Log24

Saturday, August 10, 2019

Muse Score

Filed under: General — m759 @ 1:55 PM

Tuesday, April 2, 2019

The Core Experience

Filed under: General — m759 @ 3:21 PM

"It never occurred to me that someone could so explicitly reject
the core experience of something like Chartres."

— Christopher Alexander to Peter Eisenman, 1982

For a less dramatic core experience , see Hitchcock.

Thursday, September 28, 2017

Core

Filed under: General,Geometry — Tags: — m759 @ 4:01 PM

From the New York Times Wire  last night —

"Mr. Hefner styled himself as an emblem
of the sexual revolution."

From a Log24 post on September 23 —

A different emblem related to other remarks in the above Sept. 23 post

On the wall— A Galois-geometry 'inscape'

(On the wall — a Galois-geometry inscape .)

Saturday, July 8, 2017

Common Core

Filed under: General — m759 @ 6:00 PM

Monday, April 3, 2017

Even Core

Filed under: General,Geometry — Tags: , — m759 @ 9:16 PM

4x4x4 gray cube

http://www.log24.com/log/pix11A/110625-CubeHypostases.gif

Odd Core

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

 

3x3x3 Galois cube, gray and white

Tuesday, December 13, 2016

Core

Filed under: General — Tags: — m759 @ 6:06 PM

More recently

Click the above image for some backstory.

Saturday, September 24, 2016

Core Structure

Filed under: General,Geometry — Tags: — m759 @ 6:40 AM

For the director of "Interstellar" and "Inception"

At the core of the 4x4x4 cube is …

 


                                                      Cover modified.

The Eightfold Cube

Wednesday, August 24, 2016

Core Statements

Filed under: General,Geometry — Tags: — m759 @ 1:06 PM

"That in which space itself is contained" — Wallace Stevens

An image by Steven H. Cullinane from April 1, 2013:

The large Desargues configuration of Euclidean 3-space can be 
mapped canonically to the 4×4 square of Galois geometry —

'Desargues via Rosenhain'- April 1, 2013- The large Desargues configuration mapped canonically to the 4x4 square

On an Auckland University of Technology thesis by Kate Cullinane —
On Kate Cullinane's book 'Sample Copy' - 'The core statement of this work...'
The thesis reportedly won an Art Directors Club award on April 5, 2013.

Friday, July 1, 2016

Transparent Core

Filed under: General — m759 @ 2:28 PM

"At the point of convergence the play of similarities and differences
cancels itself out in order that identity alone may shine forth.
The illusion of motionlessness, the play of mirrors of the one:
identity is completely empty; it is a crystallization and
in its transparent core the movement of analogy begins all over
once again." — The Monkey Grammarian  by Octavio Paz,
translated by Helen Lane 

A more specific "transparent core" —

See all references to this figure
in this journal.

For a more specific "monkey grammarian," 
see W. Tecumseh Fitch in this journal.

Sunday, June 26, 2016

Common Core versus Central Structure

Filed under: General,Geometry — Tags: , — m759 @ 2:56 PM

Rubik's Cube Core Assembly — Swarthmore Cube Project, 2008 —

"Children of the Common Core" —

There is also a central structure within Solomon's  Cube

'Children of the Central Structure,' adapted from 'Children of the Damned'

For a more elaborate entertainment along these lines, see the recent film

"Midnight Special" —

Friday, June 12, 2015

Core

Filed under: General — m759 @ 12:00 AM
 
Grindhouse Madonna ,
 
Children at your feet.

Thursday, April 9, 2015

Core Values

Filed under: General,Geometry — m759 @ 10:20 AM

"Yankee Doodle went to London" — Song lyric

  November Man

Geometry was very important to us in this movie.”

— The Missing ART   (Log24, November 7th, 2014)

ART —

"Faculty Approve Theater Concentration, Affirmation
of Integrity" — Recent Harvard Crimson  headline

Thursday, February 5, 2015

Core Problem

Filed under: General — Tags: — m759 @ 9:48 AM

(As opposed to "The Hard Problem")

Sharon Gaudin at computerworld.com
on artificial intelligence (AI) today—

"Google's [Geoffrey] Hinton said he's most excited
about gains in neural networks that would enable
computers to understand the content of sentences
and documents.

'That is close to the core of Google because
it involves understanding sentences, and if you can
understand what a document is saying, you can do
a much better search,' Hinton said. 'That's a core
AI problem. Can you read a document and know
what it's saying?'" 

Sometimes. How about you?

Tuesday, December 30, 2014

Core

Filed under: General — m759 @ 1:11 PM

JOSEFINE LYCHE
ABSOLUTE ALT. VOL. 2
17. april – 23. mai [2015] —

"I kjernen av mitt arbeid er en pågående
utforskning av esoteriske konsepter…."

"At the core of my work is an ongoing
exploration of esoteric concepts…."

See also 
http://issuu.com/tmrk/docs/spritenkunsthall_2015_cut .

Related material:  Hard Core.

Sunday, September 21, 2014

Uncommon Noncore

Filed under: General,Geometry — m759 @ 10:30 AM

This post was suggested by Greg Gutfeld’s Sept. 4 remarks on Common Core math.

Problem: What is 9 + 6 ?

Here are two approaches suggested by illustrations of Desargues’s theorem.

Solution 1:

9 + 6 = 10 + 5,
as in Common Core (or, more simply, as in common sense), and
10 + 5 = 5 + 10 = 15 as in Veblen and Young:

Solution 2:

In the figure below,
9 + 6 = no. of  V’s + no. of  A’s + no. of C’s =
no. of nonempty squares = 16 – 1 = 15.
(Illustration from Feb. 10, 2014.)

The silly educationists’ “partner, anchor, decompose” jargon
discussed by Gutfeld was their attempt to explain “9 + 6 = 10 + 5.”

As he said of the jargon, “That’s not math, that’s the plot from ‘Silence of the Lambs.'”

Or from Richard, Frank, and Marcus in last night’s “Intruders”
(BBC America, 10 PM).

Saturday, July 5, 2014

Core Curriculum Vocabulary:

Filed under: General — Tags: — m759 @ 5:01 PM

Separatrix  and  Mulligan

An image from this journal on September 16, 2013:

Carey Mulligan as a separatrix

IMAGE- Kipnis on Derrida's 'separatrix'

Mulligan:

“A mulligan, in a game, happens when a player gets a second chance
to perform a certain move or action.” — Wikipedia

New York Times  obituary for Richard Mellon Scaife:

“He had the caricatured look of a jovial billionaire promoting ‘family values’
in America: a real-life Citizen Kane with red cheeks, white hair, blue eyes and
a wide smile for the cameras. Friends called him intuitive but not intellectual.
He told Vanity Fair  his favorite TV show was ‘The Simpsons,’ and his favorite
book was John O’Hara’s  Appointment in Samarra , about a rich young
Pennsylvanian bent on self-destruction.” — Robert D. McFadden

Click image below for some nuclear family values in memory of Scaife:

See also the previous post,
Core Curriculum.

Core Curriculum

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

This post was suggested by reviews of the David Hare play “Skylight” at
The New York Times , at WorldSocialism.org, and at ChicagoCritic.com.

 Vide  Atoms in the Family , by Laura Fermi, a book I read in high school.

Thursday, July 3, 2014

Core Mathematics: Arrays

Filed under: General — m759 @ 11:00 AM

Mathematics vulgarizer Keith Devlin on July 1
posted an essay on Common Core math education.

His essay was based on a New York Times story from June 29,
Math Under Common Core Has Even Parents Stumbling.”

An image from that story:

The Times  gave no source, other than the photographer’s name,
for the above image.  Devlin said,

“… the image of a Common Core math worksheet
the Times  chose to illustrate its story showed
a very sensible, and deep use of dot diagrams,
to understand structure in arithmetic.”  

Devlin seems ignorant of the fact that there is
no such thing as a “Common Core math worksheet.”
The Core is a set of standards without  worksheets
(one of its failings).

Neither the Times  nor whoever filled out the worksheet
nor Devlin seemed to grasp that the image the Times  used
shows some multiplication word problems that are more
advanced than the topic that Devlin called the
“deep use of dot diagrams to understand structure in arithmetic.”

This Core topic is as follows:

For some worksheets that are  (purportedly) relevant, see,
for instance…

http://search.theeducationcenter.com/search/
_Common_Core_Label-2.OA.C.4–keywords-math_worksheets,
in particular the worksheet
http://www.theeducationcenter.com/editorial_content/multipli-city:

Some other exercises said to be related to standard 2.OA.C.4:

http://www.ixl.com/standards/
common-core/math/grade-2

The Common Core of course fails to provide materials for parents
that are easily findable on the Web and that give relevant background
for the above second-grade topic.  It leaves this crucial task up to
individual states and school districts, as well as to private enterprise.
This, and not the parents’ ignorance described in  Devlin’s snide remarks,
accounts for the frustration that the Times  story describes.

Friday, February 28, 2014

Score

Filed under: General — m759 @ 9:00 PM

"Once a verbal structure is read, and reread
often enough to be possessed, it 'freezes.'
It turns into a unity in which all parts exist at
once, without regard to the specific movement
of the narrative. We may compare it to the study
of a music score, where we can turn to any
part without regard to sequential performance."

— Northrop Frye in The Great Code

Astronaut Dale Gardner, shown retrieving a satellite, reportedly died at 65.

Gardner reportedly died at 65 on February 19.
A post linked to here on that date suggests some
musical remarks.

Saturday, May 11, 2013

Invariant Core

Filed under: General — m759 @ 11:00 PM

The title is from today's noon post, Core.

It also appears, quoted from Popovič, in Susan Bassnett's
Translation Studies  (third edition, Routledge, 2002)—

"It is an established fact in Translation Studies that if a dozen
translators tackle the same poem, they will produce a dozen
different versions. And yet somewhere in those dozen versions there
will be what Popovič calls the ‘invariant core’ of the original poem.
This invariant core, he claims, is represented by stable, basic and
constant semantic elements in the text, whose existence can be
proved by experimental semantic condensation. Transformations, or
variants, are those changes which do not modify the core of meaning
but influence the expressive form. In short, the invariant can be
defined as that which exists in common between all existing
translations of a single work. So the invariant is part of a dynamic
relationship and should not be confused with speculative arguments
about the ‘nature’, the ‘spirit’ or ‘soul’ of the text; the ‘indefinable
quality’ that translators are rarely supposed to be able to capture."

"A writer hopes to leave behind a work no one forgets…."

Song sung on NBC's Smash  tonight

Fulsere vere candidi mihi soles….

— André Weil, The Apprenticeship of a Mathematician

nam unguentum dabo, quod meae puellae
donarunt Veneres Cupidinesque….

Catullus, quoted in Bassnett's Translation Studies

http://www.log24.com/log/pix11C/111210-Wiig-Perfume.jpg

Vale puella, iam Catullus obdurat.

Core

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

Promotional description of a new book:

"Like Gödel, Escher, Bach  before it, Surfaces and Essences  will profoundly enrich our understanding of our own minds. By plunging the reader into an extraordinary variety of colorful situations involving language, thought, and memory, by revealing bit by bit the constantly churning cognitive mechanisms normally completely hidden from view, and by discovering in them one central, invariant core— the incessant, unconscious quest for strong analogical links to past experiences— this book puts forth a radical and deeply surprising new vision of the act of thinking."

"Like Gödel, Escher, Bach  before it…."

Or like Metamagical Themas

Rubik core:

Swarthmore Cube Project, 2008

Non- Rubik cores:

Of the odd  nxnxn cube:

Of the even  nxnxn cube:

The image “http://www.log24.com/theory/images/cube2x2x2.gif” cannot be displayed, because it contains errors.

Related material: The Eightfold Cube and

"A core component in the construction
is a 3-dimensional vector space  over F."

—  Page 29 of "A twist in the M24 moonshine story," 
      by Anne Taormina and Katrin Wendland.
      (Submitted to the arXiv on 13 Mar 2013.)

Friday, October 11, 2019

The Flynn Legacy

Filed under: General — Tags: — m759 @ 9:26 PM

TRON Legacy: back door

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— 

Sunday, September 22, 2019

Colorful Tale

Filed under: General — Tags: , — m759 @ 7:59 PM

“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”

— Hermann Weyl, Philosophy of  Mathematics and
    Natural Science 
, Princeton, 1949, p. 237

"The bond with reality is cut."

— Hans Freudenthal, 1962

Indeed it is.

