Log24

Sunday, July 12, 2020

Knight Moves

Filed under: General — Tags: — m759 @ 4:40 PM

As noted in the previous post, the phrase “the ability to jump
in and out of spaces” was quoted in an update this morning to
a July 2 post, “The Maxwell Enticement.” Related jumping —

See also other Log24 posts now tagged Knight Move.

Wednesday, April 25, 2018

A Deathly Triangle

Filed under: General,Geometry — Tags: , , , — m759 @ 11:27 PM

'Imprisoned in a Tesseract,' a study of novelist James Blish

Sunday, November 12, 2017

Devil’s Music

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

From the groom in the previous post — Swedenborg Chapel

And from November 7 last year —

Monday, November 7, 2016

Subway Art for Times Square Church

Filed under: Uncategorized — m759 @ 9:11 PM 

Click images for related material.

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

"The Cardinal seemed a little preoccupied today."

Saturday, September 2, 2017

Knight Moves

Filed under: General — Tags: — m759 @ 12:42 PM

Ursula K. Le Guin, in Amazing Stories , Sept. 1992, published
"The Rock That Changed Things" (pp. 9-13) and her story from
thirty years earlier, "April in Paris" (Fantastic Stories , Sept. 1962.)
The latter (pp. 14-19) was followed by some brief remarks (p. 19)
comparing the two stories.

For "The Rock," see Le Guin + Rock in this journal.

"April in Paris" is about time travel by means of an alchemist's
pentagram. The following figure from 1962 is in lieu of a pentagram —

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

See as well a search for 1962 in this journal.

Wednesday, July 22, 2015

Harvard Death

Filed under: General — Tags: — m759 @ 3:00 AM

Bloomberg.com —
July 21, 2015 — 3:51 PM EDT
Updated on July 21, 2015 — 6:04 PM EDT —

James Rothenberg of Capital Group
Dies at 69 of Heart Attack

"He was  chairman of Harvard Management Co.,
which invests the university’s $36.4 billion endowment."

See also  
The Harvard Crimson —
UPDATED: July 22, 2015, at 1:28 a.m.

"Rothenberg’s death, reportedly of a heart attack,
was unexpected."

He reportedly "chaired Harvard Management Company’s
board of directors from 2004 until his death."

Sunday, March 29, 2015

Death in East Hampton

Filed under: General — Tags: — m759 @ 1:28 PM

See also Deathtrap in this journal.

Sunday, August 10, 2014

Knight Moves

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

Some illustrations:

Springer logo - A chess knight

Chess Knight
(in German, Springer)

See also…

Katherine Neville's 'The Eight,' edition with knight on cover, on her April 4 birthday

More technically (click image for details):

Friday, November 25, 2011

Knight’s Move* for Wicker

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

Hamlet Fire

The "knight's move" of the title is the supplying of the above link.
For details, click on the link (a search on the link's two words).

* For the meaning of "knight's move," see To Make a Short Story Long.

For the meaning of the phrase  (as opposed to the search ),
    see the birthplace of Tom Wicker, who died today.

Sunday, May 23, 2010

Death Story

Filed under: General — Tags: — m759 @ 9:40 PM

Image-- Arts & Letters Daily, news item on Bloglines first posted at 12 AM Sunday, May 23, 2010

Thursday, July 2, 2020

The Maxwell* Enticement

Filed under: General — Tags: , — m759 @ 5:20 PM

[Update of Sunday morning, July 12, 2020 —

This July 2 post was suggested in part by the July 1 post Magic Child
and in part by the Sept. 15, 1984, date in the image below. For more
details about that date, possibly the death date of author Richard
Brautigan, see “The Life and Death of Richard Brautigan,” by
Lawrence Wright, in Rolling Stone  on April 11, 1985.

From that article:

Marcia called him the next night [Sept. 15, 1984]
in Bolinas. He asked if she liked his mind. “I said,
‘Yes, Richard, I like your mind. You have the ability
to jump in and out of spaces. It’s not linear thinking;
it’s exciting, catalytic, random thinking.’ “

Such thinking, though interesting, is not recommended for the
general public.  Sept. 15, 1984, was perhaps Brautigan’s last day alive.]

* See Maxwell in posts tagged Gods and Giants.

Saturday, December 28, 2019

Caballo Blanco

Filed under: General — Tags: , , , — m759 @ 9:02 AM

The key  is the cocktail that begins the proceedings.”

– Brian Harley, Mate in Two Moves

http://www.log24.com/log/pix18/180809-The_EIght-and-coordinates-for-PSL(2,7)-actions-500w.jpg

“Just as these lines that merge to form a key
Are as chess squares . . . .” — Katherine Neville, The Eight

“The complete projective group of collineations and dualities of the
[projective] 3-space is shown to be of order [in modern notation] 8! ….
To every transformation of the 3-space there corresponds
a transformation of the [projective] 5-space. In the 5-space, there are
determined 8 sets of 7 points each, ‘heptads’ ….”

— George M. Conwell, “The 3-space PG (3, 2) and Its Group,”
The Annals of Mathematics , Second Series, Vol. 11, No. 2 (Jan., 1910),
pp. 60-76.

“It must be remarked that these 8 heptads are the key  to an elegant proof….”

— Philippe Cara, “RWPRI Geometries for the Alternating Group A8,” in
Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference
(July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis,
James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97.

Wednesday, October 30, 2019

For The October Country

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

The above document was linked to here on Dec. 8, 2008

Tuesday, August 27, 2019

Tiger Leaps

Filed under: General — Tags: , — m759 @ 10:33 AM

Walter Benjamin on 'a tiger's leap into the past'

See also Tiger in this journal, esp.

The image “http://www.log24.com/log/pix05/050123-Tiger.JPG” cannot be displayed, because it contains errors.   and . . .

other "Death and the Spirit" posts.

Wednesday, January 2, 2019

Wolf as Lamb

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

The above graphic design is by Noma Bar.

See as well the lamb-in-triangle of the Dec. 27 post
A Candle for Lily

Related material —

Remarks by Evelyn  Lamb on the Deathly Hallows symbol.

Tuesday, October 30, 2018

Ojos

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

From the Hulu series 'The Path,' the Eye logo

A better term than “phase space” might be “story space.”

The Quantum Space Story

Filed under: General — Tags: — m759 @ 2:00 PM

Finkelstein reportedly died on Sunday, January 24, 2016.

“A Serious Man  kicks off with a Yiddish-language frame story that takes place in a 19th-century Eastern European shtetl, where a married couple has an enigmatic encounter with an old acquaintance who may be a dybbuk , or malevolent spirit (and who’s played by the Yiddish theater actor Fyvush Finkel). The import of this parable is cryptic to the point of inscrutability, making it a perfect introduction to the rest of the movie.”

