Log24

Monday, April 30, 2012

Decomposition– Part III

Filed under: Uncategorized — m759 @ 5:27 PM

(Continued from Part I and Part II.)

The paper excerpted below supplies some badly needed technical
background for the Wikipedia article on functional decomposition.

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

The preprint above gives the precise definitions and technical references
that are completely absent from Wikipedia's Functional decomposition.

For some related material on 4×4 arrays like those in the above figure
see Decomposition Part I and Geometry of the 4×4 Square.

Decomposition (continued)

Filed under: Uncategorized — m759 @ 10:00 AM

Compare and contrast

1. The following excerpt from Wikipedia

IMAGE- Excerpt from 'Functional decomposition' article at Wikipedia

2. A webpage subtitled "Function Decomposition Over a Finite Field."

Related material—

Decomposition and Jews Telling Stories.

Sunday, April 29, 2012

Story Theory

Filed under: Uncategorized — m759 @ 10:30 AM

“Birthday, death-day — what day is not both?”

— John Updike, The New Yorker  dated August 5, 2002, page 63

Today's date— Poincaré's birth, Wittgenstein's death.

A Saint for Clark University—

Today is also the birth date of William Edward Story,
a mathematician who taught at Clark University
in Worcester, Mass.

Story's date of death was April 10, 1930.

See the Log24 posts for that date in 2012.

“Oh, Sara!” she whispered joyfully. “It is like a story!”

“It is  a story,” said Sara. “Everything's  a story.
 You are a story— I am a story.”

— Frances Hodgson Burnett, A Little Princess

Saturday, April 28, 2012

Lottery Hermeneutics

Filed under: Uncategorized — m759 @ 9:00 PM

(Continued)

An interpretation—

Posts 953 and 2341 in this journal.

Backstory— St. Patrick's Day, 2010.

Play and Interplay

Filed under: Uncategorized — m759 @ 7:59 PM

The last paragraph of the previous post
(as updated at about 7:20 PM today)
suggests a search for the phrase
"play and interplay" that yields…

"He had accepted the world as the world,
but now he was comprehending the
organization of it, the play and interplay
of force and matter."

Martin Eden  by Jack London

This in turn suggests a review of the film "Queen to Play" —

(Background: Nabokov + Patterns.)

The review announces showings of the film at Clark University
in Worcester, Mass., on Sunday, October 30, 2011.

See also this journal on that date— "The Idea Idea"— and
references to a knight figure from today's  date in 1985.

Sprechen Sie Deutsch?

Filed under: Uncategorized — m759 @ 10:48 AM

A Log24 post, "Bridal Birthday," one year ago today linked to
"The Discrete and the Continuous," a brief essay by David Deutsch.

From that essay—

"The idea of quantization—
the discreteness of physical quantities
turned out to be immensely fruitful."

Deutsch's "idea of quantization" also appears in
the April 12 Log24 post Mythopoetic

"Is Space Digital?" 

— Cover storyScientific American 
     magazine, February 2012

"The idea that space may be digital
  is a fringe idea of a fringe idea
  of a speculative subfield of a subfield."

— Physicist Sabine Hossenfelder 
     at her weblog on Feb. 5, 2012

"A quantization of space/time
 is a holy grail for many theorists…."

— Peter Woit in a comment 
      at his weblog on April 12, 2012

It seems some clarification is in order.

Hossenfelder's "The idea that space may be digital"
and Woit's "a quantization of space/time" may not
refer to the same thing.

Scientific American  on the concept of digital space—

"Space may not be smooth and continuous.
Instead it may be digital, composed of tiny bits."

Wikipedia on the concept of quantization—

Causal setsloop quantum gravitystring theory,
and 
black hole thermodynamics all predict
quantized spacetime….

For a purely mathematical  approach to the
continuous-vs.-discrete issue, see
Finite Geometry and Physical Space.

The physics there is somewhat tongue-in-cheek,
but the geometry is serious.The issue there is not
continuous-vs.-discrete physics , but rather
Euclidean-vs.-Galois geometry .

Both sorts of geometry are of course valid.
Euclidean geometry has long been applied to 
physics; Galois geometry has not. The cited
webpage describes the interplay of both  sorts
of geometry— Euclidean and Galois, continuous
and discrete— within physical space— if not
within the space of physics.

Friday, April 27, 2012

Paradigms Lost continues…

Filed under: Uncategorized — m759 @ 9:00 PM

This post was suggested by Paradigms Lost
(a post cited here a year ago today),
by David Weinberger's recent essay "Shift Happens,"
and by today's opening of "The Raven."

David Weinberger in The Chronicle of Higher Education April 22

"… Kuhn was trying to understand how Aristotle could be such a brilliant natural scientist except when it came to understanding motion. Aristotle's idea that stones fall and fire rises because they're trying to get to their natural places seems like a simpleton's animism.

Then it became clear to Kuhn all at once. Ever since Newton, we in the West have thought movement changes an object's position in neutral space but does not change the object itself. For Aristotle, a change in position was a change in a quality of the object, and qualitative change tended toward an asymmetric actualization of potential: an acorn becomes an oak, but an oak never becomes an acorn. Motion likewise expressed a tendency for things to actualize their essence by moving to their proper place. With that, 'another initially strange part of Aristotelian doctrine begins to fall into place,' Kuhn wrote in The Road Since Structure ."

Dr. John Raven (of Raven's Progressive Matrices)

"… these tools cannot be immediately applied within our current workplaces, educational systems, and public management systems because the operation of these systems is determined, not by personal developmental or societal needs, but by a range of latent, rarely discussed, and hard to influence sociological forces.

