best to grasp what I was looking at. Then he stood up, and offered me the chair at the control.

I tried turning the hypercube around, moving it away, bringing it up close, turning it around another way. Suddenly I could feel  it!. The hypercube had leaped into palpable reality, as I learned how to manipulate it, feeling in my fingertips the power to change what I saw and change it back again. The active control at the computer console created a union of kinesthetics and visual thinking which brought the hypercube up to the level of intuitive understanding."

Thanks to the Web, a version of this experience created by Harry J. Smith
has been available to non-academics for some time.

IMAGE- The Harry J. Smith Memorial Tesseract

IMAGE- From 'Touchy-Feely: The Musical!'

Saturday, August 25, 2012

One Small Step

Filed under: General — Tags: — m759 @ 8:19 pm

Click image for some related material.

Illogical Songs*

Filed under: General — m759 @ 1:00 pm

IMAGE- Ship Ahoy

     Image from the New York Times Book Review  of August 26.
     See also a related song for Marxists who like Brecht.
     For some lighter entertainment, see a 1942 movie trailer.

* A sequel to today's noon post Logical Song (itself suggested
   by a Chautauqua, NY, end-of season event)

Logical Song

Filed under: General — m759 @ 12:00 pm

" Und ein Schiff mit acht Segeln…"

Seeräuber Jenny

For the Feast of Saint Louis

" Oed' und leer das Meer "

— Eliot, The Waste Land , from
     Wagner, Tristan und Isolde

Für Seeräuber Jenny

Filed under: General — m759 @ 2:01 am

See…

  1. Tonight's New York Times  obituaries —
    with an ad for a Terracotta Warriors  exhibit
  2. "Turn the page" in this  journal
  3. "A Page is a Door," by Remy Charlip
  4. Wendy Derleth in "Wishmaster."

Des Todes*

Filed under: General — m759 @ 1:22 am

For a racecar driver who reportedly died in
Orange, California, on August 12— 

"Never one to take it slow, Grant was also an avid boater,
motorcyclist and aerobatic pilot. He last rode his motorcycle,
a BMW R1200R, on July 12."

"I love those Bavarians… so meticulous."

"The 'Valley of Death' is the oldest
concentration camp memorial in Bavaria."

* German for "Of Death."
   For a different Todes, see an obituary of a poet.
   See also Rosetta Jacobs in this journal.

Friday, August 24, 2012

Down for the Count

Filed under: General — m759 @ 8:00 pm

IMAGE- Jerry Nelson, voice of Count von Count, is dead at 78.

"For every kind of vampire…"

IMAGE- Eight-pointed star formed by the four symmetry axes of the square

Midnight in Geneva

Filed under: General — m759 @ 6:00 pm

Six PM EDT is midnight CEST in Geneva.

For the late Marvin W. Meyer, professor at Chapman
University in Orange, California, and a graduate
of Calvin College in Grand Rapids, Michigan…

A ticket out of town .

(Some background: Marilynne Robinson.)

Formal Pattern

Filed under: General,Geometry — m759 @ 4:28 pm

(Continued from In Memoriam (Aug. 22), Chapman's Homer (Aug. 23),
and this morning's Colorful Tale)

An informative, but undated, critique of the late Marvin W. Meyer
by April D. DeConick at the website of the Society of Biblical Literature
appeared in more popular form in an earlier New York Times
op-ed piece, "Gospel Truth," dated Dec. 1, 2007.

A check, in accord with Jungian synchronicity, of this  journal
on that date yields a quotation from Plato's Phaedrus  —

"The soul or animate being has the care of the inanimate."

Related verses from T. S. Eliot's Four Quartets

"The detail of the pattern is movement."

"So we moved, and they, in a formal pattern."

Some background from pure mathematics (what the late
William P. Thurston called "the theory of formal patterns")—

The Animated Diamond Theorem.

A Colorful Tale

Filed under: General,Geometry — Tags: — m759 @ 6:06 am

(Continued from July 19, 2008)

From the Diamond 16 Puzzle

IMAGE- The Diamond 16 Puzzle

The resemblance between the "quadrants" part of
the above picture and the new Microsoft symbol

IMAGE- New Microsoft symbol, August 2012

— is of course purely coincidental, as is the fact
that the new symbol illustrates four colors.