From page 180, Logicomix — It was a dark and stormy night

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

Saturday, June 15, 2019

Actionable Daydream

Filed under: General — m759 @ 11:26 PM

— Kastalia Medrano, "The Art of Space Art," Sept. 14, 2017

Ghost in the Shell

Wednesday, June 5, 2019

Time Cube

Filed under: General — m759 @ 11:02 AM

The opening lines of Eliot's Four Quartets

"Time present and time past
Are both perhaps present in time future,
And time future contained in time past."

Perhaps.

Those who prefer geometry to rhetoric may also prefer
to Eliot's lines the immortal opening of the Transformers  saga —

"Before time began, there was the Cube."

One version of the Cube —

Tuesday, May 14, 2019

Surrealistic Pillow Talk

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

   "Plan 9 deals with the resurrection of the dead.

IMAGE- Bill Murray explains Ed Wood's 'Plan 9 from Outer Space'- 'Plan 9 deals with the resurrection of the dead.'


"When the men on the chessboard
get up and tell you where to go . . ."

Saturday, May 4, 2019

The Chinese Jars of Shing-Tung Yau

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

The title refers to Calabi-Yau spaces.

T. S. Eliot —

Four Quartets

. . . Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.

A less "cosmic" but still noteworthy code — The Golay code.

This resides in a 12-dimensional space over GF(2).

Related material from Plato and R. T. Curtis

Counting symmetries with the orbit-stabilizer theorem

A related Calabi-Yau "Chinese jar" first described in detail in 1905

Illustration of K3 surface related to Mathieu moonshine

A figure that may or may not be related to the 4x4x4 cube that
holds the classical  Chinese "cosmic code" — the I Ching

ftp://ftp.cs.indiana.edu/pub/hanson/forSha/AK3/old/K3-pix.pdf

Friday, March 29, 2019

The Blazon World*

Filed under: General — m759 @ 4:59 PM

“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

* Title suggested by that of a Siri Hustvedt novel.
   See also Blazon in this journal.

Tuesday, March 5, 2019

A Block Design 3-(16,4,1) as a Steiner Quadruple System:

Filed under: General — Tags: , — m759 @ 11:19 AM

A Midrash for Wikipedia 

Midrash —

Related material —


________________________________________________________________________________

The Miracle Octad Generator (MOG), the affine 4-space over GF(2), and the Cullinane diamond theorem

Tuesday, February 26, 2019

Ghost in the Shell

Filed under: General — m759 @ 12:00 AM

Wednesday, October 17, 2018

Aesthetics

Filed under: General,Geometry — Tags: — m759 @ 11:22 AM
 

From "The Phenomenology of Mathematical Beauty,"
by Gian-Carlo Rota —

The Lightbulb Mistake

. . . . Despite the fact that most proofs are long, and despite our need for extensive background, we think back to instances of appreciating mathematical beauty as if they had been perceived in a moment of bliss, in a sudden flash like a lightbulb suddenly being lit. The effort put into understanding the proof, the background material, the difficulties encountered in unraveling an intricate sequence of inferences fade and magically disappear the moment we become aware of the beauty of a theorem. The painful process of learning fades from memory, and only the flash of insight remains.

We would like  mathematical beauty to consist of this flash; mathematical beauty should  be appreciated with the instantaneousness of a lightbulb being lit. However, it would be an error to pretend that the appreciation of mathematical beauty is what we vaingloriously feel it should be, namely, an instantaneous flash. Yet this very denial of the truth occurs much too frequently.

The lightbulb mistake is often taken as a paradigm in teaching mathematics. Forgetful of our learning pains, we demand that our students display a flash of understanding with every argument we present. Worse yet, we mislead our students by trying to convince them that such flashes of understanding are the core of mathematical appreciation.

Attempts have been made to string together beautiful mathematical results and to present them in books bearing such attractive titles as The One Hundred Most Beautiful Theorems of Mathematics . Such anthologies are seldom found on a mathematician’s bookshelf. The beauty of a theorem is best observed when the theorem is presented as the crown jewel within the context of a theory. But when mathematical theorems from disparate areas are strung together and presented as “pearls,” they are likely to be appreciated only by those who are already familiar with them.

The Concept of Mathematical Beauty

The lightbulb mistake is our clue to understanding the hidden sense of mathematical beauty. The stark contrast between the effort required for the appreciation of mathematical beauty and the imaginary view mathematicians cherish of a flashlike perception of beauty is the Leitfaden  that leads us to discover what mathematical beauty is.

Mathematicians are concerned with the truth. In mathematics, however, there is an ambiguity in the use of the word “truth.” This ambiguity can be observed whenever mathematicians claim that beauty is the raison d’être of mathematics, or that mathematical beauty is what gives mathematics a unique standing among the sciences. These claims are as old as mathematics and lead us to suspect that mathematical truth and mathematical beauty may be related.

Mathematical beauty and mathematical truth share one important property. Neither of them admits degrees. Mathematicians are annoyed by the graded truth they observe in other sciences.

Mathematicians ask “What is this good for?” when they are puzzled by some mathematical assertion, not because they are unable to follow the proof or the applications. Quite the contrary. Mathematicians have been able to verify its truth in the logical sense of the term, but something is still missing. The mathematician who is baffled and asks “What is this good for?” is missing the sense  of the statement that has been verified to be true. Verification alone does not give us a clue as to the role of a statement within the theory; it does not explain the relevance  of the statement. In short, the logical truth of a statement does not enlighten us as to the sense of the statement. Enlightenment , not truth, is what the mathematician seeks when asking, “What is this good for?” Enlightenment is a feature of mathematics about which very little has been written.

The property of being enlightening is objectively attributed to certain mathematical statements and denied to others. Whether a mathematical statement is enlightening or not may be the subject of discussion among mathematicians. Every teacher of mathematics knows that students will not learn by merely grasping the formal truth of a statement. Students must be given some enlightenment as to the sense  of the statement or they will quit. Enlightenment is a quality of mathematical statements that one sometimes gets and sometimes misses, like truth. A mathematical theorem may be enlightening or not, just as it may be true or false.

If the statements of mathematics were formally true but in no way enlightening, mathematics would be a curious game played by weird people. Enlightenment is what keeps the mathematical enterprise alive and what gives mathematics a high standing among scientific disciplines.

Mathematics seldom explicitly acknowledges the phenomenon of enlightenment for at least two reasons. First, unlike truth, enlightenment is not easily formalized. Second, enlightenment admits degrees: some statements are more enlightening than others. Mathematicians dislike concepts admitting degrees and will go to any length to deny the logical role of any such concept. Mathematical beauty is the expression mathematicians have invented in order to admit obliquely the phenomenon of enlightenment while avoiding acknowledgment of the fuzziness of this phenomenon. They say that a theorem is beautiful when they mean to say that the theorem is enlightening. We acknowledge a theorem’s beauty when we see how the theorem “fits” in its place, how it sheds light around itself, like Lichtung — a clearing in the woods. We say that a proof is beautiful when it gives away the secret of the theorem, when it leads us to perceive the inevitability of the statement being proved. The term “mathematical beauty,” together with the lightbulb mistake, is a trick mathematicians have devised to avoid facing up to the messy phenomenon of enlightenment. The comfortable one-shot idea of mathematical beauty saves us from having to deal with a concept that comes in degrees. Talk of mathematical beauty is a cop-out to avoid confronting enlightenment, a cop-out intended to keep our description of mathematics as close as possible to the description of a mechanism. This cop-out is one step in a cherished activity of mathematicians, that of building a perfect world immune to the messiness of the ordinary world, a world where what we think should be true turns out to be true, a world that is free from the disappointments, ambiguities, and failures of that other world in which we live.

How many mathematicians does  it take to screw in a lightbulb?

Tuesday, July 31, 2018

Lexicon

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

"A blank underlies the trials of device." — Wallace Stevens

IMAGE- The ninefold square .

Sunday, June 24, 2018

For 6/24

Filed under: General,Geometry — Tags: — m759 @ 10:12 AM

A clue to the relationship between the Kummer (16, 6)
configuration and the large Mathieu group M24

Related material —

See too the diamond-theorem correlation.

Thursday, March 1, 2018

The Movement of Analogy: Hume vs. Paz

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

Hume, from posts tagged "four-set" in this journal —

"The mind is a kind of theatre, where several perceptions
successively make their appearance; pass, repass, glide away,
and mingle in an infinite variety of postures and situations.
There is properly no simplicity in it at one time, nor identity
in different, whatever natural propension we may have
to imagine that simplicity and identity."

Paz, from a search for Paz + Identity in this journal —

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by Helen Lane 

Wednesday, February 7, 2018

Conceptual Minimalism

Filed under: General,Geometry — m759 @ 10:08 AM

 

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by Helen Lane 

See also AS IS.

Friday, November 24, 2017

Scholia

Filed under: General — m759 @ 11:00 PM

From this evening's online New York Times : 

"Eric Salzman, a composer and music critic who
championed a new art form, music theater,
that was neither opera nor stage musical, died
on Nov. 12 at his home in Brooklyn. He was 84."

. . . .

"The first American Music Theater Festival 
took place in the summer of 1984.

Among that first festival’s featured works was 
'Strike Up the Band!,' Mr. Salzman’s 'reconstructed
and adapted' version of a satirical musical
with a score by George and Ira Gershwin
that had not been staged in 50 years. The director
of that production, Frank Corsaro, died 
the day before Mr. Salzman did."

Synchronology check :

"The day before" above was November 11, 2017.

Links from this  journal  on November 11

A Log24 search for Michael Sudduth and an 
October 28, 2017, Facebook post by Sudduth.

Detail of Sudduth's Nov. 11 Facebook home page

Click the above for an enlarged view of the Sudduth profile picture.

Related material :

Harold Schonberg, 1977 review of Corsaro production of Busoni's 'Dr. Faust'

Aooo.

Friday, November 10, 2017

A Mathematician’s Apology

Filed under: General — m759 @ 4:00 PM

(Click to enlarge.)

For the paper on Steiner systems, see the bibliographic link in
the previous Log24 post.

See as well Cameron's posts before and after his post above:

     .

Annals of Rarefied Scholarship

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

From Cambridge Core, suggested by a reference to
that website in the previous post and by the following
bibliographic data . . .

https://doi.org/10.1017/fmp.2016.5

Downloaded from https://www.cambridge.org/core
on 10 Nov 2017 at 19:06:19 

See Conwell + Princeton in this journal.

Related art —

Thursday, October 26, 2017

A Center

Filed under: General,Geometry — m759 @ 8:40 PM

This post was suggested by a New York Times  obituary this evening —

"Tom Mathews, Promoter of Liberal Causes and Candidates, Dies at 96."

Mathews reportedly died on October 14, 2017.

"Mr. Mathews and his business partner Roger Craver 'dreamed for years
of finding the perfect citizen-candidate,' the authors wrote, 'a man or
woman of the center-left with a feel for issues, a history of independence,
a winning television manner and, most important of all, a center — a core
of beliefs more important to him or her than getting elected.'

Dream on.

From the date of Mathews's death:

Posts now tagged A Center for Krauss

"Let no one ignorant of geometry enter"

Tuesday, October 17, 2017

Status Symbols

Filed under: General,Geometry — Tags: — m759 @ 2:02 PM

"Status: Defunct"  

As is now its owner, who reportedly
died at 80 on Sunday, October 15, 2017.

In memoriam —

Excerpts from Log24 posts on Sunday night 
and yesterday evening

http://www.log24.com/log/pix11/110203-Scholia.jpg.

" … listen: there's a hell
of a good universe next door; let's go"

— e. e. cummings

Some literary background —

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by Helen Lane 

Sunday, September 24, 2017

Figures

Filed under: General — m759 @ 8:30 PM

"On April 23, 2009 ….

'I’m reminded of the character in "The Silence of the Lambs," 
Hannibal Lecter, a very brilliant man,' the prosecutor said,
recognizing 'his ability to intelligently and articulately discuss
things occurring in society.'

'But at his core, as with Mr. Lecter at his core, he is a sociopath,' 
the prosecutor said."

— David Stout in an obituary from this evening's online
New York Times

See also this  journal on April 23, 2009, and
a figure from this morning's link Cantina —

 .

Saturday, September 23, 2017

The Turn of the Frame

Filed under: General,Geometry — Tags: , , — m759 @ 2:19 AM

"With respect to the story's content, the frame thus acts
both as an inclusion of the exterior and as an exclusion
of the interior: it is a perturbation of the outside at the
very core of the story's inside, and as such, it is a blurring
of the very difference between inside and outside."

— Shoshana Felman on a Henry James story, p. 123 in
"Turning the Screw of Interpretation,"
Yale French Studies  No. 55/56 (1977), pp. 94-207.
Published by Yale University Press.

See also the previous post and The Galois Tesseract.