But this is not a cry of despair: It points to another topic which has been widely neglected by psychologists: It tells us that human behaviour is not  mainly determined by internal  properties— such as talents, attitudes, and values— but by external  social forces. Such a transformation in psychological thinking and theorising is as great as the transformation Newton introduced into physics by noting that the movement of inanimate objects is not determined by internal, 'animistic,' properties of the objects but by invisible external forces which act upon them— invisible forces that can nevertheless be mapped, measured, and harnessed to do useful work for humankind.

So this brings us to our fourth conceptualisation and measurement topic: How are these social forces to be conceptualised, mapped, measured, and harnessed in a manner analogous to the way in which Newton made it possible to harness the destructive forces of the wind and the waves to enable sailing boats to get to their destinations?"

Before Newton, boats never arrived?

References

Filed under: Uncategorized — m759 @ 12:00 PM

"These lowbrow, popular cultural references bring the possibilities
of interpretation down to an everyday level, forcing us to acknowledge
that not every painting that looks like a splatter is necessarily a
homage/anti-homage to Jackson Pollock."

— Stina Högqvist, review of the art of Josefine Lyche

An April 27–

Filed under: Uncategorized — m759 @ 11:09 AM

IMAGE- The 3x3x3 Galois cube
The 3×3×3 Galois Cube

Backstory— The Talented, from April 26 last year,
and Atlas Shrugged, from April 27 last year.

Thursday, April 26, 2012

Rainbow Bridge for Thor’s Day

Filed under: Uncategorized — m759 @ 9:00 PM

(Not  necessarily for Rainbow People )

About the artist—

Rainbow People

Filed under: Uncategorized — m759 @ 6:29 PM

(Mythopoetic continued)

Voice of America  today—

Thousands of Norwegians Defy Confessed Killer Breivik in Song

"The demonstrators waved roses and flags
Thursday as they and Norwegian folk singer
Lillebjoern Nilsen sang an adaptation
of the children's song, 'My Rainbow Race,' 
which Breivik in court last week called
an example of Marxist brainwashing."

[See also PETE SEEGER AND LILLEBJØRN NILSEN.
Click on the image below for Seeger's original version.]

Liberia Reacts to Taylor Conviction With Mixed Emotions

"As the verdict was read out, a rainbow was seen
in the sky, encircling the sun.  For many Liberians,
superstition is a part of life.  The rainbow heralded
a new era, they said, beginning with the verdict of Taylor."

["You're not the only one… with mixed emotions."]

Narratives

Filed under: Uncategorized — m759 @ 1:00 PM

Two narratives in memory of my seventh-grade
history teacher, who died on January 27, 2012—

1.  On the history of Liberia
     (subject of a paper I wrote in seventh grade), and

2.  Comic-book history (from the above date)

Thor’s 4/26 Light Bulb Joke

Filed under: Uncategorized — m759 @ 10:25 AM

See also, in this  journal, "The Prestige."

Wednesday, April 25, 2012

The Hallowed Crucible

Filed under: Uncategorized — m759 @ 10:30 PM

(Continued)

A meditation suggested by the April 20 post Complex Reflection
and by the life and April 20 death of a scientist who worked
at Los Alamos (home of the Monte Carlo method) and at
the Santa Fe Institute (home of complexity theory).

IMAGE- The NY lottery results for midday April 20, 2012, were 0286 and 823.

A search for 286 in this journal yields "Yet Another Cartoon Graveyard."

That June 1, 2008, post linked to poem  286 in a 1919 anthology.

Here is that poem, together with poem 823.

Together, these poems may be regarded as a meditation on
Simone Weil and her brother André Weil or, 
more abstractly, on Love and Death.

Happy birthday to Al Pacino.

O for October

Filed under: Uncategorized — m759 @ 12:29 PM

(Not Olympus )

(Continued from Mythopoetic, a post of April 12)

This post was suggested by a 2010 film about fictional Olympians,
by today's New York Times obituaries, and by a bar brawl at the Olympian
New York Athletic Club in "the wee hours of April 13."

Rick Riordan in the image below advertises another large
"Demigod Gathering" on October 12, 2010.

The Riordan image is from a post at ComposersCave.com
made on October 3, 2010.

Applying Jung's principle of synchronicity to this demigod material,
we find the October 3, 2010, Log24 post Search for the Basic Picture
and the October 12, 2010, Log24 post King Solomon's Mind.

Note that the latter October date is that of the traditional
Columbus Day, and that the 2010 film of The Lightning Thief   
was directed by Chris Columbus of 1492 Pictures.

The film's release was earlier in 2010, on February 12.

Tuesday, April 24, 2012

Garden Party

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM
 

Google today

 

 

Barnett Newman, 1963-1964

Background

Click to enlarge.

See also  

"Pardon me.  J'adoube." 

— The Consul as he fastens his fly in Under the Volcano ,
     the Garden of Eden scene

Smaller Parts

Filed under: Uncategorized — m759 @ 12:20 PM

Suggested by a piece in the
Melbourne Herald Sun  dated August 1, 2007—

A link from Log24 on that date

Show Business
according to Fritz Leiber
:
“Sid thinks you’re ready for
 some of the smaller parts.”

Monday, April 23, 2012

Mate in Six

Filed under: Uncategorized — m759 @ 6:29 PM

In memory of Mike Wallace

  1. An April 8 post noting the death of Wallace—
    a NY Times  obituary notice with ad at top— "The North Face"
     
  2. An April 21 post noting the death of Charles Colson,
    reportedly at at 3:12 PM on Saturday, April 21, 2012,
    with ad at top— "Discover New Horizons" 
     
  3. An April 21 post linking to a 3/12 post (this date being
    suggested by the reported time of Colson's death)
    that has a review of the film "The Ninth Configuration"
     
  4. An April 22 post with six lines that some might
    interpret as meeting on a horizon, two lines that might
    be interpreted as meeting at a "depth horizon," and
    a ninth line that emerges from the other eight
     
  5. An April 23 post that combines a passage from
    "The Ninth Configuration" with a detail from
    the North Face ad that appeared above Wallace's
    NY TImes  obituary on April 8 and again above
    Colson's obituary on April 23
     
  6. "The game's…"

See also Knight Moves.