Thursday, August 23, 2012

Chapman’s Homer

Filed under: General,Geometry — Tags: , — m759 @ 9:48 am

Louis Sahagun in today's Los Angeles Times

The late Professor Marvin W. Meyer

 "was our Indiana Jones,"  said James L. Doti,
president of Chapman University in Orange,
where Meyer held the Griset Chair in Bible
and Christian Studies and was director of
the Albert Schweitzer Institute.

Meyer reportedly died on August 16.

IMAGE- The late Professor Marvin W. Meyer of Chapman University in Orange, CA, with the university's emblem, the eight-pointed star

Thursday, August 16, 2012

Semiotics

m759 @ 4:00 AM

IMAGE- Eight-pointed star formed by the four symmetry axes of the square

"Two clichés make us laugh, but
a hundred clichés move us
because we sense dimly that the clichés
are talking among themselves and
celebrating a reunion."

— Umberto Eco

"'Casablanca': Cult Movies and Intertextual Collage,"
by Umberto Eco in SubStance , Vol. 14, No. 2, Issue 47:
In Search of Eco's Roses  (1985), pp. 3-12.

(This paper was presented at a symposium,
"Semiotics of the Cinema: The State of the Art,"
in Toronto on June 18, 1984.)
Journal article published by U. of Wisconsin Press.
Stable URL: http://www.jstor.org/stable/3685047.

Click image for some related material.

Midnight Again

Filed under: General — m759 @ 12:00 am

See tonight's leading obituaries 
from The New York Times .

Wednesday, August 22, 2012

In Memoriam

Filed under: General — m759 @ 9:48 pm

IMAGE- Cornell mathematics department on the death of William P. Thurston on Aug. 21, 2012

A quotation from William P. Thurston,
who died yesterday—

"It may sound almost circular to say that
what mathematicians are accomplishing
is to advance human understanding of mathematics.
I will not try to resolve this
by discussing what mathematics is,
because it would take us far afield.
Mathematicians generally feel that they know
what mathematics is, but find it difficult
to give a good direct definition.
It is interesting to try. For me,
'the theory of formal patterns'
has come  the closest, but to discuss this
would be a whole essay in itself."

Related material from a literate source

"So we moved, and they, in a formal pattern"

— and from a different source, cached shortly after midnight 
on the (GMT) date of Thurston's death —

(Click for Google Cache information and to enlarge.)

Detail from the above Math Overflow discussion— 

IMAGE- A four-diamond pattern

The Company

Filed under: General — m759 @ 2:48 pm

IMAGE- Thurston obit at ams.org

Relativity Blues

Filed under: General — m759 @ 12:21 pm

(Continued from the day of Hunter S. Thompson's suicide)

See "The First Church of Marilynne Robinson."

(The New Yorker , May 30, 2012)

About the People

Filed under: General — m759 @ 3:28 am

(Continued from March 28, 2001)

"Hillbillies, Okies, Arkies—  they're all the same people."

— Hunter S. Thompson, Hell's Angels

Related cinematic art:

Hunger Games (2012)

Winter’s Bone (2010)—

For John Denver*

Filed under: General — m759 @ 1:01 am

A followup

* Of "Country Roads"

Midnight Special

Filed under: General — m759 @ 12:00 am

Coltrane, not coal train.

See also a children's version.

Tuesday, August 21, 2012

Methods

Filed under: General — Tags: — m759 @ 4:59 pm

From the July 28, 2012, post "Hey"—

"You know my methods."

Domino

Filed under: General — Tags: , — m759 @ 6:25 am

Last night's 2:01 AM post suggests …

Inaction Film

Filed under: General — Tags: — m759 @ 2:01 am

It could be worse.

Monday, August 20, 2012

Extended Metaphor

Filed under: General — Tags: — m759 @ 5:17 am

The Washington Post  on yesterday's presidential Sunday—

"Accompanied by his wife, Michelle, and daughters
Sasha and Malia on the mild, overcast morning,
Obama walked through Lafayette Square
to St. John’s Episcopal Church.

The Rev. Michael Angell delivered a sermon
from John 6 about the extended metaphor
of eating Jesus’ flesh….

The Obamas, all wearing shades of blue,
participated in Holy Communion before
motorcading back to the White House."