Friday, August 18, 2017

The Savvy Philosophers

Filed under: General — m759 @ 1:37 PM

Flashback in Genial, a post of March 6, 2017 —

From a New York Times  book review today by
James Ryerson, instructor at The School of The New York Times —

"Savvy philosophers distill their core insight into a short phrase."

"Let them eat cake."

Thursday, July 27, 2017

Keeping It Simple

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

Michiko Kakutani in The New York Times

"The detective story genre concerns the finding of clues
and the search for hidden designs, and its very form
underscores Mr. Pynchon’s obsession with conspiracies
and the existence of systems too complicated to understand."

Review of Pynchon's Bleeding Edge , Sept. 10, 2013

Background:  "Moss on the Wall," this  journal on that date.

A less complicated system —

"Plan 9 deals with the resurrection of the dead."

— Bill Murray in "Ed Wood"
 

For The Church of Plan 9

(The plan , as well as the elevation ,
of the above structure is a 3×3 grid.)

Monday, July 10, 2017

Under Bleu Cup

Filed under: General — m759 @ 10:00 AM

Publishers Weekly  on a Nov. 1, 2011, book, Under Blue Cup

"Krauss’s core argument (what she deems a 'crusade')
is that the 'white cube,' which conceptual and installation
artists have deemed obsolete, actually thrives."

For other "core arguments," see Satuday's post "Common Core"
and the Art Space posts "Odd Core" and "Even Core."

Wednesday, June 28, 2017

Maori Farewell

Filed under: General — m759 @ 3:33 PM

The second editor mentioned below reportedly died
on June 21, 2017.  A page in his memory —

See also "Detail for Hopkins" in this journal on June 21.
For a Maori finale, see "De Haut en Bas " (July 11, 2008).

Friday, May 26, 2017

Day at the Museum

Filed under: General — m759 @ 12:00 PM

From the 1994 film review linked to above —

Reality Bites – Peter Travers in Rolling Stone , Feb. 1994

"Life after college – the time between graduation and
finding a job that pays your rent without making you puke.
Panic time. By spinning something fresh out of something
familiar, Reality Bites  scores the first comedy knockout of
the new year. It also brings out the vibrant best in Winona
Ryder and Ethan Hawke as friends who resist being lovers,
makes a star of Janeane Garofalo as their tart-tongued
buddy and puts Ben Stiller on the map as a director." 

Thursday, April 27, 2017

Partner, Anchor, Decompose

Filed under: General,Geometry — Tags: — m759 @ 12:31 PM

See also a figure from 2 AM ET April 26 

" Partner, anchor, decompose. That's not math.
That's the plot to 'Silence of the Lambs.' "

Greg Gutfeld, September 2014

Monday, March 27, 2017

Groundhog Day and After

Filed under: General — m759 @ 3:13 PM

A reader suspects Coretta Scott King letter is a forgery

See also "Damning" in this journal on Feb. 8, 2017.

Monday, February 20, 2017

Mathematics and Narrative

Filed under: General,Geometry — Tags: , — m759 @ 2:40 PM

Mathematics —

Hudson's parametrization of the
4×4 square, published in 1905:

A later parametrization, from this date in 1986:

http://www.log24.com/log/pix11/110220-relativprob.jpg

A note from later in 1986 shows the equivalence of these
two parametrizations:

Narrative —

Posts tagged Memory-History-Geometry.

The mathematically challenged may prefer the narrative of the
Creation Matrix from the religion of the Transformers:

"According to religious legend, the core of the Matrix
was created from Solomus, the god of wisdom,
trapped in the form of a crystal by Mortilus, the god
of death. Following the defeat of Mortilus, Solomus
managed to transform his crystal prison into the Matrix—
a conduit for the energies of Primus, who had himself
transformed into the life-giving computer Vector Sigma."

Friday, February 17, 2017

Fake News: The Definition

Filed under: General — m759 @ 11:15 AM

See also, on Feb. 8 in this journal, Damning.

Sunday, February 12, 2017

Colorful Tales

Filed under: General — m759 @ 1:23 PM

“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”

— Hermann Weyl, Philosophy of  Mathematics and
    Natural Science 
, Princeton, 1949, p. 237

Harvard University Press on the late Angus Fletcher, author of
The Topological Imagination  and Colors of the Mind

From the Harvard webpage for Colors of the Mind

Angus Fletcher is one of our finest theorists of the arts,
the heir to I. A. Richards, Erich Auerbach, Northrop Frye.
This… book…  aims to open another field of study:
how thought— the act, the experience of thinking—
is represented in literature.

. . . .

Fletcher’s resources are large, and his step is sure.
The reader samples his piercing vision of Milton’s

Satan, the original Thinker,
leaving the pain of thinking
as his legacy for mankind.

A 1992 review by Vinay Dharwadker of Colors of the Mind —

See also the above word "dianoia" in The Echo in Plato's Cave.
Some context 

This post was suggested by a memorial piece today in
the Los Angeles Review of Books

A Florilegium for Angus Fletcher

By Kenneth Gross, Lindsay Waters, V. N. Alexander,
Paul Auster, Harold Bloom, Stanley Fish, K. J. Knoespel,
Mitchell Meltzer, Victoria Nelson, Joan Richardson,
Dorian Sagan, Susan Stewart, Eric Wilson, Michael Wood

Fletcher reportedly died on November 28, 2016.

"I learned from Fletcher how to apprehend
the daemonic element in poetic imagination."

— Harold Bloom in today's Los Angeles florilegium

For more on Bloom and the daemonic, see a Log24 post,
"Interpenetration," from the date of Fletcher's death.

Some backstory:  Dharwadker in this journal.

Wednesday, February 8, 2017

Damning

Filed under: General — m759 @ 9:42 PM

BuzzFeed, Tuesday, January 10, 2017, on "the damning letter"—

From the Jan. 10 BuzzFeed story

At the time of the hearing, Judiciary Committee Chairman Strom Thurmond never put the letter into the congressional record, and its contents remained largely unknown. In the only line that was made public at the time — published in June 1986 by Knight Ridder reporter Aaron Epstein — King made clear her opposition to Sessions’ nomination.

“For a century, the racial practices that characterized our region were established and enforced by men who, like Mr. Sessions, protested that they, too, were not personally hostile to blacks,” King’s letter said, according to Epstein’s dispatch.

A searchable text of the alleged 1986 letter, along with the
alleged attached statement, is now available at
https://www.aol.com/article/news/2017/02/08/
coretta-scott-kings-letter-opposing-jeff-sessions-1986-full-text/21709762/
.

A search of the letter and statement at that webpage yields
no instances of the phrases "racial practices," "established and enforced,"
or "personally hostile."

Hence the word "alleged" above.

Update of 1:44 PM ET on Feb. 9, 2017:

A relevant Wikipedia article —
Questioned document examination.

Tuesday, February 7, 2017

Authority Figure

Filed under: General — m759 @ 3:09 PM

Accepting for Professor Corey Thomas Pynchon.

Saturday, January 28, 2017

Cranking It Up

Filed under: General — m759 @ 12:17 PM

From "Core," a post of St. Lucia's Day, Dec. 13, 2016 —

'We are rooted in yoga and love the magic that happens when that practice is cranked up to eleven.'

In related news yesterday —

California yoga mogul’s mysterious death:
Trevor Tice’s drunken last hours detailed

"Police found Tice dead on the floor in his home office,
blood puddled around his head. They also found blood
on walls, furniture, on a sofa and on sheets in a nearby
bedroom, where there was a large bottle of Grey Goose
vodka under several blood-stained pillows on the floor."

See as well an image from "The Stone," a post of March 18, 2016 —

Some backstory —

“Lord Arglay had a suspicion that the Stone would be
purely logical.  Yes, he thought, but what, in that sense,
were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

Sunday, January 15, 2017

Career Event

Filed under: General — m759 @ 1:29 PM

See also related remarks.

Sunday, January 8, 2017

A Theory of Everything

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

The title refers to the Chinese book the I Ching ,
the Classic of Changes .

The 64 hexagrams of the I Ching  may be arranged
naturally in a 4x4x4 cube. The natural form of transformations
("changes") of this cube is given by the diamond theorem.

A related post —

The Eightfold Cube, core structure of the I Ching

Monday, September 5, 2016

Space Case

Filed under: General — m759 @ 2:00 PM

The New York Times  yesterday evening —

Michel Butor dies at 89

Butor reportedly died on August 24.

This journal on that date —

From Butor's obituary —

"He studied philosophy at the Sorbonne
under the phenomenologist
Gaston Bachelard, writing a thesis on
mathematics and the idea of necessity."

"In 2013 the Académie Française awarded
Mr. Butor its Grand Prix for his life’s work.

Explaining his philosophy in an interview
with the critic and television producer
Georges Charbonnier in 1965, Mr. Butor said,
'Every written word is a victory over death.' "

A search for Bachelard in this journal yields remarks
related to Bachelard's Poetics of Space  and to the above
phrase by Wallace Stevens.

Thursday, August 25, 2016

Diamond on the Map

Filed under: General — Tags: — m759 @ 4:38 PM

A check of Cora Diamond, editor of the 1976 Wittgenstein
book shown in the previous post, yields …

The date of the above talk was April 3, 2015.

For this journal on that date,  see a link, "by Steven H. Cullinane,"
in yesterday's post Core Statements.

Monday, August 8, 2016

A Point of Identity

Filed under: General — m759 @ 6:00 PM

For a  Monkey Grammarian  (Viennese Version)

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by Helen Lane 

A logo that may be interpreted as one-eighth of a 2x2x2 array
of cubes —

The figure in white above may be viewed as a subcube representing,
when the eight-cube array is coordinatized, the identity (i.e., (0, 0, 0)).

Shown below are a few variations on the figure by VCQ,
the Vienna Center for Quantum Science and Technology —
 

(Click image to enlarge.)

Thursday, August 4, 2016

Routine

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

Peter Gelzinis in the Boston Herald  today

"What has become painfully clear this week
is that there is no Republican campaign for
the presidency. There is only The Donald,
his 
reflex tweets, the folded pieces of paper
he pulls out of his coat pocket and a crazy
stand-up routine that is part Lenny Bruce
and part professor Irwin Corey."

APPLAUSE

Tuesday, July 5, 2016

For the Children in the Apple Tree (continued)

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

(See previous posts now tagged Apple Tree Children.)

See as well the comic book in "Midnight Special" —

(Image previously posted in "Common Core vs. Central Structure")

Sunday, July 3, 2016

Another 48 Hours

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

The Onion  on Friday, July 1, 2016 —

Investigators: First 48 Hours Most Critical
In Locating Missing Children Who Entered
Portal To Fantastical World

From Friday afternoon —

Friday, May 27, 2016

Peer Review

Filed under: General — m759 @ 7:00 AM

A review of the phrase "Innermost Kernel" in this journal
suggests the following meditation

"Who am I?" — Existential cry
in "Zoolander" and "Zoolander 2."

A similar question occurs in "Peer Gynt" —

Ben Brantley in yesterday morning's print New York Times *
expressed a nihilistic view of Peer as an onion-peeler —

"Toward the end of Ibsen’s 'Peer Gynt,' a saga of self
under siege, the title character is discovered peeling
an onion, finding in the layers of that humble vegetable
a symbol for the chapters of an eventful life . . . .

[the director’s] approach is the same one that Peer
applies to the onion: Keep stripping until you find the core.
Of course in Peer’s case what is finally found is
plenty of nothing, an apt conclusion for a man
for whom a solid self remains elusive."

I prefer a view from what Fitzgerald called
"the dark fields of the republic" — the Dordt College view —

* The Times — "A version of this review appears in print on May 26, 2016, 
on page C3 of the New York edition with the headline:
'A Saga of Self-Identity, Stripped to Its Core, Still Provokes.' "

Wednesday, March 23, 2016

Requiem for an Actress

Filed under: General — m759 @ 10:15 PM

The New York Times  this evening on the late Rita Gam:

"After generally being typecast in supporting roles
in two dozen films for what Life described as
'her sultry face and insinuating voice,' she recalled
in 1992, 'I looked into the black pit at 40 and
wondered, what do I do for an encore?' "

See also Sidney Lumet in this journal as well as
"Some cartoon graveyards are better than others."