Footnote

Filed under: Uncategorized — m759 @ 9:00 AM

IMAGE- Cutshaw in 'The Ninth Configuration' on God as a giant Foot

IMAGE- April 23, 2012, NY Times obit for Charles Colson with foot from ad for 'The North Face' running shoes

Sunday, April 22, 2012

An Elusive Notion

Filed under: Uncategorized — m759 @ 11:09 PM

"… this notion of ‘depth’ is an elusive one
even for a mathematician who can recognize it…."

— G. H. Hardy, A Mathematician's Apology

In Geometry and the Imagination , Hilbert and Cohn-Vossen
describe the Brianchon-Pascal configuration of 9 points
and 9 lines, with 3 points on each line and 3 lines through
each point, as being "the most important configuration of all geometry."

The Brianchon-Pascal configuration is also known as the Pappus configuration


Some background …

"The Theorem of Pappus: A Bridge Between Algebra and Geometry"
Elena Anne Marchisotto
The American Mathematical Monthly
Vol. 109, No. 6 (Jun. – Jul., 2002), pp. 497-516

Plan 9 from MIT

Filed under: Uncategorized — m759 @ 9:00 PM

IMAGE- Very simplified example of a Raven's Progressive Matrices test

Click image for some context from MIT.

Background from The New York Times— "Can You Make Yourself Smarter?"

See also "Plan 9" in this journal.

The Gospel According to Xbox

Filed under: Uncategorized — m759 @ 12:00 PM

"Every multiplayer game, both free-for-all and team based,
will begin with a Mexican standoff." —Wikipedia

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

"The Cardinal seemed a little preoccupied today."

Saturday, April 21, 2012

Finding a Form

Filed under: Uncategorized — Tags: , — m759 @ 11:30 PM


In "Contact," Dr. Arroway  is shown the key to the Primer

In this journal, fictional symbologist Robert Langdon is shown a cube

Symbologist Robert Langdon views a corner of Solomon's Cube

"Confusion is nothing new." — Song lyric

Split

Filed under: Uncategorized — m759 @ 11:07 PM

"So the sundering we sense between nature and culture
lies not like a canyon outside us, but splits our being
at its most intimate depths the way mind breaks off from body.
It is still another version of that bitter bifurcation
long ago decreed— our expulsion from Eden…."

— William H. Gass in Finding a Form ,
     Cornell U. Press paperback, 1997, page 138

See also…

IMAGE- 'The Line,' a post on Blatty's 'The Ninth Configuration'

For another bitter bifurcation, see La Despedida .

Meanwhile…

Filed under: Uncategorized — m759 @ 5:28 PM

Love and Death–

Filed under: Uncategorized — m759 @ 4:14 PM

— Title of a 1975 film. The late Martin Poll (previous post)
was the executive producer.

See also "A Corpse Will Be Transported by Express."

Related material—

IMAGE- 'Last Train from Cuernavaca' paperback from webpage at Walmart

But Seriously…

Filed under: Uncategorized — m759 @ 8:00 AM

From Deadline Hollywood

A film producer's death "between Friday night and early Saturday morning,"
April 13-14, 2012—

R.I.P. Martin Poll

By THE DEADLINE TEAM | Sunday April 15, 2012 @ 7:36 pm PDT

Veteran movie and TV producer Martin Poll died between Friday night and early Saturday morning of natural causes at a care facility on the Upper Westside in New York City. He was 89.

See also the post linked to on the afternoon of Friday the 13th of April—

"All the saints have powers." — Cardinal Marchisano.

Happy birthday,  James McAvoy (at left below in X-Men: First Class ).

IMAGE- James McAvoy (left) and Michael Fassbender in 'X-Men: First Class'

Volcano Dawn

Filed under: Uncategorized — m759 @ 6:14 AM

(Continued from October First, 2010)

Estas son las mañanitas….

Today's Birthdays:
Britain's Queen Elizabeth II is 86.
Actress-comedian-writer Elaine May is 80.
Actor Charles Grodin is 77.

— AP, Today in History, April 21, 2012

Friday, April 20, 2012

Uploading Levon

Filed under: Uncategorized — m759 @ 8:00 PM

Found in a Google search today—

(Click image for videos.)

I hadn't known until today that youtube.com/blogs/m759 exists.

The Arduino link under "More Channels" suggests a site
that may interest some future Arroway or Hadden.

Complex Reflection

Filed under: Uncategorized — 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…"

Thursday, April 19, 2012

The Virgin’s Tale

Filed under: Uncategorized — m759 @ 9:29 PM

Suggested by two posts today at other weblogs—

"The Ariel Thread" and "Spring in the Virgin Islands."

Background— Beach with Palms,  One Story and Descanse .

In Memoriam

Filed under: Uncategorized — m759 @ 6:48 PM

For Octavio Paz, who died on this date in 1998

… 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  online today

Under the Volcano–

Filed under: Uncategorized — m759 @ 1:31 PM

The Hot Rock

IMAGE- 'Mexican volcano hurls hot rock half-mile in air'

See also A Little Story .

Fashion Notes

Filed under: Uncategorized — m759 @ 1:06 PM
  1. Fun and Games (April 15)
  2. New York Times  today
  3. The Legend of Drunken Master

Past Eve and Adam’s

Filed under: Uncategorized — m759 @ 11:30 AM

riverrun

Wednesday, April 18, 2012

Adam in Eden

Filed under: Uncategorized — m759 @ 9:00 PM

…. and John Golding, an authority on Cubism who "courted abstraction"—

"Adam in Eden was the father of Descartes." — Wallace Stevens

Fictional symbologist Robert Langdon and a cube

Symbologist Robert Langdon views a corner of Solomon's Cube

From a Log24 post, "Eightfold Cube Revisited,"
on the date of Golding's death—

Dynkin diagram D4 for triality

A related quotation—

"… quaternions provide a useful paradigm
  for studying the phenomenon of 'triality.'"