— Dana Stevens at Slate.com on Oct. 1, 2009

See also Finkelstein in this  journal.

See as well posts now tagged Oct. 4, 2018,
in the context of today’s previous post.

Story Structure, Story Space

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

Constance Grady at Vox  today on a new Netflix series —

We don’t yet have a story structure that allows witches to be powerful for long stretches of time without men holding them back. And what makes the new Sabrina  so exciting is that it seems to be trying to build that story structure itself, in real time, to find a way to let Sabrina have her power and her freedom.

It might fail. But if it does, it will be a glorious and worthwhile failure — the type that comes with trying to pioneer a new kind of story.

See also Story Space  in this  journal.

Saturday, January 6, 2018

Yale News

Filed under: General,Geometry — Tags: — m759 @ 5:24 AM

The Yale of the title is not the university, but rather the
mathematician Paul B. Yale. Yale's illustration of the Fano
plane is below.

IMAGE- Triangular models of the 4-point affine plane A and 7-point projective plane PA

A different illustration from a mathematician named Greenberg —

This illustration of the ominous phrase "line at infinity"
may serve as a sort of Deathly Hallows  for Greenberg.
According to the AMS website yesterday, he died on
December 12, 2017:

A search of this  journal for Greenberg yields no mention of
the dead mathematician, but does yield some remarks
on art that are pehaps less bleak than the above illustration.

For instance —

Art adapted from the Google search screen. Discuss.

Saturday, April 22, 2017

Science Marches On

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

Connoisseurs of bullshit who enjoyed the previous post
might also enjoy the following:

The previous two posts introduced Mazzola's noxious combination of 
category theory and Hegel. The current version (Rev. 254) of the above 
nLab "Science of Logic" article, though not by Mazzola, displays this
combination in its full hideous splendor.

Some posts in this  journal that might be viewed as leading up to 
the original Sept. 2, 2012, "Science of Logic" article are now tagged
Death Warmed Over.

Tuesday, June 14, 2016

Model Kit

Filed under: General,Geometry — Tags: — m759 @ 12:14 PM

The title refers to the previous post, which quotes a 
remark by a poetry critic in the current New Yorker .

Scholia —

From the post Structure and Sense of June 6, 2016 —

Structure

Sense

A set of 7 partitions of the 2x2x2 cube that is invariant under PSL(2, 7) acting on the 'knight' coordinatization

From the post Design Cube of July 23, 2015 —

Broken Symmetries  in  Diamond Space 

Monday, June 6, 2016

Structure and Sense

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

"… the war of 70-some years ago
has already become something like the Trojan War
had been for the Homeric bards:
a major event in the mythic past
that gives structure and sense to our present reality."

— Justin E. H. Smith, a professor of philosophy at
     the University of Paris 7–Denis Diderot,
     in the New York Times  column "The Stone"
     (print edition published Sunday, June 5, 2016)

In memory of a British playwright who reportedly
died at 90 this morning —

Structure

Sense

A set of 7 partitions of the 2x2x2 cube that is invariant under PSL(2, 7) acting on the 'knight' coordinatization

Sunday, June 5, 2016

Sunday School: Seven Seals

Filed under: General,Geometry — Tags: — m759 @ 7:00 AM

A set of 7 partitions of the 2x2x2 cube that is invariant under PSL(2, 7) acting on the 'knight' coordinatization

Click image for some background.

See also Standard Disclaimer.

Thursday, December 17, 2015

S-Curves by Peter Dickinson

Filed under: General,Geometry — Tags: , — m759 @ 11:00 PM

British author Peter Dickinson, who reportedly died yesterday,
Dec. 16, 2015, at 88, wrote the following (published in the UK
in 1975 and in the US in 1976) —

'Chance, Luck and Destiny' by Peter Dickinson, page 34

Inverted image of the above page —

'Chance, Luck and Destiny' by Peter Dickinson, page 34

See also, from the date of Dickinson's death, a post on
"A Fight for the Soul…" and a post on the symbol "S."

Of interest too are some remarks related to today's earlier post,
"Hint of Reality" 

Hint of Reality

Filed under: General,Geometry — Tags: , , , — m759 @ 12:45 PM

From an article* in Proceedings of Bridges 2014

As artists, we are particularly interested in the symmetries of real world physical objects.

Three natural questions arise:

1. Which groups can be represented as the group of symmetries of some real-world physical object?

2. Which groups have actually  been represented as the group of symmetries of some real-world physical object?

3. Are there any glaring gaps – small, beautiful groups that should have a physical representation in a symmetric object but up until now have not?

The article was cited by Evelyn Lamb in her Scientific American  
weblog on May 19, 2014.

The above three questions from the article are relevant to a more
recent (Oct. 24, 2015) remark by Lamb:

" finite projective planes [in particular, the 7-point Fano plane,
about which Lamb is writing] 
seem like a triumph of purely 
axiomatic thinking over any hint of reality…."

For related hints of reality, see Eightfold Cube  in this journal.

* "The Quaternion Group as a Symmetry Group," by Vi Hart and Henry Segerman

Tuesday, July 21, 2015

“Ragtime” Author Dies at 84

Filed under: General — Tags: — m759 @ 11:55 PM

“…right through hell
     there is a path…”
 
  — Malcolm Lowry

E!

Filed under: General — Tags: — m759 @ 6:19 PM

Wednesday, April 29, 2015

Scenes from…

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

An Epic for Drink Boy —

Context:  The post in which the above scenes occur.

Gone

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

Update of 12:25 AM — See, too, The Oxford Murders.

Saturday, March 7, 2015

Film and Phenomenology

Filed under: General,Geometry — m759 @ 1:18 PM

Continued from All Hallows' Eve, 2014.

Last year's Halloween post displayed the
Dürer print Knight, Death, and the Devil 
(illustrated below on the cover of the book
Film and Phenomenology  by Allan Casebier).

Cover illustration: Durer's 'Knight, Death, and the Devil'

Cover illustration: Knight, Death, and the Devil
by Albrecht Dürer

Some mathematics related to a different Dürer print —

Sunday, March 1, 2015

Sunday School

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

The previous post suggests a review of
the phrase "strange loop" in this journal.

The Knight's Move, by Loder and Neidhardt

Monday, February 23, 2015

Symbolic Poetry*

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

“When life itself seems lunatic,
who knows where madness lies?

Man of La Mancha

Windmill of Time and Diamond of Eternity

Perhaps the late Sidney Lumet?

           The setting for the Sidney Lumet film "Deathtrap" (1982)

* Continued from yesterday's Backstory and Sermon.

Sunday, February 8, 2015

Hungarian Phenomenon

Filed under: General — Tags: , , , — m759 @ 2:07 PM

For Autism Sunday —

Mathematician John von Neumann
reportedly died on this date.