Friday, March 4, 2016

Chess by Other Means

Filed under: General — m759 @ 7:22 PM

On film director Stanley Kubrick:

From "Kubrick," by Michael Herr, Vanity Fair , August 1999—

"He disliked the usual references to his having been a 'chess hustler' in his Greenwich Village days, as though this impugned the gravity and beauty of the exercise, the suggestion that his game wasn’t pour le sport  or, more correctly, pour l’art . To win the game was important, to win the money was irresistible, but it was nothing compared with his game, with the searching, endless action of working on his game. But of course he was hustling, he was always hustling; as he grew older and moved beyond still photography, chess became movies, and movies became chess by other means. I doubt that he ever thought of chess as just a game, or even as a game at all. I do imagine that a lot of people sitting across the board from him got melted, fried, and fragmented when Stanley let that cool ray come streaming down out of his eyes— talk about penetrating looks and piercing intelligence; here they’d sat down to a nice game of chess, and all of a sudden he was doing the thinking for both of them."

On physics writer Peter Woit:

From Part II of an interview with Peter Woit by Gerald Alper
in Smashpipe  published March 1, 2016:

"For just a moment, he allows himself to become self reflective: 'I was always a smart kid. A very smart kid. I suppose if I ever took a standardized test I would do very well, especially, in the area of abstract reasoning.'

Peter Woit says this as matter-of-factly as if he said, 'When I was a kid my father drove a Chevrolet.' He says it as Kareem Abdul-Jabbar, if asked to describe how he became the person he is, might have said 'I was always a tall kid. A very tall kid. In school, short kids bored me.'

I felt I had to say, 'but there must be a few million people in the United States who would also score very high in abstract thinking in the standardized tests and none of them have your interests.'

'The people around here all do. And there are thousands of us all around the world.'

'But there are 7 billion people in the world.'

Peter Woit had to concede the mathematical point, but I don't think he appreciated the psychological distinction I was alluding to. There is an astonishing divide between the culture of science and the culture of humanities that C.P. Snow famously alluded to. There is even a greater divide between the culture of pure mathematics and the culture of the earthbound evolutionarily programmed biological world into which we are born.

There is a celebrated quip by Dick Cavett that encapsulates this. Reflecting on his famous interview of the then reigning world chess champion, Bobby Fischer, he observed:

'Throughout the interview I could feel the force of his IQ.'

Paraphrasing this I could say that throughout the interview, which was at times exhilarating, at times daunting, I could feel the force of his two hundred QMIQ (quantum mechanics IQ). Norman Mailer once commented that the immediacy of television— the fact that most influential people in the world can be brought into your living room— creates the illusion that you have thereby been included in their inner power circle, and to that extent vicariously empowered. But you are no closer to the corridors of power then you were before. Analogously, you can sit just a few feet away from a world-class expert, close enough to reach out and touch them, but you are no closer to their accumulated wisdom— unless you are willing to go home and put in ten thousand hours of hard work trying to raise the level of your understanding."

http://www.log24.com/log/pix09A/091109-Nicole.jpg

Illustration from a post of
Schicksalstag  2009

Monday, February 15, 2016

Global and Local

Filed under: General — m759 @ 12:36 PM

Track listing

  1. "Dirty Laundry" (Henley, Danny Kortchmar) – 5:36
  2. "The Boys of Summer" (Mike Campbell, Henley) – 4:45
  3. "All She Wants to Do Is Dance" (Kortchmar) – 4:28
  4. "Not Enough Love in the World" (Henley, Kortchmar, Benmont Tench) – 3:54
  5. "Sunset Grill" (Henley, Kortchmar, Tench) – 6:22
  6. "The End of the Innocence" (Henley, Bruce Hornsby) – 5:14
  7. "The Last Worthless Evening" (John Corey, Henley, Stan Lynch) – 6:05
  8. "New York Minute" (Henley, Kortchmar, Jai Winding) – 6:34
  9. "I Will Not Go Quietly" (Henley, Kortchmar) – 5:41
  10. "The Heart of the Matter" (Campbell, Henley, J.D. Souther) – 5:21
  11. "The Garden of Allah" (CoreyPaul Gurian, Henley, Lynch) – 7:02
  12. "You Don't Know Me at All" (Corey, Henley, Lynch) – 5:36
  13. "Everybody Knows" (Leonard CohenSharon Robinson) – 6:10

Thursday, June 4, 2015

Molly Bloom on Education

Filed under: General — m759 @ 10:18 AM

Two pieces by NPR education writer Molly Bloom:

See also yesterday's post on another NPR / Princeton education figure,
Keith Devlin:

An illustration (click for larger view with context):

Friday, May 8, 2015

Spielraum

Filed under: General,Geometry — Tags: — m759 @ 9:30 AM

Review:

Illustrating the Spiegel-Spiel des Gevierts

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth. 
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by
Helen Lane 

 

Friday December 5, 2008

m759 @ 1:06 PM
 
Mirror-Play of
the Fourfold

For an excellent commentary
 on this concept of Heidegger,

View selected pages
from the book

Dionysus Reborn:

Play and the Aesthetic Dimension
in Modern Philosophical and
Scientific Discourse

(Mihai I. Spariosu,
Cornell U. Press, 1989)

Related material:
the logo for a
web page

Logo for 'Elements of Finite Geometry'

– and Theme and Variations.

Tuesday, May 5, 2015

Paz

Filed under: General — m759 @ 11:35 AM

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth. 
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by
Helen Lane 

Thursday, April 23, 2015

Colorful Tale

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

(A sequel to yesterday's ART WARS and this
morning's De Colores )

“Perhaps the philosophically most relevant feature
of modern science is the emergence of abstract
symbolic structures as the hard core of objectivity
behind– as Eddington puts it– the colorful tale
of the subjective storyteller mind.” — Hermann Weyl
(Philosophy of  Mathematics and Natural Science ,
Princeton, 1949, p. 237)

See also Deathly Hallows.

Thursday, April 9, 2015

Translation

Filed under: General — m759 @ 6:27 PM

From an informative April 7 essay in The Nation —

In his marvelous book Is That a Fish in Your Ear?: Translation and the Meaning of Everything , David Bellos demonstrates many of the ways that translation is not only possible but ubiquitous, so thoroughly woven into the fabric of our daily lives—from classrooms to international financial markets, from instruction manuals to poems—that if translation were somehow to become impossible, the world would descend into the zombie apocalypse faster than you can say “je ne sais quoi ."

— "Forensic Translation," by Benjamin Paloff

See also searches in this  journal for Core and for Kernel.
See as well Fabric Design and Symplectic.

Tuesday, February 24, 2015

Amy’s After-Party

Filed under: General — m759 @ 2:21 PM

Continued from Putting the A in VANITY,
Putting the AI in FAIR, and Core Problem:

Tuesday, December 2, 2014

Colorful Tale

Filed under: General — m759 @ 9:45 AM

Continued.

"Perhaps the philosophically most relevant feature
of modern science is the emergence of abstract
symbolic structures as the hard core of objectivity
behind— as Eddington puts it— the colorful tale
of the subjective storyteller mind."

— Hermann Weyl in Philosophy of Mathematics
     and Natural Science
 , Princeton, 1949, p. 237

Tom Wolfe on art theorists in The Painted Word  (1975) :

"It is important to repeat that Greenberg and Rosenberg
did not create their theories in a vacuum or simply turn up
with them one day like tablets brought down from atop
Green Mountain or Red Mountain (as B. H. Friedman once
called the two men). As tout le monde  understood, they
were not only theories but … hot news,
straight from the studios, from the scene."

The Weyl quote is a continuing theme in this journal.
The Wolfe quote appeared here on Nov. 18, 2014,
the reported date of death of Yale graduate student 
Natasha Chichilnisky-Heal.

Directions to her burial (see yesterday evening) include
a mention of "Paul Robson Street" (actually Paul
Robeson Place) near "the historic Princeton Cemetery."

This, together with the remarks by Tom Wolfe posted
here on the reported day of her death, suggests a search
for "red green black" —

The late Chichilnisky-Heal was a student of political economy.

The search colors may be interpreted, if one likes, as referring
to politics (red), economics (green), and Robeson (black).

See also Robeson in this journal.

Thursday, September 25, 2014

Mystery

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

"Welcome to America." — Harrison Ford in "The Devil's Own"

America  (current issue):

On readings at Mass on Sunday, Sept. 21, 2014 —

"Isaiah 55:8-9: 'For my thoughts are not your thoughts,
neither are your ways my ways, says the Lord.
For as the heavens are higher than the earth,
so are my ways higher than your ways
and my thoughts than your thoughts.'

The Gospel reading… was a perfect complement to
the passage from Isaiah…."

The America  piece quoting Isaiah was titled "The Mystery of God."

The author "currently works at Xavier College Preparatory
in Palm Desert, CA, where he teaches theology…."

Related material: This  journal that Sunday morning:

See also "The Mystery of God, Part II" —

Other secular stand-ins for "the thing one doesn't know"—
The mysteries of the late Joseph D. McNamara.

Sunday, September 21, 2014

Sermon

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

The previous post discussed the anatomy of the sum 9 + 6.

A different approach:  “A” and “The 6 spreads in A” below —

Thursday, September 18, 2014

Them Apples

Filed under: General — m759 @ 12:00 PM

John Baez at Google+ has an interesting post on crackpots,
dated September 13, 2014.

Related recent material from this  journal:

Sense (Sept. 13) and Sensibility (Sept. 14 and later).

See also a New York Times  piece from 2009:

Related material:

An Apple for Devlin and

“You don’t need to eat a whole apple to know it’s rotten.”
Warren Siegel

Thursday, September 11, 2014

Oh, Moon of Alabama

Filed under: General — Tags: — m759 @ 11:09 AM

The mention of Gauss in today's previous post, along with
recent news, suggested this post.

"How do you  get young people excited about space?"

— Megan Garber in The Atlantic , Aug. 16, 2012

Further details:  Child Buyers (July 16, 2013).

Thursday, September 4, 2014

Halloween Manifestos, 2013:

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

Here and at Catholics for Classical Education.

See also Tom Wolfe on manifestos —

Wolfe on manifestos in 'From Bauhaus to Our House'

— and part of an interesting Sept. 2, 2014, manifesto by
Common Core supporter Keith Devlin:

“Graduate students of mathematics are introduced to further
assumptions (about handling the infinite, and various other issues),
equally reasonable and useful, and in accord both with our everyday
intuitions (insofar as they are relevant) and with the rest of
mainstream mathematics. And on the basis of those assumptions,
you can prove that

1 + 2 + 3 + … = –1/12.

That’s right, the sum of all the natural numbers equals –1/12.

This result is so much in-your-face, that people whose mathematics
education stopped at the undergraduate level (if they got that far)
typically say it is wrong. It’s not. Just as with the 0.999… example,
where we had to construct a proper meaning for an infinite decimal
expansion before we could determine what its value is, so to we
have to define what that infinite sum means. ….”

For a correction to Devlin’s remarks, see a physics professor’s weblog post —

“From a strictly mathematical point of view,
the equation 1+2+3+4+ … = -1/12 is incorrect,
and involves confusing the Dirichlet series with
the zeta function.”  — Greg Gbur, May 25, 2010

Sunday, July 13, 2014

Numbers

Filed under: General — m759 @ 7:00 PM

Friday, July 4, 2014

Knockout

Filed under: General,Geometry — m759 @ 9:29 AM

(Continued from yesterday’s noon post, from  “Block That Metaphor,”
and from “Mystery Box III: Inside, Outside“)

“In one corner are the advocates of the Common Core,
led by the Bill and Melinda Gates Foundation, which
helped develop the standards and has defended them
against efforts by some states to roll them back. In the
challengers’ corner, a lineup of foundations and
philanthropists…. Other funders in the opponents’ corner
read like a ‘who’s who’ of well-heeled conservative
philanthropists, including Pittsburgh media magnate
Richard Mellon Scaife….”

— “Meet the Funders Fighting the Common Core,”
from Inside Philanthropy , Feb. 10, 2014

Scaife reportedly died this morning.

Thursday, July 3, 2014

Gates and Windows:

Filed under: General — m759 @ 12:00 PM

The Los Alamos Vision

“Gates said his foundation is an advocate for the Common Core State Standards
that are part of the national curriculum and focus on mathematics and language
arts. He said learning ‘needs to be on the edge’ where it is challenging but not
too challenging, and that students receive the basics through Common Core.

‘It’s great to teach other things, but you need that foundation,’ he said.”

— T. S. Last in the Albuquerque Journal , 12:05 AM Tuesday, July 1, 2014

See also the previous post (Core Mathematics: Arrays) and, elsewhere
in this journal,

“Eight is a Gate.” — Mnemonic rhyme:

Wednesday, July 2, 2014

An Apple for Devlin

Filed under: General — Tags: — m759 @ 2:56 PM

A columnist for the Mathematical Association of America,
Keith Devlin, yesterday posted an essay on Common Core
math education. A response:

IMAGE- Sign: 'Rotten to the Common Core'

Screenshot from a June 14, 2014, New York Times  video.