  — David A. Richter's webpage Zometool Triality

See also quaternions in another Log24 post
from the date of Golding's death— Easter Act.

Eve in the Garden

Filed under: Uncategorized — m759 @ 7:59 PM

"… he continued to make brief appearances
  on the show, including the one this past 
  New Year's Eve.* "

— Bruce Weber, New York Times

"The only stars Clark coveted
  for his show in those early years
  but could not get were
  the Beatles and Ricky Nelson…."

— Geoff Boucher, Los Angeles Times

"I don't know why you say goodbye"

"There was … magic in the air"

* The link is to another eve, Bridget's .

Tuesday, April 17, 2012

Space Speech

Filed under: Uncategorized — Tags: — m759 @ 11:30 AM

"Here space itself truly spoke…."

Monday, April 16, 2012

Happy Birthday, Benedict XVI

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

F.A. Porsche:

„Ein formal stimmiges Produkt braucht keine Verzierung,
 es soll durch die reine Form erhöht werden.“

"My friends all drive Porsches,
 I must make amends."
 — Janis Joplin, Pearl Sessions CD
      reissue released today at Amazon.co.uk

http://www.log24.com/log/pix12/120416-Popemobile.jpg

Carroll Thanks the Academy

Filed under: Uncategorized — Tags: , — m759 @ 11:30 AM

Gary Gutting, "Arguing About Language," in "The Stone,"
The New York Times  philosophy column, yesterday—

There's a sense in which we speak language
and a sense in which, in Mallarmé's famous phrase,
“language itself speaks.”

Famous? A Google Book Search for

"language itself speaks" Mallarmé

yields 2 results, neither helpful.

But a Google Book Search for

"language itself speaks" Heidegger

yields "about 312 results."

A related search yields the following

Paul Valéry, encountering Un Coup de Dés  in Mallarmé’s worksheets in 1897, described the text as tracing the pattern of thought itself:

It seemed to me that I was looking at the form and pattern of a thought, placed for the first time in finite space. Here space itself truly spoke, dreamed, and gave birth to temporal forms….

… there in the same void with them, like some new form of matter arranged in systems or masses or trailing lines, coexisted the Word! (Leonardo  309*)

* The page number is apparently a reference to The Collected Works of Paul Valéry: Leonardo, Poe, Mallarmé , translated by Malcolm Cowley and James R. Lawler, Princeton University Press, 1972. (As a temporal  form, "309" might be interpreted as a reference to 3/09, March 9, the date of a webpage on the Void.)

For example—

Symbologist Robert Langdon views a corner of Solomon's Cube

Background:
Deconstructing Alice
and Symbology.

Sunday, April 15, 2012

Ghost Humor

Filed under: Uncategorized — Tags: — m759 @ 10:12 PM

This afternoon's post Tally quotes "Day-O,"
a song performed, notably, in the 1988 film
"Beetlejuice"—

More merriment —

Tummler  Lou Goldstein died at 90 on April 2, 2012,
according to this evening's online New York Times .

In his honor, figures from a Sept. 17, 2009, post

http://www.log24.com/log/pix12/120415-Corner-Symbology.jpg

See also "Boo Boo Boo."

Those not amused by tummler  humor may prefer
a post from the date of Goldstein's death
related to the object viewed above by the fictional
symbologist Robert Langdon.

Tally

Filed under: Uncategorized — m759 @ 12:06 PM

Background—

Celebrity War Games and Hunger Games.

 http://www.log24.com/log/pix12/120415-NYTfront1039AM-360w.jpg

"Come, Mr. Tally Man"

Sermon

Filed under: Uncategorized — m759 @ 10:30 AM

The Devil Likes Metamorphoses.

Fun and Games

Filed under: Uncategorized — m759 @ 9:00 AM

"with Mearingstone in Fore ground"

IMAGE- 'Philosopher's Stone' album cover

"…the Somerville group has grown…."

Irish Geometry

Filed under: Uncategorized — m759 @ 2:01 AM

"Now (lens"

Finnegans Wake , Book II,
     Episode 2, page 293

Background—

Saturday, April 14, 2012

Scottish Algebra

Filed under: Uncategorized — Tags: — m759 @ 11:59 PM

Two papers suggested by Google searches tonight—

[PDF] PAPERS HELD OVER FROM THEME ISSUE ON ALGEBRA AND …

ajse.kfupm.edu.sa/articles/271A_08p.pdf

File Format: PDF/Adobe Acrobat – View as HTML

by RT Curtis2001Related articles

This paper is based on a talk given at the Scottish Algebra Day 1998 in Edinburgh. ……

Curtis discusses the exceptional outer automorophism of S6
as arising from group actions of PGL(2,5).

See also Cameron and Galois on PGL(2,5)—

[PDF] ON GROUPS OF DEGREE n AND n-1, AND HIGHLY-SYMMETRIC

citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.104…

File Format: PDF/Adobe Acrobat – Quick View

by PJ CAMERON1975Cited by 14Related articles

PETER J. CAMERON. It is known that, if G is a triply transitive permutation group
on a finite set X with a regular S3 the symmetric group on 3 letters, and PGL (2, 5)
the 2-dimensional projective general linear Received 24 October, 1973

Illustration from Cameron (1973)—

http://www.log24.com/log/pix12/120414-CameronFig1.jpg

Friday, April 13, 2012

Meditation for Friday the 13th

Filed under: Uncategorized — m759 @ 1:44 PM

From Friday, May 13, 2005

“All the saints have powers.”