In related news—

" We praised him and then we ate him,
all courtesy of a generous catering budget
from film director Tony Scott."

— "Death in the Center Ring:
      Timothy Leary's High Dive,"
      by Douglas Rushkoff, May 13, 2008

See also…

Sunday, August 19, 2012

O Marks the Spot

Filed under: General — m759 @ 9:00 pm

(Continued :  See Identity,  decomposition, and Sunshine Cleaning . )

"What, one might ask, does the suave, debonaire
Roger Thornhill have to do with the notion of
decomposition (emphasized by the unusual
coffin-shaped 'O') implied in the acronym
formed by his initials?" 

— Paul Gordon, Dial "M" for Mother ,
     Fairleigh Dickinson University Press, 2008, page 97

"To stay with the context of Cavell's brilliant reading 
of the film's relation to Hamlet, 'there is something rot -ten
in North by Northwest ' that also needs to be explained."

— Paul Gordon, op. cit., page 98

Related remarks— Sunday morning, May 20, 2007.

Identity

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

On the middle initial of the Cary Grant character
in yesterday's post Summer Reading

IMAGE- Matchbook with initials ROT in 'North by Northwest'

Click image for further details.

"The concept of nothingness follows Roger Thornhill throughout North by Northwest , first as another identity imposes itself upon him and later as circumstances force him to run from Vandamm as well as the police. When Eve asks him what the 'O' in 'ROT' stands for, Thornhill can only answer 'nothing.' His middle initial's lack of meaning connects well to the overall theme of the human self as possibly nothing." —Hitchcock and Identity, by Emily Pilgrim

Related material— Elementary Finite Geometry (Aug. 1).

See, too, a post for Holy Cross Day in 2002.

Saturday, August 18, 2012

Nightmare Alley

Filed under: General — m759 @ 11:00 pm

"History instructs. History also has
a very dark sense of humor.
Irish history, especially."

John Kelly in The Daily Beast  this morning

See also Joyce's Nightmare and
Nightmare Alley in this journal.

Summer Reading

Filed under: General — m759 @ 2:56 pm

On the author of a novel published August 14th,
 "Where'd You Go, Bernadette"—

"Semple moved to the Pacific Northwest several years ago
seeking refuge from Los Angeles, but that doesn't mean
that the Emerald City gets a free pass from Semple's
sharp, satirical eye." 

— Stewart Oksenhorn yesterday in The Aspen Times

Related art

IMAGE- 3x3 grid of movie stills with 'North by Northwest' at center

See also a detail from Thursday's 1.3 MB image
"Search for the Lost Tesseract"—

Update of 9 PM EDT (6 PM LA time) the same day, Saturday, Aug. 18—

IMAGE- Cover of 'This One Is Mine,' a novel by Maria Semple

Actually, that one is hers.

Centre

Filed under: General — m759 @ 4:01 am

"Art indeed, so far from being
a playful diversion of the human race,
is the place of its most fundamental insight,
and the centre to which the more uncertain
steps of metaphysics must constantly return"

— Iris Murdoch, "On 'God' and 'Good,'" in
Existentialists and Mystics , Penguin Books,
1999, page 360

Related material —

Wendy Derleth

" 'In the West,' she observed, 'anything that must be hidden
is suspect; availability and honesty are interlinked. This clashes
irreconcilably with Islam… where the things that are
most precious, most perfect and most holy are always hidden….' "

— Pauls Toutonghi, review of a recent novel, Alif the Unseen

(page BR19, New York Times Sunday Book Review , August 12, 2012

Friday, August 17, 2012

Hidden

Filed under: General,Geometry — Tags: , — m759 @ 12:25 pm

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

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

Another figure—

IMAGE- Serbian chess innovator Svetozar Gligoric dies at 89

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

From this journal on that date

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

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

Thursday, August 16, 2012

Royal Wrap

Filed under: General — Tags: — m759 @ 11:00 pm

For Elvis's Wrap Party 
  ( image, 1.3 MB )

Raiders of the Lost Tesseract

Filed under: General,Geometry — Tags: — m759 @ 8:00 pm

(Continued from August 13. See also Coxeter Graveyard.)

Coxeter exhuming Geometry

Here the tombstone says
"GEOMETRY… 600 BC — 1900 AD… R.I.P."