“He belonged  to that so-called
Hungarian phenomenon….”

A webpage titled
“Von Neumann, Jewish Catholic”

Illustrations of another Hungarian phenomenon:

IMAGE- Anthony Hopkins exorcises a Rubik cube

Friday, October 31, 2014

For the Late Hans Schneider

Filed under: General — Tags: — m759 @ 3:30 AM

See a University of Wisconsin obituary for Schneider,
a leading expert on linear algebra who reportedly died
at 87 on Tuesday, October 28, 2014.

Some background on linear algebra and “magic” squares:
tonight’s 3 AM (ET) post and a search in this
journal for Knight, Death, and the Devil.

Click image to enlarge.

Friday, October 10, 2014

Both Hands and an Ass Map

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

(Continued from Grids and Space and posts tagged Riddle for Caltech)

IMAGE- Scene from 'Deathtrap,' with subtitle

Tuesday, October 7, 2014

Grids and Space

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

In honor of the late Sidney Lumet

(See Makom Kadosh , April 9, 2011.)

IMAGE- Christopher Reeve in the 1982 film 'Deathtrap,' illustrating concepts of space

Tuesday, November 12, 2013

Soundtrack

Filed under: General,Geometry — Tags: , — m759 @ 6:45 AM

IMAGE- 'Devil Music' from 'Kaleidoscopes- Selected Writings of H.S.M. Coxeter'

"DEVIL – MUSIC

20 pages of incidental music written at school
for G. K. Chesterton's play MAGIC

by D. Coxeter."

See also

Related material —  Chesterton + Magic in this journal.

Sunday, December 2, 2012

Realism

Filed under: General — Tags: , — m759 @ 4:30 PM

From the Los Angeles Times  yesterday

"Chess player Elena Akhmilovskaya Donaldson sits
in deep concentration at the U.S. chess championship
in Seattle in 2002. (Greg Gilbert / Seattle Times / 
January 5, 2002)"

Linda Shaw, Seattle Times :

"Elena Akhmilovskaya Donaldson, who was once the world's
second-ranked women's chess player and eloped in 1988
with the captain of the U.S. chess team when they were both
playing at a tournament in Greece, has died. She was 55.

Donaldson, who earned the title of international women's
grandmaster, died Nov. 18 in her adopted hometown of Seattle…."

more »

From the Log24 post "Sermon" on the date of Donaldson's death,
Sunday, Nov. 18, 2012—

"You must allow us to play every conceivable combination of chess."
— Marie-Louise von Franz in Number and Time

An October 2011 post titled  Realism in Plato's Cave displays
the following image:

Cover illustration: Durer's 'Knight, Death, and the Devil'

Cover illustration: Knight, Death, and the Devil,
by Albrecht Dürer

George Steiner and myself  in Closing the Circle, a Log24 post
of Sept. 4, 2009: 

“Allegoric associations of death with chess are perennial….”

"Yes, they are."

For related remarks on knight moves and the devil, see
today's previous two posts, Knight's Labyrinth and The Rite.

Sunday, September 2, 2012

The Word in the Desert

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

(Continued)

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

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

Related material:

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

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

(Click for further details.)

See also St. Stephen's Day, 2011.

Saturday, September 1, 2012

College of the Desert

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

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

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

— Don DeLillo, Point Omega

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

Maybe it was the desert near Twentynine Palms.

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

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

— Ending of Point Omega

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

Friday, August 31, 2012

Translation

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

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

The late William P. Thurston

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

Related cinematic imagery

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

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

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

"Biddies still cleaned the student rooms."

IMAGE- Shower wall in 'Sunshine Cleaning'

Thursday, August 30, 2012

The Cruelest Month

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

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

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

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

Images, including the late Richard Zanuck

For Amy, from the current New Yorker

The Master

* N.O.C.D.

Wednesday, August 29, 2012

It’s 10 PM…

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

Do you know where your children are?

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

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

See also this  weblog's post on that date.

Hexagram 18

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

(Continued from June 14, 2007)

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

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

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

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

Tuesday, August 28, 2012

Dark and Stormy

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

It  was a  dark and stormy night.

A Wrinkle in Time  (brought  up to date)

Up to Date

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

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

— Keith Devlin in Mathematics: The Science of Patterns

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

"Plan 9 deals with the resurrection of the dead.

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

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

Hope and Pope

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

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

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

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

— Alexander Pope in An Essay on Man

Monday, August 27, 2012

Plan 9

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

(Continued)

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

See also "Or Only Die" and Corpus Hypercubus .

Touchy-Feely

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

A remark by the late William P. Thurston

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

Noted. But see this passage—

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

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

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

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

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

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

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

IMAGE- The Harry J. Smith Memorial Tesseract

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

Saturday, August 25, 2012

One Small Step

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

Click image for some related material.

Monday, April 23, 2012

Mate in Six

Filed under: General — Tags: — 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.

Thursday, December 1, 2011

Dog Tale

Filed under: General — Tags: — m759 @ 8:20 PM

"I love gazing into things. Can you imagine with me how glorious it is, for example, to see into a dog, in passing— into him… to ease oneself into the dog exactly at his center, the place out of which he exists as a dog, that place in him where God would, so to speak, have sat down for a moment when the dog was complete, in order to watch him at his first predicaments and notions and let him know with a nod that he was good, that he lacked nothing, that no better dog could be made. For a while one can endure being in the middle of the dog, but one has to be sure to jump out in time, before the world closes in around him completely, otherwise one would remain the dog within the dog and be lost to everything else."

— Rainer Maria Rilke, quoted in The New York Times  in 1988

http://www.log24.com/log/pix11C/111201-DogTale.jpg

Omitting unneeded narrative details,
a madman's knight move

A novel search in memory of the late
uncrowned crown prince of Albania—

Nabokov, Pale Fire

Related narratives—

Prose Tale and The Meadow.

Oh, and happy birthday to Woody Allen (76 today)—

"Outside of a dog, a book is man's best friend.
Inside of a dog it's too dark to read." —Groucho Marx

Wednesday, October 26, 2011

Erlanger and Galois

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

Peter J. Cameron yesterday on Galois—

"He was killed in a duel at the age of 20…. His work languished for another 14 years until Liouville published it in his Journal; soon it was recognised as the foundation stone of modern algebra, a position it has never lost."

Here Cameron is discussing Galois theory, a part of algebra. Galois is known also as the founder* of group theory, a more general subject.

Group theory is an essential part of modern geometry as well as of modern algebra—

"In der Galois'schen Theorie, wie hier, concentrirt sich das Interesse auf Gruppen von Änderungen. Die Objecte, auf welche sich die Änderungen beziehen, sind allerdings verschieden; man hat es dort mit einer endlichen Zahl discreter Elemente, hier mit der unendlichen Zahl von Elementen einer stetigen Mannigfaltigkeit zu thun."