See also Friday, April 13, 2007 and Friday, February 13, 2009.

Constructive

Filed under: Uncategorized — m759 @ 12:00 PM

The two previous posts have referred to the HBO series "Big Love."

For a more constructive production related to a Latter-Day Saint,
see the video of the 1989 song "Sacred Emotion."
The visually impaired may be forgiven for thinking
the voice in the video is that of Michael Jackson.

"Our love is like a sacred emotion." — Donny Osmond

Putting the Prime in “Primate”

Filed under: Uncategorized — m759 @ 11:30 AM

See Prime Cut and Lavender Blue, Dilly Dilly
as well as Sissy Spacek on "Big Love."

See also Zenna Henderson and the Latter-Day Saints.

Askew Crews

Filed under: Uncategorized — m759 @ 10:01 AM

IMAGE- NY Times obits- Actor Luke Askew, Bishop Agustin Roman

From the day Askew died

A Large & Startling Figure:
The Harry Crews Online Bibliography
www.harrycrews.org/Features/News/index.html
Page updated: March 29, 2012, 08:16 PM
Copyright © 1998 – 2010

The "large and startling" phrase is from Flannery O'Connor—

From Georgia College, Milledgeville, GA

… in Flannery O'Connor's essay "The Fiction Writer and His Country"… she explains why she writes the way she does: "When you can assume that your audience holds the same beliefs you do, you can relax a little and use more normal means of talking to it; when you have to assume that it does not, then you have to make your vision apparent by shock— to the hard of hearing you shout, and for the almost-blind you draw large and startling figures" (Mystery and Manners , p. 34).

For a large and startling figure played by Askew, see a scene from "Big Love."

IMAGE- Luke Askew as Hollis Greene in 'Big Love'

The Primate and the Bee

Filed under: Uncategorized — m759 @ 9:00 AM

George Steiner —

"Man is, in Lévi-Strauss's view, a mythopoetic primate
(it's a difficult phrase but we don't have a better one)…."

Wikipedia —

"Primate is a title or rank bestowed on some bishops in certain Christian churches." 

Pope Benedict XVI at the 2012 Easter Vigil on April 7 —

"The great hymn of the Exsultet, which the deacon sings at the beginning of the Easter liturgy, points us quite gently towards a further aspect. It reminds us that this object, the candle, has its origin in the work of bees. So the whole of creation plays its part. In the candle, creation becomes a bearer of light.

But in the mind of the Fathers, the candle also in some sense contains a silent reference to the Church. The cooperation of the living community of believers in the Church in some way resembles the activity of bees. It builds up the community of light."

http://twitter.com/#!/skdh —

Sabine Hossenfelder's (Bee's) Easter Tweet

Thursday, April 12, 2012

Mythopoetic*

Filed under: Uncategorized — m759 @ 9:29 PM

"Is Space Digital?" 

Cover storyScientific American  magazine, February 2012

"The idea that space may be digital
  is a fringe idea of a fringe idea
  of a speculative subfield of a subfield."

— Physicist Sabine Hossenfelder
     at her weblog on Feb. 5, 2012

"A quantization of space/time
 is a holy grail for many theorists…."

— Peter Woit in a comment at his physics weblog today

See also 

* See yesterday's Steiner's Systems.

Chess

Filed under: Uncategorized — m759 @ 8:23 AM

A link for Katherine Neville

Classroom

Filed under: Uncategorized — m759 @ 3:18 AM

IMAGE- Bogart in 'Casablanca' with chessboard

IMAGE- NY Times obituaries, 3 AM EDT Thursday, April 12, 2012. The ad 'THIS IS YOUR CLASSROOM' is from Wagner College.

Wednesday, April 11, 2012

Steiner’s Systems

Filed under: Uncategorized — m759 @ 12:00 PM

Background— George Steiner in this journal
and elsewhere—

"An intensity of outward attention —
interest, curiosity, healthy obsession —
was Steiner’s version of God’s grace."

Lee Siegel in The New York Times
     March 12, 2009

(See also Aesthetics of Matter in this  journal on that date.)

Steiner in 1969  defined man as "a language animal."

Here is Steiner in 1974  on another definition—

IMAGE- George Steiner on Levi-Strauss viewing man as 'a mythopoetic primate'

Related material—

IMAGE- Daniel Gorenstein quotes Freeman Dyson on physics and the monster group

Also related — Kantor in 1981 on "exquisite finite geometries," and The Galois Tesseract.

Tuesday, April 10, 2012

Death on Good Friday

Filed under: Uncategorized — Tags: — m759 @ 11:07 PM
 

Edward Reed Whittemore Jr. was born
on Sept. 11, 1919, in New Haven, 
where his father was a doctor. 
He earned a bachelor’s degree in English from Yale.
As a sophomore there, with his roommate
James Jesus Angleton (who would later become
the Central Intelligence Agency’s counterintelligence chief),
he founded a literary magazine, Furioso.

— The New York Times

In memoriam:

PART I —

PART II —

  1. Computers in "23"
  2. Der Einsatz
  3. The Borges Compass

Carpenter Song…

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Where Entertainment is God

(Continued from April 4 and April 8)

"Hot dog… I'm a winner either way."
Mary Chapin Carpenter

The Christening

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

Today's Times  teasers—

Location, Location, Location.

Click on image for further details.

See also April 3rd's Catholic View.

Cameo

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

IMAGE- Video- Indiana Jones teaches archaeology.

See also Argyle in this journal.

Poem

Filed under: Uncategorized — Tags: — m759 @ 11:30 AM

IMAGE- Poem, 404x529

IMAGE- Scots dictionary- 'farther east' is 'easter.'

See also Marks the Spot and Hell Enough.

Dehors*

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"A New York Jew imitates D. H. Lawrence at his peril."