Friday, March 14, 2014

Quotation

Filed under: General — Tags: , — m759 @ 1:09 PM

Edward Frenkel in a vulgar and stupid
LA Times  opinion piece, March 2, 2014 —

"In the words of the great mathematician Henri Poincare, mathematics is valuable because 'in binding together elements long-known but heretofore scattered and appearing unrelated to one another, it suddenly brings order where there reigned apparent chaos.' "

My attempts to find the source of these alleged words of Poincaré were fruitless.* Others may have better luck.

The search for Poincaré's words did, however, yield the following passage —

HENRI POINCARÉ
THE FUTURE OF MATHEMATICS

If a new result is to have any value, it must unite elements long since known, but till then scattered and seemingly foreign to each other, and suddenly introduce order where the appearance of disorder reigned. Then it enables us to see at a glance each of these elements in the place it occupies in the whole. Not only is the new fact valuable on its own account, but it alone gives a value to the old facts it unites. Our mind is frail as our senses are; it would lose itself in the complexity of the world if that complexity were not harmonious; like the short-sighted, it would only see the details, and would be obliged to forget each of these details before examining the next, because it would- be incapable of taking in the whole. The only facts worthy of our attention are those which introduce order into this complexity and so make it accessible to us.

Mathematicians attach a great importance to the elegance of their methods and of their results, and this is not mere dilettantism. What is it that gives us the feeling of elegance in a solution or a demonstration? It is the harmony of the different parts, their symmetry, and their happy adjustment; it is, in a word, all that introduces order, all that gives them unity, that enables us to obtain a clear comprehension of the whole as well as of the parts. But that is also precisely what causes it to give a large return; and in fact the more we see this whole clearly and at a single glance, the better we shall perceive the analogies with other neighbouring objects, and consequently the better chance we shall have of guessing the possible generalizations. Elegance may result from the feeling of surprise caused by the unlooked-for occurrence together of objects not habitually associated. In this, again, it is fruitful, since it thus discloses relations till then unrecognized. It is also fruitful even when it only results from the contrast between the simplicity of the means and the complexity of the problem presented, for it then causes us to reflect on the reason for this contrast, and generally shows us that this reason is not chance, but is to be found in some unsuspected law. ….

HENRI POINCARÉ
L'AVENIR DES MATHÉMATIQUES

Si un résultat nouveau a du prix, c'est quand en reliant des éléments connus depuis longtemps, mais jusque-là épars et paraissant étrangers les uns aux autres, il introduit subitement l'ordre là où régnait l'apparence du désordre. Il nous permet alors de voir d'un coup d'œil chacun de ces éléments et la place qu'il occupe dans l'ensemble. Ce fait nouveau non-seulement est précieux par lui-même, mais lui seul donne leur valeur à tous les faits anciens qu'il relie. Notre esprit est infirme comme le sont nos sens; il se perdrait dans la complexité du monde si cette complexité n'était harmonieuse, il n'en verrait que les détails à la façon d'un myope et il serait forcé d'oublier chacun de ces détails avant d'examiner le suivant, parce qu'il serait incapable de tout embrasser. Les seuls faits dignes de notre attention sont ceux qui introduisent de l'ordre dans cette complexité et la rendent ainsi accessible.

Les mathématiciens attachent une grande importance à l'élégance de leurs mé-thodes et de leurs résultats; ce n'est pas là du pur dilettantisme. Qu'est ce qui nous donne en effet dans une solution, dans une démonstration, le sentiment de l'élégance? C'est l'harmonie des diverses parties, leur symétrie, leur heureux balancement; c'est en un mot tout ce qui y met de l'ordre, tout ce qui leur donne de l'unité, ce qui nous permet par conséquent d'y voir clair et d'en comprendre l'ensemble en même temps que les détails. Mais précisément, c'est là en même temps ce qui lui donne un grand rendement ; en effet, plus nous verrons cet ensemble clairement et d'un seul coup d'œil, mieux nous apercevrons ses analogies avec d'autres objets voisins, plus par conséquent nous aurons de chances de deviner les généralisations possibles. L'élé-gance peut provenir du sentiment de l'imprévu par la rencontre inattendue d'objets qu'on n'est pas accoutumé à rapprocher; là encore elle est féconde, puisqu'elle nous dévoile ainsi des parentés jusque-là méconnues; elle est féconde même quand elle ne résulte que du contraste entre la simplicité des moyens et la complexité du problème posé ; elle nous fait alors réfléchir à la raison de ce contraste et le plus souvent elle nous fait voir que cette raison n'est pas le hasard et qu'elle se trouve dans quelque loi insoupçonnée. ….

* Update of 1:44 PM ET March 14 — A further search, for "it suddenly brings order," brought order. Words very close to Frenkel's quotation appear in a version of Poincaré's "Future of Mathematics" from a 1909 Smithsonian report

"If a new result has value it is when, by binding together long-known elements, until now scattered and appearing unrelated to each other, it suddenly brings order where there reigned apparent disorder."

Friday, February 28, 2014

Code

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

From Northrop Frye's The Great Code: The Bible and Literature , Ch. 3: Metaphor I —

"In the preceding chapter we considered words in sequence, where they form narratives and provide the basis for a literary theory of myth. Reading words in sequence, however, is the first of two critical operations. Once a verbal structure is read, and reread often enough to be possessed, it 'freezes.' It turns into a unity in which all parts exist at once, without regard to the specific movement of the narrative. We may compare it to the study of a music score, where we can turn to any part without regard to sequential performance. The term 'structure,' which we have used so often, is a metaphor from architecture, and may be misleading when we are speaking of narrative, which is not a simultaneous structure but a movement in time. The term 'structure' comes into its proper context in the second stage, which is where all discussion of 'spatial form' and kindred critical topics take their origin."

Related material: 

"The Great Code does not end with a triumphant conclusion or the apocalypse that readers may feel is owed them or even with a clear summary of Frye’s position, but instead trails off with a series of verbal winks and nudges. This is not so great a fault as it would be in another book, because long before this it has been obvious that the forward motion of Frye’s exposition was illusory, and that in fact the book was devoted to a constant re-examination of the same basic data from various closely related perspectives: in short, the method of the kaleidoscope. Each shake of the machine produces a new symmetry, each symmetry as beautiful as the last, and none of them in any sense exclusive of the others. And there is always room for one more shake."

— Charles Wheeler, "Professor Frye and the Bible," South Atlantic Quarterly  82 (Spring 1983), pp. 154-164, reprinted in a collection of reviews of the book.
 

For code  in a different sense, but related to the first passage above,
see Diamond Theory Roullete, a webpage by Radamés Ajna.

For "the method of the kaleidoscope" mentioned in the second
passage above, see both the Ajna page and a webpage of my own,
Kaleidoscope Puzzle.

Thursday, February 6, 2014

The Representation of Minus One

Filed under: General,Geometry — Tags: , — m759 @ 6:24 AM

For the late mathematics educator Zoltan Dienes.

"There comes a time when the learner has identified
the abstract content of a number of different games
and is practically crying out for some sort of picture
by means of which to represent that which has been
gleaned as the common core of the various activities."

— Article by "Melanie" at Zoltan Dienes's website

Dienes reportedly died at 97 on Jan. 11, 2014.

From this journal on that date —

http://www.log24.com/log/pix11/110219-SquareRootQuaternion.jpg

A star figure and the Galois quaternion.

The square root of the former is the latter.

Update of 5:01 PM ET Feb. 6, 2014 —

An illustration by Dienes related to the diamond theorem —

See also the above 15 images in

http://www.log24.com/log/pix11/110220-relativprob.jpg

and versions of the 4×4 coordinatization in  The 4×4 Relativity Problem
(Jan. 17, 2014).

Monday, August 19, 2013

Tale

Filed under: General — Tags: — m759 @ 8:00 PM

IMAGE- NY Times online front page with caption- 'Thereby hangs a tale.'

The tale is not Thomas Nagel's remarks on philosophy
summarized above, but rather the late John Hollander's
remarks on Nowhere:

"We all know where it is they've gone, the dead:
Beyond Noplace, far into wide Nowhere."

See also Nagel's book The View from Nowhere .

Sunday, June 30, 2013

Book Award

Filed under: General,Geometry — m759 @ 5:01 PM
 

"What on earth is
a 'concrete universal'?
"

— Said to be an annotation
(undated) by Robert M. Pirsig
of A History of Philosophy ,
by Frederick Copleston,
Society of Jesus.

In the spirit of the late Thomas Guinzburg

See also "Concrete Universal" in this journal.

Related material— From a Bloomsday reply
to a Diamond Theory  reader's comment, an excerpt—

The reader's comment suggests the following passages from
the book by Stirling quoted above—

 

Here Stirling plays a role analogous to that of Professor Irwin Corey
accepting the National Book Award for Gravity's Rainbow  in 1974.

Monday, May 13, 2013

Game Show

Filed under: General — m759 @ 10:00 PM

For the late Bob Stewart:

"She was a panelist on many game shows, including
'What’s My Line?' and 'The Hollywood Squares.'"

Translation Studies Continued:

See Cameron's Kernel and

Image-- The Three-Point Line: A Finite Projective Space
 (Click image for some background.)

Sunday, April 28, 2013

C’mon Baby…

Filed under: General — Tags: — m759 @ 3:13 AM
 

Let's do the twist.

The image at left
is from a poster
for a film released
on March 28, 2003.

See this journal
on that date.

A phrase from yesterday's noon post:

Sinking the Magic 8-Ball .

A scene from the above film is related to this phrase.
Another image from the film poster:

A review of the film:

"The final 'twist' seems to negate the entire story,
like a bad shaggy-dog joke."

Such a joke:

“Words and numbers are of equal value,
  for, in the cloak of knowledge,
  one is warp and the other woof.”

— The princesses Rhyme and Reason
      in The Phantom Tollbooth

"A core component in the construction
is a 3-dimensional vector space over F."

—  Page 29 of "A twist in the M24 moonshine story,"
      by Anne Taormina and Katrin Wendland.
      (Submitted to the arXiv on 13 Mar 2013.)

The number of points in such a space is, of course, 8.

Friday, April 5, 2013

Reflections (continued)

Filed under: General — m759 @ 4:30 PM

From a search for Mirror-Play in this journal:

That search was suggested by a much lengthier
search, for Core, that itself was suggested
by yesterday's post (on Katherine Neville's birthday)
titled A Philosopher's Stone.

See, too, Tom Hanks (shown above as symbologist
Robert Langdon) in "Lucky Guy" (reviewed by TIME
yesterday), and a related poem:

Yes, you! You’re the Lucky One

Prospective purchasers of the poet's work
may consult a press release from LSU Press
dated 4/4/2013. The poet died, apparently*
unlamented by his publisher, on 3/30.

* But only  apparently.

Thursday, April 4, 2013

A Philosopher’s Stone

Filed under: General — m759 @ 4:00 PM

"Core" (in the original, Kern ) is perhaps
not the best translation of hypokeimenon :

IMAGE- Hypokeimenon in Liddell and Scott's Greek-English Lexicon

See also Heidegger's original German:

Related material: In this journal, "underlie" and "underlying."

Friday, March 29, 2013

Where Credit Is Due

Filed under: General — Tags: — m759 @ 5:01 PM

Ape to Affleck:

Score by Boston Pops.

Backstory credit— Boston Moms:

IMAGE- Christopher Ann Boldt and Patricia Collinge in 'A Liberal Education'

Sunday, December 23, 2012

Digital Recreation

Filed under: General — m759 @ 2:29 AM

Denzel Washington in Deja Vu  (2006), directed by Tony Scott—

Click to enlarge.

IMAGE- Denzel Washington in 'Deja Vu' (2006)

See also Tony Scott and four and a half days ago* —

  
Japanese character
       for "field"

Related material from five  days ago

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth. 
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by 
Helen Lane (Kindle edition of 
2011-11-07, Kindle locations 
1207-1210).

* More precisely, what will be 4.5 days ago at 3:09 AM ET.

Tuesday, December 18, 2012

Monkey Grammar

Filed under: General,Geometry — Tags: , — m759 @ 2:29 AM

For a modern Adam and Eve—

W. Tecumseh Fitch and Gesche Westphal Fitch,
editors of a new four-volume collection titled
Language Evolution  (Feb. 2, 2012, $1,360)—

Related material—

"At the point of convergence
the play of similarities and differences
cancels itself out in order that 
identity alone may shine forth. 
The illusion of motionlessness,
the play of mirrors of the one: 
identity is completely empty;
it is a crystallization and
in its transparent core
the movement of analogy 
begins all over once again."

— The Monkey Grammarian 

by Octavio Paz, translated by
Helen Lane (Kindle edition of
2011-11-07, Kindle locations
1207-1210).