— Felix Christian Klein, Erlanger Programm , 1872

("In the Galois theory, as in ours, the interest centres on groups of transformations. The objects to which the transformations are applied are indeed different; there we have to do with a finite number of discrete elements, here with the infinite number of elements in a continuous manifoldness." (Translated by M.W. Haskell, published in Bull. New York Math. Soc. 2, (1892-1893), 215-249))

Related material from Hermann Weyl, Symmetry , Princeton University Press, 1952 (paperback reprint of 1982, pp. 143-144)—

"A field is perhaps the simplest algebraic structure we can invent. Its elements are numbers…. Space is another example of an entity endowed with a structure. Here the elements are points…. What we learn from our whole discussion and what has indeed become a guiding principle in modern mathematics is this lesson: Whenever you have to do with a structure-endowed entity  Σ try to determine is 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 Σ in this way."

For a simple example of a group acting on a field (of 8 elements) that is also a space (of 8 points), see Generating the Octad Generator and Knight Moves.

* Joseph J. Rotman, An Introduction to the Theory of Groups , 4th ed., Springer, 1994, page 2

Monday, October 3, 2011

Realism in Plato’s Cave

Filed under: General — m759 @ 8:08 PM

In memory of the late combinatorialist-philosopher Gian-Carlo Rota

Excerpts from the introduction to Allan Casebier's

Film and Phenomenology: Towards a Realist Theory of Cinematic Representation
(Cambridge Studies in Film, Cambridge University Press, 1991) —

Pages 1-2,  pages 3-4,  pages 5-6.

Cover illustration: Durer's 'Knight, Death, and the Devil'

Cover illustration: Knight, Death, and the Devil, by Albrecht Dürer

Wednesday, June 22, 2011

ART WARS continued

Filed under: General,Geometry — Tags: — m759 @ 8:06 PM

This evening's New York Times  obituaries—

http://www.log24.com/log/pix11A/110622-NYTobits720PM.jpg

A work of art suggested by the first and third items above—

http://www.log24.com/log/pix11A/110614-TarantinoCar.jpg

I prefer a work of art that is structurally similar—

IMAGE- The Klein group as art

and is related to a picture, Portrait of O, from October 1, 1983—

IMAGE- A work by Cullinane pirated by artist Steve RIchards in his contribution to London's 'Piracy Project'

For a recent unexpected Web appearance of Portrait of O,
aee Abracadabra from the midnight of June 18-19.

Tuesday, June 14, 2011

Expressionistic Depth

Filed under: General — Tags: — m759 @ 6:20 AM

http://www.log24.com/log/pix11A/110614-DoubleDown.jpg

Update of 7 AM —

Carl Gardner's 1956 hit "Down in Mexico" was featured in the following Hollywood classic:

http://www.log24.com/log/pix11A/110614-TarantinoCar.jpg

Click image for video.

Sunday, May 23, 2010

For Your Consideration —

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

Cannes Festival Readies for Awards Night

Uncertified Copy

Image-- Uncertified copy of 1986 figures by Cullinane in a 2009 art exhibit in Oslo

The pictures in the detail are copies of
figures created by S. H. Cullinane in 1986.
They illustrate his model of hyperplanes
and points in the finite projective space
known as PG(3,2) that underlies
Cullinane's diamond theorem.

The title of the pictures in the detail
is that of a film by Burkard Polster
that portrays a rival model of PG(3,2).

The artist credits neither Cullinane nor Polster.

Sunday School

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

"Mathematics is forever."
— Gian-Carlo Rota   

"Nine is a very powerful
  Nordic number."
— Katherine Neville    

 "Nine tailors make a man."
— Dorothy Sayers 

Annals of Philosophy

Filed under: General — Tags: — m759 @ 3:33 AM

Busy Night at the Lyche Gate

http://www.log24.com/log/pix10A/100523-NYTobits.jpg

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

Annals of Conceptual Art

Filed under: General — Tags: — m759 @ 2:02 AM

Josefine Lyche's
  "Theme and Variations" (Oslo, 2009)

http://www.log24.com/log/pix10A/100523-LycheTandV.jpg

Some images in reply—

  Frame Tale

Image by R. T. Curtis from 'Further Elementary Techniques...'

Click on images for further details.

"In the name of the former
and of the latter
and of their holocaust.
  Allmen."

Finnegans Wake

Friday, May 21, 2010

The Oslo Version

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

From an art exhibition in Oslo last year–

Image-- Josefine Lyche's combination of Polster's phrase with Cullinane's images in her gallery show, Oslo, 2009-- 'The Smallest Perfect Universe -- Points and Hyperplanes'

The artist's description above is not in correct left-to-right order.
Actually the hyperplanes above are at left, the points at right.

Compare to "Picturing the Smallest Projective 3-Space,"
a note of mine from April 26, 1986—

Image-- Points and hyperplanes in the finite 3-space PG(3,2), April 1986, by Cullinane

Click for the original full version.

Compare also to Burkard Polster's original use of
the phrase "the smallest perfect universe."

Polster's tetrahedral model of points and hyperplanes
is quite different from my own square version above.

See also Cullinane on Polster.

Here are links to the gallery press release
and the artist's own photos.

Tuesday, February 16, 2010

Mysteries of Faith

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

From today's NY Times

http://www.log24.com/log/pix10/100216-NYTobits.jpg

Obituaries for mystery authors
Ralph McInerny and Dick Francis

From the date (Jan. 29) of McInerny's death

"…although a work of art 'is formed around something missing,' this 'void is its vanishing point, not its essence.'"

Harvard University Press on Persons and Things (Walpurgisnacht, 2008), by Barbara Johnson

From the date (Feb. 14) of Francis's death

2x2x2 cube

The EIghtfold Cube

The "something missing" in the above figure is an eighth cube, hidden behind the others pictured.

This eighth cube is not, as Johnson would have it, a void and "vanishing point," but is instead the "still point" of T.S. Eliot. (See the epigraph to the chapter on automorphism groups in Parallelisms of Complete Designs, by Peter J. Cameron. See also related material in this journal.) The automorphism group here is of course the order-168 simple group of Felix Christian Klein.