In the geometry of Plato illustrated below,
"the figure of eight [square] feet" is not , at this point
in the dialogue, the diamond in Jowett's picture.

An 1892 figure by Jowett illustrating Plato's Meno

Jowett's picture is nonetheless of interest for
its resemblance to a figure drawn some decades later
by the Toronto geometer H. S. M. Coxeter.

A similar 1950 figure by Coxeter illustrating a tesseract

For a less scholarly, but equally confusing, view of the number 8,
see The Eight , a novel by Katherine Neville.

The Ninth Year

Filed under: General — Tags: — m759 @ 2:01 pm

A passage from the Benjamin Jowett translation of Plato's Meno

" 'For in the ninth year* Persephone sends the souls of those from whom she has received the penalty of ancient crime back again from beneath into the light of the sun above, and these are they who become noble kings and mighty men and great in wisdom and are called saintly heroes in after ages  .' The soul, then, as being immortal, and having been born again many times, and having seen all things that exist, whether in this world or in the world below, has knowledge of them all; and it is no wonder that she should be able to call to remembrance all that she ever knew about virtue, and about everything; for as all nature is akin, and the soul has learned all things; there is no difficulty in her eliciting or as men say learning, out of a single recollection all the rest, if a man is strenuous and does not faint; for all enquiry and all learning is but recollection."

* See this journal nine years ago, in August 2003.
 Jowett's note— "Pindar, Frag. 98 (Boeckh)"

Wikipedia authors like Protious, an alleged resident of Egypt and 
creator of The Socrates Swastika , may enjoy a less scholarly account:

From Babylon A. D.  (a 2008 film)— Toorop with Egyptian Sacred Scarab tattoo—           

— and Toorop with Aurora (who may be regarded as "the soul" in the Meno  passage above)—

Toorop's neck tattoo in the second image above is from a fictional book
described in the writings of H. P. Lovecraft.

As swastika-like sacred symbols go, I prefer St. Bridget's Cross.

Semiotics

Filed under: General — Tags: — m759 @ 4:00 am

"Two clichés make us laugh, but
a hundred clichés move us
because we sense dimly that the clichés
are talking among themselves and
celebrating a reunion."

Umberto Eco

"'Casablanca': Cult Movies and Intertextual Collage,"
by Umberto Eco in SubStance , Vol. 14, No. 2, Issue 47:
In Search of Eco's Roses  (1985), pp. 3-12.
(This paper was presented at a symposium,
"Semiotics of the Cinema: The State of the Art,"
in Toronto on June 18, 1984.)
Journal article published by U. of Wisconsin Press.
Stable URL: http://www.jstor.org/stable/3685047.

Click image for some related material.

Wednesday, August 15, 2012

Levity

Filed under: General — m759 @ 6:29 pm

(Continued)

"Here, Bochner plays with these elements with the philosophical levity that made Conceptual art (which art historians see Bochner as one of the kingpins) so refreshing, graceful, and funny, especially after a generation of painters made artmaking seem so serious, heavy, emotional." —ArtSlant.com

See also The Wikipedia Meno  and Bochner in this journal.

Tuesday, August 14, 2012

Hacking 1984

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

Ian Hacking in 1984

"… 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 by using a proof in geometry to argue for the transmigration of souls. As reported by Plato in Meno , the boy who invents a proof of a theorem did not experiment on the physical world, but used only his mind in response to Socratic questions. Hence he must have had inborn knowledge of the proof and he must have got this knowledge in a previous incarnation.

Mathematics has never since been a subject for such philosophical levity."

See also this afternoon's post.

Space Odyssey

Filed under: General — m759 @ 1:00 pm

(An episode of Art Wars )

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

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

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

Philip Kennicott, quoted here on July 22, 2012

See also today's date in 2003.

Monday, August 13, 2012

Something Between

Filed under: General — m759 @ 6:07 pm

"I am a skeptic to whom the idea that a benign God 
created us and watches over us is something between
a fairy story and a bad joke." 

— The late art critic Robert Hughes in Things I Didn't Know*

A followup to this afternoon's previous Amy Adams post—

"Here was finality indeed, and cleavage!" 