The "play of mirrors" link above is my own.

Click on W. Tecumseh Fitch for links to some
examples of mirror-play in graphic design—
from, say, my own work in a version of 1977, not from
the Fitches' related work published online last June—

See also Log24 posts from the publication date
of the Fitches' Language Evolution

Groundhog Day, 2012.

Happy birthday to the late Alfred Bester.

Sunday, November 18, 2012

Kernel

Filed under: General — m759 @ 5:24 AM

(Continued)

Rachel Dodes in The Wall Street Journal
on All Souls' Day, 2012

"In one of the first lines uttered by Daniel Day-Lewis, playing Abraham Lincoln in the new Steven Spielberg film opening Nov. 9, he says, 'I could be bounded in a nutshell, and count myself a king of infinite space— were it not that I have bad dreams.'

The line was ripped straight from 'Hamlet,' by Lincoln's favorite writer, William Shakespeare. Tony Kushner, the Pulitzer Prize-winning playwright ('Angels in America') who wrote the script for the film, says that Shakespeare, much like Lincoln, 'had extraordinary mastery over the darkest parts of the human spirit.'"

The above quotation omits Shakespeare's words prefacing the nutshell part— "O God."

These same words in a different tongue—  "Hey Ram"— have often been quoted as the last words of Gandhi. (See yesterday's noon post.)

"… for the Highest Essence (brahman ),
which is the core of the world, is identical
with the Highest Self (ātman ), the kernel
of man's existence."

— Heinrich Zimmer, Myths and Symbols
in Indian Art and Civilization
, Pantheon
Books, 1946, page 142 

Related material: A post linked to here on Friday night
that itself links to a different Shakespeare speech.

Sunday, November 4, 2012

Shakespeare’s Rhyme

Filed under: General — m759 @ 5:01 AM

From Saturday Night Live  last night—

IMAGE- Louis C. K. as Shakespeare on SNL

Related material from the Log24 post "Now Lens"
(March 11, 2011)—

Errol Morris in The New York Times  on March 9, 2011

"If everything is incommensurable, then everything
is seen through the lens of the present, the lens of now ."

"Borges concluded by quoting Chesterton, 'there is nothing
more frightening than a labyrinth that has no center.' [72]"

See also Borges on Shakespeare, everything, and nothing 
in a note from September 7, 2006.

Everything and nothing in Peter J. Cameron's weblog yesterday—

The existence of everything entails the existence of nothing;
indeed, the existence of anything (any set A) entails
the existence of the empty set (the set {x∈A:x≠x}).
But not the other way round.

Right, I had better put on my anorak and go out now …

Illustration added by m759—

How many miles to Babylon?*
Three score miles and ten.
Can I get there by candle-light?**
Yes, and back again.

* Suggested by the Pindar link in this journal yesterday.

** Quoted in the "Seven is Heaven" post on All Souls' Day.

Sunday, September 23, 2012

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.

Friday, June 29, 2012

The Uploading (continued)*

Filed under: General — m759 @ 9:29 PM

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 —

Video uploaded on Jan. 26, 2008, of talk, 'The Lively Kernel,' on object-oriented software

* This post's title refers to the above uploading date—  Jan. 26, 2008.

Friday, April 20, 2012

Complex Reflection

Filed under: General — m759 @ 11:32 AM

Yesterday's post in memory of Octavio Paz

… the free-standing, two-sided “Life-Death Figure,”
carved from stone in Mexico some time between
A.D. 900 and 1250, 
has multiple personalities.

Holland Cotter,  New York Times 

An earlier post yesterday, Fashion Notes, linked to a Sting video—

IMAGE- Sting meets his own reflection in a mirror in 'We'll Be Together' video

From "Loo Ree," by Zenna Henderson

"It's so hard to explain–"

"Oh, foof!" I cried defiantly, taking off my glasses and, smearing the tears across both lenses with a tattered Kleenex. "So I'm a dope, a moron! If I can explain protective coloration to my six-year-olds and the interdependence of man and animals, you can tell me something of what the score is!" I scrubbed the back of my hand across my blurry eyes. "If you have to, start out 'Once upon a time."' I sat down– hard.  

Loo Ree smiled and sat down, too. "Don't cry, teacher. Teachers aren't supposed to have tears."  

"I know it," I sniffed. "A little less than human-that's us."

"A little more than human, sometimes." Loo Ree corrected gently. "Well then, you must understand that I'll have to simplify. You will have to dress the bare bones of the explanation according to your capabilities.  

"Once upon a time there was a classroom. Oh, cosmic in size, but so like yours that you would smile in recognition if you could see it all. And somewhere in the classroom something was wrong. Not the whispering and murmuring– that's usual. Not the pinching and poking and tattling that goes on until you get so you don't even hear it." I nodded. How well I knew.  

"It wasn't even the sudden blow across the aisle or the unexpected wrestling match in the back of the room. That happens often, too. But something else was wrong. It was an undercurrent, a stealthy, sly sort of thing that has to be caught early or it disrupts the whole classroom and tarnishes the children with a darkness that will never quite rub off.  

"The teacher could feel it –as all good teachers can– and she spoke to the principal. He, being a good principal, immediately saw the urgency of the matter and also saw that it was beyond him, so he called in an Expert." "You?" I asked, feeling quite bright because I had followed the analogy so far.  

Loo Ree smiled. "Well, I'm part of the Expert."  

"If you have to, start out 'Once upon a time.'"

Yesterday's Paz post was at 6:48 PM EDT.

For the autistic, here is some related mathematics.

Yesterday's Fashion Notes post was at 1:06 PM  EDT.

A related chronological note from Rolling Stone  yesterday—

"Levon Helm, singer and drummer for the Band,
 died on April 19th in New York of throat cancer.
 He was 71. 

"He passed away peacefully at 1:30 this afternoon…."

Helm and The Band performing "The Weight"—

"I pulled into Nazareth, I was a-feelin' 'bout half past dead…"

Tuesday, November 1, 2011

For All Hallows Day

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

The following was suggested by the Sermon
of October 30 (the day preceding Devil's Night)
and by yesterday's Beauty, Truth, Halloween.

"The German language has itself been influenced by Goethe's Faust , particularly by the first part. One example of this is the phrase 'des Pudels Kern ,' which means the real nature or deeper meaning of something (that was not evident before). The literal translation of 'des Pudels Kern ' is 'the core of the poodle,' and it originates from Faust's exclamation upon seeing the poodle (which followed him home) turn into Mephistopheles." —Wikipedia

See also the following readings (click to enlarge)—

Hans Primas on Pauli's 'des Pudels Kern'

Suzanne Gieser on Pauli's 'des Pudels Kern'

Note particularly…

"The main enigma of any description of a patternless
unus mundus  is to find appropriate partitions which
create relevant patterns." —Hans Primas, above

"In general, the partition of into right cosets
can differ from its partition into left cosets. Galois
was the first to recognize the importance of when
these partitions agree. This happens when the
subgroup is normal." — David A. Cox,
Galois Theory , Wiley, 2004, p. 510

Saturday, September 17, 2011

The Uploading

Filed under: General — m759 @ 11:32 AM

(Continued from March 9.)

A detail from "Feist Sings 1, 2, 3, 4"—

"Uploaded by SesameStreet on Jul 18, 2008"

Those who prefer, as Weyl put it,
"
the hard core of objectivity"
to, as Eddington put it,
"the colorful tale of the subjective storyteller mind"
may consult this journal on the same day… July 18, 2008.

Friday, September 16, 2011

Icons

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

Background: Jung's Aion in this journal discusses this
figure from finite geometry's diamond theorem

http://www.log24.com/log/pix11B/110915-FourDiamondsIcon.gif

Fig. A

This resembles a figure that served Jung
as a schema of the Self

http://www.log24.com/log/pix11B/110915-Jung-FourDiamonds.gif

Fig. B

Fig. A, with color variations, serves as the core
of many automatically generated Identicons
a different sort of self-symbol.

Examples from Sept. 6 at MathOverflow

http://www.log24.com/log/pix11B/110915-ChuangGravatar.png     http://www.log24.com/log/pix11B/110915-JacobLurieGravatar.png

A user wanting to custom-tailor his self-symbol should consider
the following from the identicon service Gravatar

1. User Submissions.  " you hereby do and shall grant to Automattic a worldwide, perpetual, irrevocable, royalty-free and fully-paid, transferable (including rights to sublicense) right to perform the Services (e.g., to use, modify, reproduce, distribute, prepare derivative works of, display, perform, and otherwise fully exercise and exploit all intellectual property, publicity, and moral rights with respect to any User Submissions, and to allow others to do so)."

Sounds rather Faustian.

Thursday, July 21, 2011

The Race

Filed under: General — m759 @ 7:14 AM
 
IMAGE- From Esther Dyson- Boats on the Charles- 'Race you to the bridge!'

An image related to
the Flesh obituary below—

See "As It Lays" in this journal.

Vegas background for 'Play It As It Lays'

(Not as it lies .)

New York Times 
obituaries today—

Click to enlarge.

http://www.log24.com/log/pix11B/110721-NYT-Gayler-240w.jpg

http://www.log24.com/log/pix11B/110721-NYT-Flesh-240w.jpg

     "That's GUY-ler, not GAY-ler."

      See also Time and the River, Number of the Beast, and Story Theory.

Monday, July 11, 2011

And/Or Problem

Filed under: General,Geometry — Tags: — m759 @ 11:59 PM

"It was the simultaneous emergence
and mutual determination
of probability and logic
that von Neumann found intriguing
and not at all well understood."

Miklós Rédei

Context:

Update of 7 AM ET July 12, 2011—

Freeman Dyson on John von Neumann's
Sept. 2, 1954, address to the International
Congress of Mathematicians on
"Unsolved Problems in Mathematics"—

                                     …."The hall was packed with
mathematicians, all expecting to hear a brilliant
lecture worthy of such a historic occasion. The
lecture was a huge disappointment. Von Neumann
had probably agreed several years earlier to give
a lecture about unsolved problems and had then
forgotten about it. Being busy with many other
things, he had neglected to prepare the lecture.
Then, at the last moment, when he remembered
that he had to travel to Amsterdam and say something
about mathematics, he pulled an old lecture
from the 1930s out of a drawer and dusted it off.
The lecture was about rings of operators, a subject
that was new and fashionable in the 1930s. Nothing
about unsolved problems.
Nothing about the
future."

Notices of the American Mathematical Society ,
February 2009, page 220

For a different account, see Giovanni Valente's
2009 PhD thesis from the University of Maryland,
Chapter 2, "John von Neumann's Mathematical
'Utopia' in Quantum Theory"—

"During his lecture von Neumann discussed operator theory and its con-
nections with quantum mechanics and noncommutative probability theory,
pinpointing a number of unsolved problems. In his view geometry was so tied
to logic that he ultimately outlined a logical interpretation of quantum prob-
abilities. The core idea of his program is that probability is invariant under
the symmetries of the logical structure of the theory. This is tantamount to
a formal calculus in which logic and probability arise simultaneously. The
problem that exercised von Neumann then was to construct a geometrical
characterization of the whole theory of logic, probability and quantum me-
chanics, which could be derived from a suitable set of axioms…. As he
himself finally admitted, he never managed to set down the sought-after
axiomatic formulation in a way that he felt satisfactory."

Sunday, June 19, 2011

Metalibrarianship

Filed under: General — m759 @ 7:59 AM

IMAGE- Germany's MathGuide project, an alternative to London's 'Piracy Project'

This screenshot was suggested by the word "metalibrarianship" in a Bloomsday 2011 post by artist Steve Richards.

Note the words in the search field.

The phrase "Dublin Core metadata" refers to a city in Ohio, not in Ireland.

Related material— The highlighted phrase below is in the epigraph to Borges's "The Library of Babel"—

"I would, for these causes, wish him that is melancholy, to use both humane and divine authors, voluntarily to impose some taske upon himself, to divert his melancholy thoughts; to study the art of memory, Cosmus Rosselius, Pet. Ravennas, Scenkelius Detectus, or practise brachygraphy, &c. that will aske a great deal of attention: or let him demonstrate a proposition in Euclide in his five last books, extract a square root, or studie Algebra: than which, as gClavius holds, in all humane disciplines nothing can be more excellent and pleasant, so abstruse and recondite, so bewitching, so miraculous, so ravishing, so easie withal and full of delight, omnem humanum captum superare videtur . By this means you may define ex ungue leonem , as the diverbe is, by his thumb alone the bigness of Hercules, or the true dimensions of the great  hColossus, Solomons temple, and Domitians amphitheater, out of a little part. By this art you may contemplate the variation of the 23 letters…."

g Ad. 2. definit.2. elem.   In disciplinis humanis nihil praestantius reperitur: quippe miracula quaedam numerorum eruit tam abstrusa et recondita, tanta nihilo minus facilitate et voluptate, ut, &c.

h Which contained 1080000 weight of brass.