For a connection to horses, see
a March 31, 2004, post
commemorating the birth of Descartes
  and the death of Coxeter–

Putting Descartes Before Dehors

     Binary coordinates for a 4x2 array  Chess knight formed by a Singer 7-cycle

For a more Protestant meditation,
see The Cross of Descartes

Descartes

Descartes's Cross

"I've been the front end of a horse
and the rear end. The front end is better."
— Old vaudeville joke

For further details, click on
the image below–

Quine and Derrida at Notre Dame Philosophical Reviews

Notre Dame Philosophical Reviews

Thursday, October 8, 2009

Thursday October 8, 2009

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

Knight Moves

Deborah Solomon, New York Times Magazine, Sunday, June 27, 1999:

“While modern art began as an assault on the academy, post-modern art might be described as a return to the academy. Instead of the old academy of rules, now we have the Academy of Cool, schools that treat avant-garde rebellion as a learned occupation.”

Christopher Knight, LA Times art critic, on Solomon:

“Back in the day, Solomon interviewed Knight for a Times Magazine story on Los Angeles art schools. ‘Having been a journalist (at that time) for almost two decades, I also did my homework,’ Knight writes [in a letter to the New York Press]. ‘I prepared a couple of quotable quotes on the subject, which might encapsulate larger ideas.’ One of Knight’s pearls of wisdom, ‘Modern art began as an assault on the academy, but post-modern art might be described as a return to the academy,’ excited Solomon so much that, according to Knight, she printed it as her own observation in her final piece, which bore no mention of the Knight interview. In the final story, a seriously bitter Knight writes, ‘It was not a quote; my words had become her words.'” —Gawker, Oct. 11, 2007

A reference to Solomon’s piece appeared in this journal in 2003.

See also yesterday’s entry, today’s 9 AM entry, and (for the Academy) an example of knight’s move thinking.

Friday, April 3, 2009

Friday April 3, 2009

Filed under: General,Geometry — Tags: , — m759 @ 5:24 AM
Knight Moves

“Lord, I remember”
Bob Seger 


“Philosophers ponder the idea of identity: what it is to give something a name on Monday and have it respond to that name on Friday….”

Bernard Holland in The New York Times of Monday, May 20, 1996

Yesterday’s afternoon entry cited philosopher John Holbo on chess. This, together with Holland’s remark above and Monday’s entries on Zizek, suggests…

Holbo on Zizek
(pdf, 11 pages)

In this excellent analysis,
Holbo quotes Kierkegaard:

“… the knight of faith
‘has the pain of being unable to
make himself intelligible to others'”

(Kierkegaard, Fear and Trembling)

For some material that may serve to illustrate Kierkegaard’s remark, see Log24 on Twelfth Night and Epiphany this year.

“… 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

Perhaps a game for bishops?

Henry Edward Cardinal Manning

Cardinal Manning

Click on the cardinal
for a link to some remarks
related to the upcoming film
 “Angels & Demons” and to
a Paris “Sein Feld.”


Context: the five entries
ending at 9:26 AM
on March 10, 2009…
and, for Kierkegaard,
Diamonds Are Forever.

Monday, July 21, 2008

Monday July 21, 2008

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

Knight Moves:

The Relativity Theory
of Kindergarten Blocks

(Continued from
January 16, 2008)

"Hmm, next paper… maybe
'An Unusually Complicated
Theory of Something.'"

Garrett Lisi at
Physics Forums, July 16

Something:

From Friedrich Froebel,
who invented kindergarten:

Froebel's Third Gift: A cube made up of eight subcubes

Click on image for details.

An Unusually
Complicated Theory:

From Christmas 2005:

The Eightfold Cube: The Beauty of Klein's Simple Group

Click on image for details.

For the eightfold cube
as it relates to Klein's
simple group, see
"A Reflection Group
of Order 168
."

For an even more
complicated theory of
Klein's simple group, see

Cover of 'The Eightfold Way: The Beauty of Klein's Quartic Curve'

Click on image for details.

Sunday, June 1, 2008

Sunday June 1, 2008

Filed under: General,Geometry — Tags: , — m759 @ 2:14 PM
Yet Another
Cartoon Graveyard

The conclusion of yesterday’s commentary on the May 30-31 Pennsylvania Lottery numbers:

Thomas Pynchon, Gravity’s Rainbow:

“The fear balloons again inside his brain. It will not be kept down with a simple Fuck You…. A smell, a forbidden room, at the bottom edge of his memory. He can’t see it, can’t make it out. Doesn’t want to. It is allied with the Worst Thing.

He knows what the smell has to be: though according to these papers it would have been too early for it, though he has never come across any of the stuff among the daytime coordinates of his life, still, down here, back here in the warm dark, among early shapes where the clocks and calendars don’t mean too much, he knows that’s what haunting him now will prove to be the smell of Imipolex G.

Then there’s this recent dream he is afraid of having again. He was in his old room, back home. A summer afternoon of lilacs and bees and

286”

What are we to make of this enigmatic 286? (No fair peeking at page 287.)

One possible meaning, given The Archivists claim that “existence is infinitely cross-referenced”–

Page 286 of Ernest G. Schachtel, Metamorphosis: On the Conflict of Human Development and the Psychology of Creativity (first published in 1959), Hillsdale NJ and London, The Analytic Press, 2001 (chapter– “On Memory and Childhood Amnesia”):

“Both Freud and Proust speak of the autobiographical [my italics] memory, and it is only with regard to this memory that the striking phenomenon of childhood amnesia and the less obvious difficulty of recovering any past experience may be observed.”

The concluding “summer afternoon of lilacs and bees” suggests that 286 may also be a chance allusion to the golden afternoon of Disney’s Alice in Wonderland. (Cf. St. Sarah’s Day, 2008)

Some may find the Disney afternoon charming; others may see it as yet another of Paul Simon’s dreaded cartoon graveyards.

More tastefully, there is poem 286 in the 1919 Oxford Book of English Verse– “Love.”

For a midrash on this poem, see Simone Weil, who became acquainted with the poem by chance:

“I always prefer saying chance rather than Providence.”

— Simone Weil, letter of about May 15, 1942

Weil’s brother André might prefer Providence (source of the Bulletin of the American Mathematical Society.)

Andre Weil and his sister Simone, summer of 1922(Photo from Providence)

 

Related material:


Log24, December 20, 2003–
White, Geometric, and Eternal

A description in Gravity’s Rainbow of prewar Berlin as “white and geometric”  suggested, in combination with a reference elsewhere to “the eternal,” a citation of the following illustration of the concept “white, geometric, and eternal”–

For more on the mathematical significance of this figure, see (for instance) Happy Birthday, Hassler Whitney, and Combinatorics of Coxeter Groups, by Anders Björner and Francesco Brenti, Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005.

This book is reviewed in the current issue (July 2008) of the above-mentioned Providence Bulletin.

The review in the Bulletin discusses reflection groups in continuous spaces.

For a more elementary approach, see Reflection Groups in Finite Geometry and Knight Moves: The Relativity Theory of Kindergarten Blocks.

See also a commentary on
the phrase “as a little child.”