             — Under the Volcano

     * Vintage paperback, December 2007, page 7

Raiders of the Lost Tesseract

Filed under: General,Geometry — Tags: — m759 @ 3:33 pm

(An episode of Mathematics and Narrative )

A report on the August 9th opening of Sondheim's Into the Woods

Amy Adams… explained why she decided to take on the role of the Baker’s Wife.

“It’s the ‘Be careful what you wish’ part,” she said. “Since having a child, I’m really aware that we’re all under a social responsibility to understand the consequences of our actions.” —Amanda Gordon at businessweek.com

Related material—

Amy Adams in Sunshine Cleaning  "quickly learns the rules and ropes of her unlikely new market. (For instance, there are products out there specially formulated for cleaning up a 'decomp.')" —David Savage at Cinema Retro

Compare and contrast…

1.  The following item from Walpurgisnacht 2012

IMAGE- Excerpt from 'Unified Approach to Functional Decompositions of Switching Functions,' by Marek A. Perkowski et al., 1995

2.  The six partitions of a tesseract's 16 vertices 
       into four parallel faces in Diamond Theory in 1937

Sunday, August 12, 2012

Doctor Who

Filed under: General,Geometry — m759 @ 2:00 pm

On Robert A. Heinlein's novel Glory Road

"Glory Road  (1963) included the foldbox , a hyperdimensional packing case that was bigger inside than outside. It is unclear if Glory Road  was influenced by the debut of the science fiction television series Doctor Who  on the BBC that same year. In Doctor Who , the main character pilots a time machine called a TARDIS, which is built with technology which makes it 'dimensionally transcendental,' that is, bigger inside than out."

— Todd, Tesseract article at exampleproblems.com

From the same exampleproblems.com article—

"The connection pattern of the tesseract's vertices is the same as that of a 4×4 square array drawn on a torus; each cell (representing a vertex of the tesseract) is adjacent to exactly four other cells. See geometry of the 4×4 square."

For further details, see today's new page on vertex adjacency at finitegeometry.org.

Thursday, August 9, 2012

Just Once

Filed under: General — m759 @ 5:18 am

IMAGE- Dr. James West, a recovering alcoholic who became Betty Ford Center director, died at 98 on July 24, 2012

In Dr. West's memory…

Wednesday, August 8, 2012

Quadruple Bypass

Filed under: General — m759 @ 9:29 pm

"The first human to walk on the moon, Neil Armstrong,
is 'doing great' after undergoing cardiac bypass surgery,
his wife reported…..

… Armstrong… went to the hospital on Monday
for a stress test. He flunked, and on Tuesday,
surgeons bypassed four blockages in his
coronary arteries. His wife reports that his spirits
are high, and the doctors expect no problems
with his recovery…." — Alan Boyle, NBCNews.com

Over the life of Man
We watch and wait,
The Four who manage
His fallen estate:

We who are four were
Once but one,
Before his act of
Rebellion;

We were himself when
His will was free,
His error became our
Chance to be.

Powers of air and fire,
Water and earth,
Into our hands is given
Man from his birth….

Auden, not Goethe

See also Tuesday morning's post.

Tuesday was Charlize Theron's birthday.
See June 9, 2012.

Tuesday, August 7, 2012

The Space of Horizons

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 am

"In the space of horizons that neither love nor hate"
— Wallace Stevens, "Things of August"

Seven years ago yesterday—

IMAGE- 3x3 grid related to Borofsky's 'Four Gods'

For some context, see Rosetta Stone as a Metaphor.

Related material from the University of Western Australia

Projective plane of order 3

(The four points on the curve
at the right of the image are
the points on the line at infinity.)

Art critic Robert Hughes,  who nearly died in Western
Australia in a 1999 car crash, actually met his death
yesterday at Calvary Hospital in the Bronx.

See also Hughes on "slow art" in this journal.

Sunday, August 5, 2012

Cube Partitions

Filed under: General,Geometry — Tags: , , , — m759 @ 7:59 am

The second Logos  figure in the previous post
summarized affine group actions on partitions
that generate a group of about 1.3 trillion
permutations of a 4x4x4 cube (shown below)—

IMAGE by Cullinane- 'Solomon's Cube' with 64 identical, but variously oriented, subcubes, and six partitions of these 64 subcubes

Click for further details.