The Anatomy of Melancholy, Part. 2, Sec. 2, Mem. 4

Friday, November 19, 2010

Absolute Ambition

Filed under: General — Tags: , — m759 @ 10:30 AM

"It's my absolute ambition that you are touched to the core of your being with the content…."

— Julie Taymor on Spider-Man: Turn Off the Dark  (Playbill video, undated)

Another ambitious comic-book promotion —

"What Logicomix  does that few works in any medium do is to make intellectual passion palpable. That is its greatest strength. And it’s here that its form becomes its substance."

— Judith Roitman, review (pdf, 3.7 MB) of Logicomix: An Epic Search for Truth , in …

http://www.log24.com/log/pix10B/101119-AMSnoticesSm.jpg

 The December 2010 AMS Notices  cover has excerpts from Logicomix.

Related material:

"In the classical grammarians’ sense of the power of form over 'content' and style over 'substance,' he originated the phrase, 'the medium is the message.'"

— Joseph P. Duggan on Marshall McLuhan at The University Bookman

See also, in this  journal, The Medium is the Message, Wechsler, and Blockheads .

Saturday, September 18, 2010

Yom Kippur Special

Filed under: General — m759 @ 9:29 AM

John Hooper in The Guardian  quotes the Pope in Westminster Cathedral this morning—

"Here too I think of the immense suffering caused by the abuse of children, especially within the church and by her ministers. Above all, I express my deep sorrow to the innocent victims of these unspeakable crimes.

"I also acknowledge, with you, the shame and humiliation which all of us have suffered because of these sins; and I invite you to offer it to the Lord with trust that this chastisement will contribute to the healing of the victims and the purification of the church and the renewal of her age-old commitment to the education and care of young people."

The pope made his comments at a service that was the occasion for religious pageantry of a sort rarely seen in Britain. He was preceded into the cathedral by more than 100 scarlet-robed priests and a constellation of bishops and cardinals. To a volley of applause from the congregation, he appeared at the climax of a musical build-up that could have come from the score for a sci-fi movie epic.

Related material— Childhood's Rear End.

Sunday, August 15, 2010

The Game

Filed under: General — Tags: — m759 @ 11:07 PM
'Magister Ludi,' or 'The Glass Bead Game,' by Hermann Hesse

We shall now give a brief summary of the beginnings of the Glass Bead Game. It appears to have arisen simultaneously in Germany and in England. In both countries, moreover, it was originally a kind of exercise employed by those small groups of musicologists and musicians who worked and studied in the new seminaries of musical theory. If we compare the original state of the Game with its subsequent developments and its present form, it is much like comparing a musical score of the period before 1500, with its primitive notes and absence of bar lines, with an eighteenth-century score, let alone with one from the nineteenth with its confusing excess of symbols for dynamics, tempi, phrasing, and so on, which often made the printing of such scores a complex technical problem.

The Game was at first nothing more than a witty method for developing memory and ingenuity among students and musicians. And as we have said, it was played both in England and Germany before it was ‘invented’ here in the Musical Academy of Cologne, and was given the name it bears to this day, after so many generations, although it has long ceased to have anything to do with glass beads.

The inventor, Bastian Perrot of Calw, a rather eccentric but clever, sociable, and humane musicologist, used glass beads instead of letters, numerals, notes, or other graphic symbols. Perrot, who incidentally has also bequeathed to us a treatise on the Apogee and Decline of Counterpoint, found that the pupils at the Cologne Seminary had a rather elaborate game they used to play. One would call out, in the standardized abbreviations of their science, motifs or initial bars of classical compositions, whereupon the other had to respond with the continuation of the piece, or better still with a higher or lower voice, a contrasting theme, and so forth. It was an exercise in memory and improvisation quite similar to the sort of thing probably in vogue among ardent pupils of counterpoint in the days of Schütz, Pachelbel, and Bach — although it would then not have been done in theoretical formulas, but in practice on the cembalo, lute, or flute, or with the voice.

Bastian Perrot in all probability was a member of the Journeyers to the East. He was partial to handicrafts and had himself built several pianos and clavichords in the ancient style. Legend has it that he was adept at playing the violin in the old way, forgotten since 1800, with a high-arched bow and hand-regulated tension of the bow hairs. Given these interests, it was perhaps only natural that he should have constructed a frame, modeled on a child’s abacus, a frame with several dozen wires on which could be strung glass beads of various sizes, shapes, and colors. The wires corresponded to the lines of the musical staff, the beads to the time-values of the notes, and so on. In this way he could represent with beads musical quotations or invented themes, could alter, transpose, and develop them, change them and set them in counterpoint to one another. In technical terms this was a mere plaything, but the pupils liked it; it was imitated and became fashionable in England too. For a time the game of musical exercises was played in this charmingly primitive manner. And as is so often the case, an enduring and significant institution received its name from a passing and incidental circumstance. For what later evolved out of that students’ sport and Perrot’s bead-strung wires bears to this day the name by which it became popularly known, the Glass Bead Game.

Hermann Hesse

“For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.”

— “Albertus Secundus,” epigraph to The Glass Bead Game

From DownloadThat.com

(Click to enlarge.)

http://www.log24.com/log/pix10B/100815-ThePaletteSm.jpg

Monday, June 14, 2010

Birkhoff on the Galois “Theory of Ambiguity”

Filed under: General,Geometry — m759 @ 9:48 PM

The Principle of Sufficient Reason

by George David Birkhoff

from "Three Public Lectures on Scientific Subjects,"
delivered at the Rice Institute, March 6, 7, and 8, 1940

EXCERPT 1—

My primary purpose will be to show how a properly formulated
Principle of Sufficient Reason plays a fundamental
role in scientific thought and, furthermore, is to be regarded
as of the greatest suggestiveness from the philosophic point
of view.2

In the preceding lecture I pointed out that three branches
of philosophy, namely Logic, Aesthetics, and Ethics, fall
more and more under the sway of mathematical methods.
Today I would make a similar claim that the other great
branch of philosophy, Metaphysics, in so far as it possesses
a substantial core, is likely to undergo a similar fate. My
basis for this claim will be that metaphysical reasoning always
relies on the Principle of Sufficient Reason, and that
the true meaning of this Principle is to be found in the
Theory of Ambiguity” and in the associated mathematical
“Theory of Groups.”

If I were a Leibnizian mystic, believing in his “preestablished
harmony,” and the “best possible world” so
satirized by Voltaire in “Candide,” I would say that the
metaphysical importance of the Principle of Sufficient Reason
and the cognate Theory of Groups arises from the fact that
God thinks multi-dimensionally3 whereas men can only
think in linear syllogistic series, and the Theory of Groups is

2 As far as I am aware, only Scholastic Philosophy has fully recognized and ex-
ploited this principle as one of basic importance for philosophic thought

3 That is, uses multi-dimensional symbols beyond our grasp.
______________________________________________________________________

the appropriate instrument of thought to remedy our deficiency
in this respect.

The founder of the Theory of Groups was the mathematician
Evariste Galois. At the end of a long letter written in
1832 on the eve of a fatal duel, to his friend Auguste
Chevalier, the youthful Galois said in summarizing his
mathematical work,4 “You know, my dear Auguste, that
these subjects are not the only ones which I have explored.
My chief meditations for a considerable time have been
directed towards the application to transcendental Analysis
of the theory of ambiguity. . . . But I have not the time, and
my ideas are not yet well developed in this field, which is
immense.” This passage shows how in Galois’s mind the
Theory of Groups and the Theory of Ambiguity were
interrelated.5

Unfortunately later students of the Theory of Groups
have all too frequently forgotten that, philosophically
speaking, the subject remains neither more nor less than the
Theory of Ambiguity. In the limits of this lecture it is only
possible to elucidate by an elementary example the idea of a
group and of the associated ambiguity.

Consider a uniform square tile which is placed over a
marked equal square on a table. Evidently it is then impossible
to determine without further inspection which one
of four positions the tile occupies. In fact, if we designate
its vertices in order by A, B, C, D, and mark the corresponding
positions on the table, the four possibilities are for the
corners A, B, C, D of the tile to appear respectively in the
positions A, B, C, D;  B, C, D, A;  C, D, A, B; and D, A, B, C.
These are obtained respectively from the first position by a

4 My translation.
5 It is of interest to recall that Leibniz was interested in ambiguity to the extent
of using a special notation v (Latin, vel ) for “or.” Thus the ambiguously defined
roots 1, 5 of x2-6x+5=0 would be written x = l v 5 by him.
______________________________________________________________________

null rotation ( I ), by a rotation through 90° (R), by a rotation
through 180° (S), and by a rotation through 270° (T).
Furthermore the combination of any two of these rotations
in succession gives another such rotation. Thus a rotation R
through 90° followed by a rotation S through 180° is equivalent
to a single rotation T through 270°, Le., RS = T. Consequently,
the "group" of four operations I, R, S, T has
the "multiplication table" shown here:

http://www.log24.com/log/pix10A/100614-BirkhoffTable.jpg
This table fully characterizes the group, and shows the exact
nature of the underlying ambiguity of position.
More generally, any collection of operations such that
the resultant of any two performed in succession is one of
them, while there is always some operation which undoes
what any operation does, forms a "group."
__________________________________________________

EXCERPT 2—

Up to the present point my aim has been to consider a
variety of applications of the Principle of Sufficient Reason,
without attempting any precise formulation of the Principle
itself. With these applications in mind I will venture to
formulate the Principle and a related Heuristic Conjecture
in quasi-mathematical form as follows:

PRINCIPLE OF SUFFICIENT REASON. If there appears
in any theory T a set of ambiguously determined ( i e .
symmetrically entering) variables, then these variables can themselves
be determined only to the extent allowed by the corresponding
group G. Consequently any problem concerning these variables
which has a uniquely determined solution, must itself be
formulated so as to be unchanged by the operations of the group
G ( i e . must involve the variables symmetrically).

HEURISTIC CONJECTURE. The final form of any
scientific theory T is: (1) based on a few simple postulates; and
(2) contains an extensive ambiguity, associated symmetry, and
underlying group G, in such wise that, if the language and laws
of the theory of groups be taken for granted, the whole theory T
appears as nearly self-evident in virtue of the above Principle.

The Principle of Sufficient Reason and the Heuristic Conjecture,
as just formulated, have the advantage of not involving
excessively subjective ideas, while at the same time
retaining the essential kernel of the matter.

In my opinion it is essentially this principle and this
conjecture which are destined always to operate as the basic
criteria for the scientist in extending our knowledge and
understanding of the world.

It is also my belief that, in so far as there is anything
definite in the realm of Metaphysics, it will consist in further
applications of the same general type. This general conclu-
sion may be given the following suggestive symbolic form:

Image-- Birkhoff diagram relating Galois's theory of ambiguity to metaphysics

While the skillful metaphysical use of the Principle must
always be regarded as of dubious logical status, nevertheless
I believe it will remain the most important weapon of the
philosopher.

___________________________________________________________________________

A more recent lecture on the same subject —

"From Leibniz to Quantum World:
Symmetries, Principle of Sufficient Reason
and Ambiguity in the Sense of Galois
"

by Jean-Pierre Ramis (Johann Bernoulli Lecture at U. of Groningen, March 2005)

Theory of Ambiguity

Filed under: General,Geometry — m759 @ 5:01 PM

Théorie de l'Ambiguité

According to a 2008 paper by Yves André of the École Normale Supérieure  of Paris—

"Ambiguity theory was the name which Galois used
 when he referred to his own theory and its future developments."

The phrase "the theory of ambiguity" occurs in the testamentary letter Galois wrote to a friend, Auguste Chevalier, on the night before Galois was shot in a duel.

Hermann Weyl in Symmetry, Princeton University Press, 1952—

"This letter, if judged by the novelty and profundity of ideas it contains, is perhaps
  the most substantial piece of writing in the whole literature of mankind."