The New York Times  today

“Our focus is on creating very high quality, highly artistically produced programs that bring together worlds that usually don’t talk to each other,” said Dr. Greene, a physics and math professor at Columbia and well-known popularizer of science. “We’ve tried to inject the drama of science into these highly produced programs, so people leave the event saying, ‘Wow, I didn’t know that’s what science is like.’ ”

As for D. H. Lawrence, see this journal on September 10, 2003.

* For the title, see last night's Turing Gate.

Turing Gate

Filed under: Uncategorized — Tags: , — m759 @ 2:02 AM

In memory of Christine Brooke-Rose,
an image from the date of her death

IMAGE- Excerpt from book 'Turing's Cathedral'

See also A Little Story and Before Dehors.

Monday, April 9, 2012

Eightfold Cube Revisited

Filed under: Uncategorized — m759 @ 12:00 PM

A search today (Élie Cartan's birthday) for material related to triality*

Dynkin diagram D4 for triality

yielded references to something that has been called a Bhargava cube .

Two pages from a 2006 paper by Bhargava—

Bhargava's reference [4] above for "the story of the cube" is to…

Higher Composition Laws I:
A New View on Gauss Composition,
and Quadratic Generalizations

Manjul Bhargava

The Annals of Mathematics
Second Series, Vol. 159, No. 1 (Jan., 2004), pp. 217-250
Published by: Annals of Mathematics
Article Stable URL: http://www.jstor.org/stable/3597249

A brief account in the context of embedding problems (click to enlarge)—

For more ways of slicing a cube,
see The Eightfold Cube —

* Note (1) some remarks by Tony Smith
   related to the above Dynkin diagram
   and (2) another colorful variation on the diagram.

Easter Act

Filed under: Uncategorized — Tags: — m759 @ 10:00 AM

Acts 12:4 —  

"And when he had apprehended him,
he put him  in prison, and delivered him 
to four quaternions of soldiers to keep him;
intending after Easter to bring him forth to the people."

With six you get egg roll.

Sunday, April 8, 2012

Time Goes By

Filed under: Uncategorized — m759 @ 12:20 PM

IMAGE- Mike Wallace NY Times obit with North Face shoe ad

Steiner System

Filed under: Uncategorized — m759 @ 12:00 PM

For Autism Awareness Month

See George Steiner on Autistic Enchantment, as well as…

(Click images for further details.)

IMAGE- Brower plugins 'puzzle piece' logo

IMAGE- 'Puzzle Piece' symbol on 'Queen to Play' page

This year, Autism Awareness Day  was April 2.

The Two Towers

Filed under: Uncategorized — m759 @ 9:00 AM

Click to enlarge.

See also March 9, 2007 and the film Queen to Play  (NY-LA release: 2011, April 1).

The U.S. premiere of Queen to Play  was on April 25, 2009 at the Tribeca Festival.

"Now, I'll open up a line of credit for you.
You'll be wantin' a few toys."

— A Robert De Niro character quoted in
     Lines (St. Andrew's Day, 2011)

Update of 10:10 AM EDT April 8 (Easter Day)— 

See an "old Brooklyn haunt" in The Easter Phantom.

Saturday, April 7, 2012

Appeasing Epstein

Filed under: Uncategorized — Tags: — m759 @ 7:14 PM

… On Holy Saturday

"'If only they could send us something grown-up… a sign or something.' 
And a sign does come from the outside. That night, unknown to the children,
a plane is shot down and its pilot parachutes dead to earth and is caught
in the rocks on the mountain. It requires no more than the darkness of night
together with the shadows of the forest vibrating in the signal fire to distort
the tangled corpse with its expanding silk 'chute into a demon that must
be appeased."

— Claire Rosenfield, 1961 essay about Lord of the Flies

Flies-related death from April 1

Edmund L. Epstein, Scholar Who Saved ‘Lord of the Flies,’ Dies at 80

See also Holy Saturday, 2004.

Requiem for Kinkade

Filed under: Uncategorized — m759 @ 2:10 PM

Que descanse en paz.

Foreground

Filed under: Uncategorized — m759 @ 1:44 PM

ART WARS continues…

(Click to enlarge.)

IMAGE-'Thomas Kinkade's artistic legacy'

See also today's previous post and Foreground in this journal.

Background

Filed under: Uncategorized — Tags: — m759 @ 12:29 PM

From Joyce's 1912 Trieste lecture on Blake:

"Michelangelo's influence is felt in all of Blake's work, and especially in some passages of prose collected in the fragments, in which he always insists on the importance of the pure, clean line that evokes and creates the figure on the background of the uncreated void."

For a related thought from Michelangelo, see Marmo Solo .

For pure, clean lines, see Galois Geometry.

As for "the uncreated void," see the Ernst Gombrich link in Marmo Solo  for "an almost medieval allegory of how man confronts the void."

For some related religious remarks suited to the Harrowing of Hell on this Holy Saturday, see August 16, 2003

The Void

Filed under: Uncategorized — Tags: — m759 @ 5:01 AM

(Continued from March 10, 2012)

An inaccuracy in a passage linked to yesterday

"The created universe, the whole of things, is, 
in words from Joyce's Ulysses , 'predicated on the void.'"

The "predicated" phrase seems to be absent from Ulysses .