Thursday, August 2, 2012

Logos

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

(Continued from December 26th, 2011)

IMAGE- Current math.stackexchange.com logo and a 1984 figure from 'Notes on Groups and Geometry, 1978-1986'

Some material at math.stackexchange.com related to
yesterday evening's post on Elementary Finite Geometry

Questions on this topic have recently been
discussed at Affine plane of order 4? and at
Turning affine planes into projective planes.

(For a better discussion of the affine plane of order 4,
see Affine Planes and Mutually Orthogonal Latin Squares
at the website of William Cherowitzo, professor at UC Denver.)

Wednesday, August 1, 2012

Triple Feature

Filed under: General — m759 @ 11:11 pm

IMAGE- Triple Feature: 'Twelve Monkeys,' Reagan National Airport on July 31, 2012, and 'Die Hard 2'

For related material, see this morning's post Defining Form.

Elementary Finite Geometry

Filed under: General,Geometry — Tags: , , , — m759 @ 7:16 pm

I. General finite geometry (without coordinates):

A finite affine plane of order has n^2 points.

A finite projective plane of order n  has n^2 + n + 1 

points because it is formed from an order-n finite affine 

plane by adding a line at infinity  that contains n + 1 points.

Examples—

Affine plane of order 3

Projective plane of order 3

II. Galois finite geometry (with coordinates over a Galois field):

A finite projective Galois plane of order n has n^2 + n + 1

points because it is formed from a finite affine Galois 3-space

of order n with n^3 points by discarding the point (0,0,0) and 

identifying the points whose coordinates are multiples of the

(n-1) nonzero scalars.

Note: The resulting Galois plane of order n has 

(n^3-1)/(n-1)= (n^2 + n + 1) points because 

(n^2 + n + 1)(n – 1) =

(n^3 + n^2 + n – n^2 – n – 1) = (n^3 – 1) .
 

III. Related art:

Another version of a 1994 picture that accompanied a New Yorker
article, "Atheists with Attitude," in the issue dated May 21, 2007:

IMAGE- 'Four Gods,' by Jonathan Borofsky

The Four Gods  of Borofsky correspond to the four axes of 
symmetry
  of a square and to the four points on a line at infinity 
in an order-3 projective plane as described in Part I above.

Those who prefer literature to mathematics may, if they like,
view the Borofsky work as depicting

"Blake's Four Zoas, which represent four aspects
of the Almighty God" —Wikipedia

Defining Form

Filed under: General — m759 @ 11:01 am

Continued from July 29 in memory of filmmaker Chris Marker,
who reportedly* died on that date at 91 at his home in Paris.

See Slides and Chantingand Where Madness Lies.

See also Sherrill Grace on Malcolm Lowry.

* Washington Post. Other sources say Marker died on July 30.

 These notably occur in Marker's masterpiece
     La Jetée (review with spoilers).

Gore Vidal

Filed under: General — m759 @ 1:09 am

IMAGE- Gore Vidal has died.

IMAGE- Gore Vidal at Movie Nation

Tuesday, July 31, 2012

Happy Birthday, J. K. Rowling

Filed under: General — Tags: — m759 @ 10:31 pm

IMAGE- Google Book Search for 'Malcom Lowry' + 'thinking of treadmills'

See also a July 19 death, this journal on that date, and
Down the Up Staircase.

Logo

Filed under: General,Geometry — Tags: , — m759 @ 2:18 pm

IMAGE- 'Yankee Puzzle' quilt block pattern on cover of Northrop Frye's 'Anatomy of Criticism'

On Universals and
A Passage to India
 :
 
"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."
 
– Betty Jay, reader's guide to A Passage to India

http://www.log24.com/log/pix08/080413-Marabar.jpg

Judy Davis in the Marabar Caves

The above image is from this journal on Sunday, April 13, 2008.

The preceding cover of a book by Northrop Frye was suggested
by material in this journal from February 2003.

See also Yankee Puzzle and Doodle Dandy.

Monday, July 30, 2012

Logos

Filed under: General — m759 @ 10:48 pm

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.

Geometry and Death

Filed under: General,Geometry — m759 @ 2:23 pm

(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.

Something to Read

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

(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:

Olivier as Dr. Christian Szell

The icosahedron (a source of duads and synthemes)

Is it safe?"

 Annals of Art Education: 
     Geometry and Death

Unnecessary* Truth?

Filed under: General — m759 @ 12:26 pm

"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

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