Conclusion of the Galois testamentary letter, according to
the 1897 Paris edition of Galois's collected works—

Image-- Galois on his theory of ambiguity, from Collected Works, Paris, 1897

The original—

Image-- Concluding paragraphs, Galois's 'last testament' letter to Chevalier, May 29, 1832

A transcription—

Évariste GALOIS, Lettre-testament, adressée à Auguste Chevalier—

Tu sais mon cher Auguste, que ces sujets ne sont pas les seuls que j'aie
explorés. Mes principales méditations, depuis quelques temps,
étaient dirigées sur l'application à l'analyse transcendante de la théorie de
l'ambiguité. Il s'agissait de voir a priori, dans une relation entre des quantités
ou fonctions transcendantes, quels échanges on pouvait faire, quelles
quantités on pouvait substituer aux quantités données, sans que la relation
put cesser d'avoir lieu. Cela fait reconnaitre de suite l'impossibilité de beaucoup
d'expressions que l'on pourrait chercher. Mais je n'ai pas le temps, et mes idées
ne sont pas encore bien développées sur ce terrain, qui est
immense.

Tu feras imprimer cette lettre dans la Revue encyclopédique.

Je me suis souvent hasardé dans ma vie à avancer des propositions dont je n'étais
pas sûr. Mais tout ce que j'ai écrit là est depuis bientôt un an dans ma
tête, et il est trop de mon intérêt de ne pas me tromper pour qu'on
me soupconne d'avoir énoncé des théorèmes dont je n'aurais pas la démonstration
complète.

Tu prieras publiquement Jacobi et Gauss de donner leur avis,
non sur la vérité, mais sur l'importance des théorèmes.

Après cela, il y aura, j'espère, des gens qui trouveront leur profit
à déchiffrer tout ce gachis.

Je t'embrasse avec effusion.

                                               E. Galois   Le 29 Mai 1832

A translation by Dr. Louis Weisner, Hunter College of the City of New York, from A Source Book in Mathematics, by David Eugene Smith, Dover Publications, 1959–

You know, my dear Auguste, that these subjects are not the only ones I have explored. My reflections, for some time, have been directed principally to the application of the theory of ambiguity to transcendental analysis. It is desired see a priori  in a relation among quantities or transcendental functions, what transformations one may make, what quantities one may substitute for the given quantities, without the relation ceasing to be valid. This enables us to recognize at once the impossibility of many expressions which we might seek. But I have no time, and my ideas are not developed in this field, which is immense.

Print this letter in the Revue Encyclopédique.

I have often in my life ventured to advance propositions of which I was uncertain; but all that I have written here has been in my head nearly a year, and it is too much to my interest not to deceive myself that I have been suspected of announcing theorems of which I had not the complete demonstration.

Ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of the theorems.

Subsequently there will be, I hope, some people who will find it to their profit to decipher all this mess.

J t'embrasse avec effusion.
                        
                                                     E. Galois.   May 29, 1832.

Translation, in part, in The Unravelers: Mathematical Snapshots, by Jean Francois Dars, Annick Lesne, and Anne Papillaut (A.K. Peters, 2008)–

"You know, dear Auguste, that these subjects are not the only ones I have explored. For some time my main meditations have been directed on the application to transcendental analysis of the theory of ambiguity. The aim was to see in a relation between quantities or transcendental functions, what exchanges we could make, what quantities could be substituted to the given quantities without the relation ceasing to take place. In that way we see immediately that many expressions that we might look for are impossible. But I don't have the time and my ideas are not yet developed enough in this vast field."

Another translation, by James Dolan at the n-Category Café

"My principal meditations for some time have been directed towards the application of the theory of ambiguity to transcendental analysis. It was a question of seeing a priori in a relation between quantities or transcendent functions, what exchanges one could make, which quantities one could substitute for the given quantities without the original relation ceasing to hold. That immediately made clear the impossibility of finding many expressions that one could look for. But I do not have time and my ideas are not yet well developed on this ground which is immense."

Related material

"Renormalisation et Ambiguité Galoisienne," by Alain Connes, 2004

"La Théorie de l’Ambiguïté : De Galois aux Systèmes Dynamiques," by Jean-Pierre Ramis, 2006

"Ambiguity Theory, Old and New," preprint by Yves André, May 16, 2008,

"Ambiguity Theory," post by David Corfield at the n-Category Café, May 19, 2008

"Measuring Ambiguity," inaugural lecture at Utrecht University by Gunther Cornelissen, Jan. 16, 2009

Sunday, April 18, 2010

For Trevanian

Filed under: General — m759 @ 8:00 PM

Where Entertainment Is God
(continued)

Google News at about 7:37 PM —

Image -- Google News, 'Dragon' Edges Out 'Kick-Ass' At Box Office

The Eiger Sanction, by Trevanian –

"Because CII men worked in foreign countries without invitation, and often to the detriment of the established governments, they had no recourse to official protection. Organization men to the core, the CII heads decided that another Division must be established to combat the problem. They relied on their computers to find the ideal man to head the new arm, and the card that survived the final sorting bore the name Yurasis Dragon. In order to bring Mr. Dragon to the United States, it was necessary to absolve him of accusations lodged at the War Crimes Tribunal concerning certain genocidal peccadillos, but CII considered him worth the effort."

Thursday, August 6, 2009

Thursday August 6, 2009

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

The Running

"Budd Schulberg, who wrote the award-winning screenplay for 'On the Waterfront' and created a classic American archetype of naked ambition, Sammy Glick, in his novel What Makes Sammy Run?, died on Wednesday. He was 95…."

Running man with blue background on the cover of 'Eye of Cat,' by Roger Zelazny

Log24, Dec. 16, 2003:

See, too, Blue Matrices, and
a link for Beethoven's birthday:

Juliette Binoche with musical score from Kieslowski's 'Blue'

Song for the
Unification of Europe

Tuesday, March 10, 2009

Tuesday March 10, 2009

Filed under: General,Geometry — m759 @ 9:26 AM
Language Game

“Music, mathematics, and chess are in vital respects dynamic acts of location. Symbolic counters are arranged in significant rows. Solutions, be they of a discord, of an algebraic equation, or of a positional impasse, are achieved by a regrouping, by a sequential reordering of individual units and unit-clusters (notes, integers, rooks or pawns). The child-master, like his adult counterpart, is able to visualize in an instantaneous yet preternaturally confident way how the thing should look several moves hence. He sees the logical, the necessary harmonic and melodic argument as it arises out of an initial key relation or the preliminary fragments of a theme. He knows the order, the appropriate dimension, of the sum or geometric figure before he has performed the intervening steps. He announces mate in six because the victorious end position, the maximally efficient configuration of his pieces on the board, lies somehow ‘out there’ in graphic, inexplicably clear sight of his mind….”

“… in some autistic enchantment, pure as one of Bach’s inverted canons or Euler’s formula for polyhedra.”

— George Steiner, “A Death of Kings,” in The New Yorker, issue dated Sept. 7, 1968

Related material:

“Classrooms are filled with discussions not of the Bible and Jesus but of 10 ‘core values’– perseverance and curiosity, for instance– that are woven into the curriculum.”

— “Secular Education, Catholic Values,” by Javier C. Hernandez, The New York Times, Sunday, March 8, 2009

“… There was a problem laid out on the board, a six-mover. I couldn’t solve it, like a lot of my problems. I reached down and moved a knight…. I looked down at the chessboard. The move with the knight was wrong. I put it back where I had moved it from. Knights had no meaning in this game. It wasn’t a game for knights.”


— Raymond Chandler, The Big Sleep

The Chandler quotation appears in “Language Game,” an entry in this journal on April 7, 2008.

Some say the “Language Game” date, April 7, is the true date (fixed, permanent) of the Crucifixion– by analogy, Eliot’s “still point” and Jung’s “centre.” (See yesterday, noon.)

Friday, October 3, 2008

Friday October 3, 2008

Filed under: General — m759 @ 4:30 PM
The Prize

Paul Newman and Elke Sommer in 'The Prize'

“The secret to life, and
to love, is getting started,
keeping going, and then
getting started again.”

Nobel Laureate
Seamus Heaney
at Sanders Theatre,
Harvard College,
September 30, 2008

On Elke Sommer:

“…Young Elke… studied
in the prestigious
Gymnasium School
in Erlangen….”

Film Fatales

Erlangen Prize Lecture:

Variations on a Theme of
Plato, Goethe, and Klein

(Background:
Christmas Knot, Sept. 26,
and Hard Core, July 17-18.)

Saturday, July 19, 2008

Saturday July 19, 2008

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

(continued from yesterday)

Bertram Kostant, Professor Emeritus of Mathematics at MIT, on an object discussed in this week’s New Yorker:

A word about E(8). In my opinion, and shared by others, E(8) is the most magnificent ‘object’ in all of mathematics. It is like a diamond with thousands of facets. Each facet offering a different view of its unbelievable intricate internal structure.”

Hermann Weyl on the hard core of objectivity:

“Perhaps the philosophically most relevant feature of modern science is the emergence of abstract symbolic structures as the hard core of objectivity behind– as Eddington puts it– the colorful tale of the subjective storyteller mind.” (Philosophy of Mathematics and Natural Science, Princeton, 1949, p. 237)


Steven H. Cullinane on the symmetries of a 4×4 array of points:

A Structure-Endowed Entity

“A guiding principle in modern mathematics is this lesson: Whenever you have to do with a structure-endowed entity S, try to determine its group of automorphisms, the group of those element-wise transformations which leave all structural relations undisturbed.  You can expect to gain a deep insight into the constitution of S in this way.”

— Hermann Weyl in Symmetry

Let us apply Weyl’s lesson to the following “structure-endowed entity.”

4x4 array of dots

What is the order of the resulting group of automorphisms?

The above group of
automorphisms plays
a role in what Weyl,
following Eddington,
  called a “colorful tale”–

The Diamond 16 Puzzle

The Diamond 16 Puzzle

This puzzle shows
that the 4×4 array can
also be viewed in
thousands of ways.

“You can make 322,560
pairs of patterns. Each
 pair pictures a different
symmetry of the underlying
16-point space.”

— Steven H. Cullinane,
July 17, 2008

For other parts of the tale,
see Ashay Dharwadker,
the Four-Color Theorem,
and Usenet Postings
.

Friday, July 18, 2008

Friday July 18, 2008

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

Hard Core

David Corfield quotes Weyl in a weblog entry, "Hierarchy and Emergence," at the n-Category Cafe this morning:

"Perhaps the philosophically most relevant feature of modern science is the emergence of abstract symbolic structures as the hard core of objectivity behind– as Eddington puts it– the colorful tale of the subjective storyteller mind." (Philosophy of Mathematics and Natural Science [Princeton, 1949], p. 237)

For the same quotation in a combinatorial context, see the foreword by A. W. Tucker, "Combinatorial Problems," to a special issue of the IBM Journal of Research and Development, November 1960 (1-page pdf).

See also yesterday's Log24 entry.
 

Thursday, July 3, 2008

Thursday July 3, 2008

Filed under: General — m759 @ 7:11 PM
De Haut en Bas

“… this hard prize,
Fully made, fully apparent,
     fully found”

— Wallace Stevens,
“Credences of Summer”

Marlon Brando and Robert De Niro in 'The Score'

Marlon Brando and Robert De Niro
in “The Score

The Prize:

Billie Holiday, 'On the Sentimental Side' 3-CD set

Friday, June 6, 2008

Friday June 6, 2008

Filed under: General — Tags: , — m759 @ 1:00 PM
Order and Disorder

Robin Williams observes the Keystone State lottery of June 5, 2008: Mid-day 025, Evening 761
Midrash:
The Dance of Chance

Associated Press
"Today in History"
 Thought for Today:

"Two dangers constantly threaten
the world: order and disorder."
— Paul Valery, French poet
(1871-1945).
[La Crise de l'Esprit]

Also from Valéry:

«Notre esprit est fait d'un désordre,
plus un besoin de mettre en ordre
.»
(Mauvaises Pensées et Autres)

«L’ordre pèse toujours à l’individu. Le désordre lui fait désirer la police ou la mort. Ce sont deux circonstances extrêmes où la nature humaine n’est pas à l’aise. L’individu recherche une époque tout agréable, où il soit le plus libre et le plus aidé. Il la trouve vers le commencement de la fin d’un système social. Alors, entre l’ordre et le désordre, règne un moment délicieux. Tout le bien possible que procure l’arrangement des pouvoirs et des devoirs étant acquis, c’est maintenant que l’on peut jouir des premiers relâchements de ce système. Les institutions tiennent encore. Elles sont grandes et imposantes. Mais sans que rien de visible soit altéré en elles, elles n’ont guère plus que cette belle présence; leurs vertus se sont toutes produites; leur avenir est secrètement épuisé; leur caractère n’est plus sacré, ou bien il n’est plus que sacré; la critique et le mépris les exténuent et les vident de toute valeur prochaine. Le corps social perd doucement son lendemain. C’est l’heure de la jouissance et de la consommation générale.»

Paul Valéry, Préface aux Lettres Persanes (1926), recueillie dans Variété, II, 1930

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