Joyce does, however, have the following (from ricorso.net)—

William Blake” (March 1912) – cont.: ‘Armed with this two-edged sword, the art of Michaelangelo and the revelations of Swedenborg, Blake killed the dragon of experience and natural wisdom, and, by minimising space and time and denying the existence of memory and the senses, he tried to paint his works on the void of the divine bosom. [See note, infra.]To him, each moment shorter than a pulse-beat was equivalent in its duration to six thousand years, because in such an infinitely short instant the work of the poet is conceived and born. To him, all space larger than a red globule of human blood was visionary, created by the hammer of Los, while in a space smaller than a globule of blood we approach eternity, of which our vegetable world is but a shadow. Not with the eye, then, but beyond the eye, the soul and the supreme move must look, because the eye, which was born in the night while the soul was sleeping in rays of light, will also die in the night. […] The mental process by which Blake arrives at the threshold of the infinite is a similar process. Flying from the infinitely small to the infinitely large, from a drop of blood to the universe of stars, his soul is consumed by the rapidity of flight, and finds itself renewed and winged and immortal on the edge of th dark ocean of God. And althought he based his art on such idealist premises, convinced that eternity was in love with the products of time, this sons of God with the sons of [MS ends here].’ (Critical Writings, 1959, 1966 Edn., pp.221-22; quoted [in part] in Richard Ellmann, James Joyce, 1965 Edn., p.330.) [For full text, see RICORSO Library, “Major Authors”, via index, or direct.] Note – for “void” [supra] , cf. Stephen in “Scylla & Charybdis”: ‘Fatherhood […] is a mystical estate, an apostolic succession, from only begetter to only begotten. On that mystery and not on the madonna which the cunning Italian intellect flung to the mob of Europe the church is founded and founded irremovably because founded, like the world, macro- and microcosm, upon the void.’ (Ulysses, Penguin Edn. 1967, p.207; [my itals.].)

Some academics may prefer a more leftist version of
"predicated on the void"—

Knowing Brooklyn

Filed under: Uncategorized — Tags: — m759 @ 3:59 AM

For St. Dismas,  a Holy Saturday story

"Mr. Rosensaft told another story to illustrate his friend's mix of grit and wit. Mr. Steinberg was negotiating one day with the French culture minister to recover paintings stolen from Jews during the Holocaust. The minister huffed that Mr. Steinberg knew nothing about art.

'You're right,' Mr. Steinberg said. 'I don't know anything about art. I'm from Brooklyn. I know about stolen goods.'"

New York Times  this morning

See also yesterday afternoon's Good Friday post
and the passage on Aquinas that it links to.

Friday, April 6, 2012

For Good Friday

Filed under: Uncategorized — Tags: — m759 @ 3:00 PM

From St. Dismas, a link: http://www.scribd.com/doc/62700189/9/nine *

And in this journal… "Nine is a Vine."

* Aquinas, Ethics, and Philosophy of Religion:
  Metaphysics and Practice ,
by Thomas Hibbs,
  Indiana University Press, Bloomington and Indianapolis, 2007

Reine Form

Filed under: Uncategorized — Tags: — m759 @ 9:29 AM

F.A. Porsche:

„Ein formal stimmiges Produkt braucht keine Verzierung,
 es soll durch die reine Form erhöht werden.“

Spectral Theory

Filed under: Uncategorized — Tags: , — m759 @ 8:00 AM

"And we may see the meadow in December,
 icy white and crystalline" — Johnny Mercer

"At another end of the sexual confusion spectrum…."

IMAGE- Frank Langella and Liam Neeson in 'Unknown'

"The devil likes metamorphoses."

Thursday, April 5, 2012

Go Ask Emma*

Filed under: Uncategorized — m759 @ 11:07 PM

From Katherine Neville's novel The Eight  (see also April 4, Der Einsatz )—

IMAGE- Porsche racecar decorated with the White Queen, Emma Frost of X-Men

"You walked out of my dreams and into my car…"

* Frost

In the Details

Filed under: Uncategorized — m759 @ 6:00 PM

An image from 62 years ago:

Click image for details.

For the religious significance of "62," see Strong Emergence Illustrated.

See also a related search.

Meanwhile, back in 1950…

Filed under: Uncategorized — Tags: — m759 @ 10:30 AM

See also Solomon's Cube.

Leap Day of Faith

Filed under: Uncategorized — m759 @ 9:48 AM

Presidential candidate Mitt Romney on Monday, April 2, 2012—

"I think there is in this country a war on religion.
 I think there is a desire to establish a religion
 in America known as secularism."

Nancy Haught of The Oregonian  on Leap Day, Feb. 29, 2012

IMAGE- Theologian William Hamilton at the University of St. Andrews, Scotland, February 10, 1950

William Hamilton, the retired theologian who declared in the 1960s that God was dead, died Tuesday [Feb. 28, 2012] in his downtown Portland apartment at 87. Hamilton said he'd been haunted by questions about God since he was a teenager. Years later, when his conclusion was published in the April 8, 1966, edition of Time Magazine, he found himself in a hornet's nest.

Time christened the new movement "radical theology" and Hamilton, one of its key figures, received death threats and inspired angry letters to the editor in newspapers that carried the story. He encountered hostility at Colgate Rochester Crozer Divinity School, where he had been teaching theology,  and lost his endowed chair in 1967.

Hamilton moved on to teach religion at New College in Sarasota, Fla.

(See also this  journal on Leap Day.)

From New College: The Honors College of Florida

History Highlights

Oct. 11, 1960: New College is founded as a private college

1961: Trustees obtain options to purchase the former Charles Ringling estate on Sarasota Bay and 12 acres of airport land facing U.S. 41 held by private interests. The two pieces form the heart of the campus

Nov. 18, 1962: the campus is dedicated. Earth from Harvard is mixed with soil from New College as a symbol of the shared lofty ideals of the two institutions.

See also, in this journal, "Greatest Show on Earth" and The Harvard Crimson

The Harvard Crimson,
Online Edition
Sunday,
Oct. 8, 2006

POMP AND
CIRCUS-STANCE


CRIMSON/ MEGHAN T. PURDY

Friday, Oct. 6:

 

The Ringling Bros. Barnum & Bailey Circus has come to town, and yesterday the animals were disembarked near MIT and paraded to their temporary home at the Banknorth Garden.