Monday, February 25, 2008

Monday February 25, 2008

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 PM
A System of Symbols

A book from
Yale University Press
discussed in Log24
four years ago today:

Inside Modernism: Relativity Theory, Cubism, Narrative

Click on image for details.

The book is titled
Inside Modernism:
Relativity Theory,
 Cubism, Narrative
.

For a narrative about relativity
and cubes, see Knight Moves.

Related material:

Geek chic in
this week's New Yorker

"… it takes a system of symbols  
to make numbers precise–
      to 'crystallize' them…."

— and a mnemonic for three
 days in October 2006
following a memorial to
 the Amish schoolchildren
slain that month:

Seven is Heaven,
Eight is a Gate,
Nine is a Vine.

Saturday, February 23, 2008

Saturday February 23, 2008

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

"An acute study of the links
between word and fact"
Nina daVinci Nichols

 
Thanks to a Virginia reader for a reminder:
 
Virginia /391062427/item.html? 2/22/2008 7:37 PM
 
The link is to a Log24 entry
that begins as follows…

An Exercise

of Power

Johnny Cash:
"And behold,
a white horse."

Springer logo - A chess knight
Chess Knight
(in German, Springer)

This, along with the "jumper" theme in the previous two entries, suggests a search on springer jumper.That search yields a German sports phrase, "Springer kommt!"  A search on that phrase yields the following:
"Liebe Frau vBayern,
mich würde interessieren wie man
mit diesem Hintergrund
(vonbayern.de/german/anna.html)
zu Springer kommt?"

Background of "Frau vBayern" from thePeerage.com:

Anna-Natascha Prinzessin zu Sayn-Wittgenstein-Berleburg 

F, #64640, b. 15 March 1978Last Edited=20 Oct 2005

     Anna-Natascha Prinzessin zu Sayn-Wittgenstein-Berleburg was born on 15 March 1978. She is the daughter of Ludwig Ferdinand Prinz zu Sayn-Wittgenstein-Berleburg and Countess Yvonne Wachtmeister af Johannishus. She married Manuel Maria Alexander Leopold Jerg Prinz von Bayern, son of Leopold Prinz von Bayern and Ursula Mohlenkamp, on 6 August 2005 at Nykøping, Södermanland, Sweden.

 

The date of the above "Liebe Frau vBayern" inquiry, Feb. 1, 2007, suggests the following:

From Log24 on
St. Bridget's Day, 2007:

The quotation
"Science is a Faustian bargain"
and the following figure–

Change

The 63 yang-containing hexagrams of the I Ching as a Singer 63-cycle

From a short story by
the above Princess:

"'I don't even think she would have wanted to change you. But she for sure did not want to change herself. And her values were simply a part of her.' It was true, too. I would even go so far as to say that they were her basis, if you think about her as a geometrical body. That's what they couldn't understand, because in this age of the full understanding for stretches of values in favor of self-realization of any kind, it was a completely foreign concept."

To make this excellent metaphor mathematically correct,
change "geometrical body" to "space"… as in

"For Princeton's Class of 2007"

Review of a 2004 production of a 1972 Tom Stoppard play, "Jumpers"–

John Lahr on Tom Stoppard's play Jumpers

Related material:

Knight Moves (Log24, Jan. 16),
Kindergarten Theology (St. Bridget's Day, 2008),
and

The image “My space -(the affine space of six dimensions over the two-element field
(Click on image for details.)

Friday, February 1, 2008

Friday February 1, 2008

Filed under: General,Geometry — Tags: — m759 @ 5:01 AM
Kindergarten Theology

On the late James Edwin Loder,
a Presbyterian minister and
a professor of Christian education
at Princeton Theological Seminary,
co-author of The Knight’s Move (1992):

“At his memorial service his daughter Tami told the story of ‘little Jimmy,’ whose kindergarten teacher recognized a special quality of mind that set him apart. ‘Every day we read a story, and after the story is over, Jimmy gets up and wants to tell us what the story means.'” — Dana R. Wright

For a related story about
knight moves and kindergarten,
see Knight Moves: The Relativity
Theory of Kindergarten Blocks
,
and Log24, Jan. 16, 17, and 18.

See also Loder’s book
(poorly written, but of some
interest in light of the above):

The Knight's Move, by Loder and Neidhardt

Opening of The Knight’s Move —

“In a game of chess, the knight’s move is unique because it alone goes around corners. In this way, it combines the continuity of a set sequence with the discontinuity of an unpredictable turn in the middle. This meaningful combination of continuity and discontinuity in an otherwise linear set of possibilities has led some to refer to the creative act of discovery in any field of research as a ‘knight’s move’ in intelligence.

The significance of the title of this volume might stop there but for Kierkegaard’s use of the ‘knight’ image. The force of Kierkegaards’s usage might be described in relation to the chess metaphor by saying that not merely does Kierkegaard’s ‘knight of faith’ undertake a unique move within the rules of the human game, but faith transposes the whole idea of a ‘knight’s move’ into the mind of the Chess Master Himself. That is to say, chess is a game of multiple possibilities and interlocking strategies, so a chess master must combine the  continuity represented by the whole complex of the game with the unpredictable decision he must make every time it is his turn. A master chess player, then, does not merely follow the rules; in him the game becomes a construct of consciousness. The better the player the more fully the game comes into its own as a creation of human intelligence. Similarly, for Kierkegaard, the knight of faith is a unique figure in human experience. The knight shows how, by existing in faith as a creative act of Christ’s Spirit, human existence comes into its own as an expression of the mind of Christ. Thus, the ultimate form of a ‘knight’s move’ is a creative act raised to the nth power by Spiritus Creator, but it still partakes fully in the concrete pieces and patterns that comprise the nature of the human game and the game of nature.”

— James E. Loder and W. Jim Neidhardt (Helmers & Howard Publishing, 1992)

For a discussion, see Triplett’s
Thinking Critically as a Christian.”

Many would deny that such
a thing is possible; let them
read the works of T. S. Eliot.

Related material:

The Knight’s Move
discusses (badly) Hofstadter’s
“strange loop” concept; see
Not Mathematics but Theology
(Log24, July 12, 2007).

Thursday, January 17, 2008

Thursday January 17, 2008

Filed under: General — Tags: , — m759 @ 5:24 PM
Well, she was
   just seventeen…
 
(continued)

"Mazur introduced the topic of prime numbers with a story from Don Quixote in which Quixote asked a poet to write a poem with 17 lines. Because 17 is prime, the poet couldn't find a length for the poem's stanzas and was thus stymied."