OPINION

At Last, a
Guiding Philosophy

The General Education report is a strong cornerstone, though further scrutiny is required.

After four long years, the Curricular Review has finally found its heart.

The Trouble
With the Germans

The College is a little under-educated these days.

By SAHIL K. MAHTANI
Harvard College– in the best formulation I’ve heard– promulgates a Japanese-style education, where the professoriate pretend to teach, the students pretend to learn, and everyone is happy.

Wednesday, April 4, 2012

Carpenter Song

Filed under: Uncategorized — m759 @ 9:00 PM

I said, "Look out, boys, I've got a license to fly"
And that Caddy pulled over and let us by

Followup story to this morning's Easter Prayer Breakfast

Why Walk?

Finishing School

Filed under: Uncategorized — m759 @ 12:00 PM

For Frank Langella

Der Einsatz

Filed under: Uncategorized — m759 @ 10:31 AM

Continues

 ”Confusion is nothing new.”
– Song lyric, Cyndi Lauper  

(This may serve as today's tribute to Katherine Neville.)

Death Proof

Filed under: Uncategorized — m759 @ 9:48 AM

(Continued

In memory of 

Bill Jenkins, 81, Drag Racing
Driver and Innovator
— 

Pulled out of San Pedro late one night

Jenkins died on Thursday, March 29, 2012.

See also this morning's SPECTRE and
http://www.spectreperformance.com/#GARAGE.

SPECTRE

Filed under: Uncategorized — m759 @ 8:48 AM

Meanwhile, back in June 2004

The Marilyn Monroe Rose and JFK …

The image “http://www.log24.com/log/pix04A/040604-Feeling.jpg” cannot be displayed, because it contains errors.

… meet The Crimson Spectre

(Suggested by this morning's
New York Times  obituaries
"A spectre is haunting…"— Karl Marx)

Tuesday, April 3, 2012

Community*

Filed under: Uncategorized — m759 @ 9:00 PM

Monday in Cuernavaca—

… and in Cambridge—

* See the Latin version in this journal.

Catholic View

Filed under: Uncategorized — m759 @ 9:48 AM

"When shall we three meet again?"

Left to right— John von Neumann, Richard Feynman, Stanislaw Ulam

The source of the above book's title, "Analogies between Analogies,"
was misattributed in a weblog post linked to here on March 4th, 2012.
It occurs in a quote due not to Stanislaw Ulam but to Stefan Banach

IMAGE- 'Catholic view' quote in foreword of book 'Analogies between Analogies'

Ulam was Jewish. Banach was not.

From a webpage on Banach

"On 3 April 1892, he was baptized in the Roman Catholic
 Parish of St. Nicholas in Krakow."

See also…

  1. a post of Sunday, April 2, 2006,
  2. yesterday's Pennsylvania lottery, and
  3. post 585 in this journal. 

(At Los Alamos, Ulam developed the Monte Carlo method.)

Monday, April 2, 2012

Intelligence Test

Filed under: Uncategorized — Tags: , — m759 @ 6:00 PM

This journal on June 18, 2008

http://www.log24.com/log/pix11B/110724-Hustvedt-WechslerCubes.jpg

The Wechsler Cubes story continues with a paper from December 2009…

"Learning effects were assessed for the block design (BD) task,
on the basis of variation in 2 stimulus parameters:
perceptual cohesiveness (PC) and set size uncertainty (U)." —

(Click image for some background.)

The real intelligence test is, of course, the one Wechsler flunked—
investigating the properties of designs made with sixteen
of his cubes instead of nine.

Nine Stories

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

See a search for the title in this journal.

See also Stories about Nine.

Group Actions

Filed under: Uncategorized — Tags: — m759 @ 11:30 AM

Suggested by the post for Christmas 2010

A Saint for Patrick —

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

The Hallowed Crucible  continues…

IMAGE- NY Times online front page item referring to Los Alamos as 'hallowed' and a 'crucible'

From today's New York Times , page B8 of the New York edition—

IMAGE- Paul S. Boyer, 78, Historian; Studied A-Bomb and Witches

Sunday, April 1, 2012

The Palpatine Dimension

Filed under: Uncategorized — Tags: — m759 @ 9:00 AM

A physics quote relayed at Peter Woit's weblog today—

"The relation between 4D N=4 SYM and the 6D (2, 0) theory
is just like that between Darth Vader and the Emperor.
You see Darth Vader and you think 'Isn’t he just great?
How can anyone be greater than that? No way.'
Then you meet the Emperor."

— Arkani-Hamed

Some related material from this  weblog—

(See Big Apple and Columbia Film Theory)

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

The Meno Embedding:

http://www.log24.com/log/pix10B/101128-TheEmbedding.gif

Some related material from the Web—

IMAGE- The Penrose diamond and the Klein quadric

See also uses of the word triality  in mathematics. For instance…

A discussion of triality by Edward Witten

Triality is in some sense the last of the exceptional isomorphisms,
and the role of triality for n = 6  thus makes it plausible that n = 6
is the maximum dimension for superconformal symmetry,
though I will not give a proof here.

— "Conformal Field Theory in Four and Six Dimensions"

and a discussion by Peter J. Cameron

There are exactly two non-isomorphic ways
to partition the 4-subsets of a 9-set
into nine copies of AG( 3,2).
Both admit 2-transitive groups.

— "The Klein Quadric and Triality"

Exercise: Is Witten's triality related to Cameron's?
(For some historical background, see the triality  link from above
and Cameron's Klein Correspondence and Triality.)

Cameron applies his  triality to the pure geometry of a 9-set.
For a 9-set viewed in the context of physics, see A Beginning

From MIT Commencement Day, 2011—

A symbol related to Apollo, to nine, and to "nothing"

A minimalist favicon—

IMAGE- Generic 3x3 square as favicon

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

Happy April 1.

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