— Undated American Mathematical Society news item about a Nov. 1, 2007, event

Related material:

Desconvencida,
Jueves, Enero 17, 2008

Horses of a Dream
(Log24, Sept. 12, 2003)

Knight Moves
(Log24 yesterday–
anniversary of the
Jan. 16 publication
of Don Quixote)

Windmill and Diamond
(St. Cecilia's Day 2006)

Wednesday, January 16, 2008

Wednesday January 16, 2008

Filed under: General,Geometry — Tags: , , , — m759 @ 12:25 PM
Knight Moves:
Geometry of the
Eightfold Cube

Actions of PSL(2, 7) on the eightfold cube

Click on the image for a larger version
and an expansion of some remarks
quoted here on Christmas 2005.

Monday, December 24, 2007

Monday December 24, 2007

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

From Saturday's entry
(Log24, Dec. 22, 2007)
a link goes to–
The five entries of June 14, 2007.

From there, the link
"One Two Three Four,
Who Are We For?"
goes to–
Princeton: A Whirligig Tour
(Log24, June 5, 2007).

From there, the link
"Taking Christ to Studio 60"
goes to–
The five Log 24 entries
prior to midnight Sept. 18, 2006.

From there, the link
"Log24, January 18, 2004"
goes to–
A Living Church.

From there, the link
"click here"
goes to–
In the Bleak Midwinter
(Internet Movie Database)…

Tagline:

The drama. The passion. The intrigue… And the rehearsals haven't even started.

Plot Summary:

Out of work actor Joe volunteers to help try and save his sister's local church
for the community by putting on a Christmas production of Hamlet…

"… were it not that
  I have bad dreams."
— Hamlet

Related material:

The New York Times online
obituaries of December 22,

 Ike Turner's
 "Bad Dreams" album
(see Log24, July 12, 2004),

"Devil Music," a composition
by H. S. M. Coxeter,

and

King of Infinite Space.

Those desiring more literary depth
may consult the G. K. Chesterton
play "Magic" for which Coxeter
wrote his "Devil Music" and
the Ingmar Bergman film
"The Magician" said to have
been inspired by Chesterton.

Friday, June 15, 2007

Friday June 15, 2007

Filed under: General,Geometry — Tags: — m759 @ 10:31 PM
Geometry and Death

(continued from Dec. 11, 2006):

J. G. Ballard on "the architecture of death":

"… a huge system of German fortifications that included the Siegfried line, submarine pens and huge flak towers that threatened the surrounding land like lines of Teutonic knights. Almost all had survived the war and seemed to be waiting for the next one, left behind by a race of warrior scientists obsessed with geometry and death."

The Guardian, March 20, 2006

From the previous entry, which provided a lesson in geometry related, if only by synchronicity, to the death of Jewish art theorist Rudolf Arnheim:

"We are going to keep doing this until we get it right."

Here is a lesson related, again by synchronicity, to the death of a Christian art scholar of "uncommon erudition, wit, and grace"– Robert R. Wark of the Huntington Library.  Wark died on June 8, a date I think of as the feast day of St. Gerard Manley Hopkins, a Jesuit priest-poet of the nineteenth century.

From a Log24 entry on the date of Wark's death

Samuel Pepys on a musical performance (Diary, Feb. 27, 1668):

"When the Angel comes down"

"When the Angel Comes Down, and the Soul Departs," a webpage on dance in Bali:

"Dance is also a devotion to the Supreme Being."

Julie Taymor, interview:

"I went to Bali to a remote village by a volcanic mountain…."

The above three quotations were intended to supply some background for a link to an entry on Taymor, on what Taymor has called "skewed mirrors," and on a related mathematical concept named, using a term Hopkins coined, "inscapes."

They might form part of an introductory class in mathematics and art given, like the class of the previous entry, in Purgatory.

Wark, who is now, one imagines, in Paradise, needs no such class.  He nevertheless might enjoy listening in.

A guest teacher in
the purgatorial class
on mathematics
and art:

Olivier as Dr. Christian Szell

The icosahedron (a source of duads and synthemes)

"Is it safe?"

Monday, June 11, 2007

Monday June 11, 2007

Filed under: General — Tags: — m759 @ 12:00 AM
Continued from June 7

Second Billing, Part III:

Philosophy of
Communication

Obituaries: Richard Rorty, Ousmane Sembene

Pictures are more accessible
than words. See Logos
(May 17) and Torbellino
(June 10), as well as
the entries for June 8,
the date of Rorty's death.

Friday, June 8, 2007

Friday June 8, 2007

Filed under: General — Tags: — m759 @ 4:00 PM
For the Author of
the Word "Inscape"

n His Feast Day


Samuel Pepys on a musical performance (Diary, Feb. 27, 1668):

"When the Angel comes down"

"When the Angel Comes Down, and the Soul Departs," a webpage on dance in Bali:

"Dance is also a devotion to the Supreme Being."

Julie Taymor, interview:

"I went to Bali to a remote village by a volcanic mountain…."

Under the Volcano:

"No se puede vivir sin amar.

Log24 on St. Peter's Day, 2004:

"And so to bed."

Thursday, March 8, 2007

Thursday March 8, 2007

Filed under: General — Tags: — m759 @ 7:13 PM
Introduction to Logic
for International Women's Day

"The logic behind such utterances is the logic
of binary opposition, the principle of non-contra-
diction, often thought of as the very essence of
Logic as such….

Now, my understanding of what is most radical
in deconstruction is precisely that it questions
this basic logic of binary opposition….

Instead of a simple 'either/or' structure,
deconstruction attempts to elaborate a discourse
that says neither "either/or", nor "both/and"
nor even "neither/nor", while at the same time
not totally abandoning these logics either."

Harvard professor Barbara Johnson
in "Nothing Fails Like Success."
(See the previous entry, Day Without Logic.)

The 16 Binary Connectives, with Venn Diagrams

Click to enlarge.

Those who value literary theory
more than they value truth
may prefer, on this
International Women's Day,
the "mandorla" interpretation
of the above diagrams.

For this interpretation, see
Death and the Spirit III,
Burning Bright,
and
The Agony and the Ya-Ya.

Tuesday, December 27, 2005

Tuesday December 27, 2005

Filed under: General — Tags: — m759 @ 12:11 PM
Dance of the Numbers
(continued)

The Pennsylvania lottery 
on St. Stephen's Day–

Midday: 105
Evening: 064

From a new
branch of theology, 
lottery hermeneutics:

See Log24, 1/05,
Death and the Spirit,

and the 64 hexagrams of
the box-style I Ching.

From the Wikipedia
article on hermeneutics:

"One prominent theme which arises in contemporary philosophical hermeneutics (i.e., the work of Hans-Georg Gadamer) is a serious calling into question of scientism. Scientism is the more or less unquestioned belief in the supremacy of the natural sciences when it comes to serving as models of knowledge. By calling scientism into question, hermeneutics is arguing for the legitimacy of (among other things) aesthetic, literary, spiritual, and philosophical knowledge, alongside (but not instead of) scientific knowledge."

Saturday, December 10, 2005

Saturday December 10, 2005

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

Roger Shattuck, Scholar, Is Dead at 82

In his honor, some excerpts from previous entries:

Wednesday, January 19, 2005

I just subscribed to The New York Review of Books online for another year,
prompted by my desire to read Roger Shattuck on Rimbaud….

"How did this poetic sensibility come to burn so bright?"

The Shattuck piece is from 1967, the year of The Doors' first album.

(See Death and the Spirit, Part II.)

The image “http://www.log24.com/log/pix05B/051210-Blue.jpg” cannot be displayed, because it contains errors.

The photo of Nicole Kidman
is from Globe Song
(Log24, Jan. 18, 2005).

The Times says Shattuck died
on Thursday (Dec. 8, 2005).

Here, from 4:00 AM on the
morning of Shattuck's death,
is a brief companion-piece
to Eight is a Gate:

Four is a Door:

From Carole A. Holdsworth,
Dulcinea and Pynchon's V:

Tanner may have stated it best:

“V. is whatever lights you to
 the end of the street:
 she is also the dark annihilation
 waiting at the end of the street.”

(Tony Tanner, page 36,
 "V. and V-2," in
 Pynchon: A Collection
 of Critical Essays.

 Ed. Edward Mendelson.
 Englewood Cliffs, N. J.:
 Prentice-Hall, 1978. 16-55).

She's a mystery
She's everything
   a woman should be
Woman in black
   got a hold on me

Foreigner 4

She's in midnight blue,
 still the words ring true;
woman in blue
got a hold on you.

Sunday, November 20, 2005

Sunday November 20, 2005

Filed under: General,Geometry — Tags: — m759 @ 4:04 PM

An Exercise
of Power

Johnny Cash:
“And behold,
a white horse.”

The image “http://www.log24.com/log/pix05B/051120-SpringerLogo9.gif” cannot be displayed, because it contains errors.
Adapted from
illustration below:

The image “http://www.log24.com/log/pix05B/051120-NonEuclideanRev.jpg” cannot be displayed, because it contains errors.

“There is a pleasantly discursive treatment of Pontius Pilate’s unanswered question ‘What is truth?'”

H. S. M. Coxeter, 1987, introduction to Richard J. Trudeau’s remarks on the “Story Theory” of truth as opposed to  the “Diamond Theory” of truth in The Non-Euclidean Revolution

“A new epistemology is emerging to replace the Diamond Theory of truth. I will call it the ‘Story Theory’ of truth: There are no diamonds. People make up stories about what they experience. Stories that catch on are called ‘true.’ The Story Theory of truth is itself a story that is catching on. It is being told and retold, with increasing frequency, by thinkers of many stripes*….”

Richard J. Trudeau in
The Non-Euclidean Revolution

“‘Deniers’ of truth… insist that each of us is trapped in his own point of view; we make up stories about the world and, in an exercise of power, try to impose them on others.”

— Jim Holt in The New Yorker.

(Click on the box below.)

The image “http://www.log24.com/log/pix05B/050819-Critic4.jpg” cannot be displayed, because it contains errors.

Exercise of Power:

Show that a white horse–

A Singer 7-Cycle

a figure not unlike the
symbol of the mathematics
publisher Springer–
is traced, within a naturally
arranged rectangular array of
polynomials, by the powers of x
modulo a polynomial
irreducible over a Galois field.

This horse, or chess knight
“Springer,” in German–
plays a role in “Diamond Theory”
(a phrase used in finite geometry
in 1976, some years before its use
by Trudeau in the above book).

Related material

On this date:

 In 1490, The White Knight
 (Tirant lo Blanc The image “http://www.log24.com/images/asterisk8.gif” cannot be displayed, because it contains errors. )–
a major influence on Cervantes–
was published, and in 1910

The image “http://www.log24.com/log/pix05B/051120-Caballo1.jpg” cannot be displayed, because it contains errors.

the Mexican Revolution began.

Illustration:
Zapata by Diego Rivera,
Museum of Modern Art,
New York

The image “http://www.log24.com/images/asterisk8.gif” cannot be displayed, because it contains errors. Description from Amazon.com

“First published in the Catalan language in Valencia in 1490…. Reviewing the first modern Spanish translation in 1969 (Franco had ruthlessly suppressed the Catalan language and literature), Mario Vargas Llosa hailed the epic’s author as ‘the first of that lineage of God-supplanters– Fielding, Balzac, Dickens, Flaubert, Tolstoy, Joyce, Faulkner– who try to create in their novels an all-encompassing reality.'”

Sunday, January 23, 2005

Sunday January 23, 2005

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

Death and the Spirit,
Part IV

From Tuesday:

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Seriously.

See also

Death and the Spirit, Part I,

Death and the Spirit, Part II, and

Death and the Spirit, Part III.

 

Wednesday, January 19, 2005

Wednesday January 19, 2005

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

But seriously…

A follow-up to the previous "tiger" entry (which was about an old but good dirty joke).

I just subscribed to The New York Review of Books online for another year, prompted by my desire to read Roger Shattuck on Rimbaud, a tiger of another sort:

"How did this poetic sensibility come to burn so bright?"

The Shattuck piece is from 1967, the year of The Doors' first album.  (See Sunday's Death and the Spirit, Part II.)

Tuesday, January 18, 2005

Tuesday January 18, 2005

Filed under: General — Tags: — m759 @ 1:44 PM
Death and
the Spirit, Part III

In memory of comedian
Gene Baylos, who died
on Jan. 10, 2005:

From the dark jungle
as a tiger bright,
Form from the viewless Spirit
leaps to light.

— Rumi, "Reality and Appearance"

The image “http://www.log24.com/log/pix05/050118-Tiger2.gif” cannot be displayed, because it contains errors.

 

Related material:

Sunday, January 16, 2005

Sunday January 16, 2005

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

Death and the
Spirit, Part II

Readings

Are you a lucky little lady
in The City of Light
Or just another lost angel…

City of Night

— Jim Morrison, L.A. Woman

Fourmillante cité,
cité pleine de rêves,
Où le spectre en plein jour
raccroche le passant

— Baudelaire,
Les Fleurs du Mal,
and T. S. Eliot,
Notes to The Waste Land

"When you got the mojo, brother —
when you're on the inside —
the world is fantastic."

— Pablo Tabor in Robert Stone's
A Flag for Sunrise,
Knopf, 1981, p. 428

Now it was Avril's turn to understand and he was frightened out of his wits.

"The Science of Luck," he said cautiously. "You watch, do you?  That takes a lot of self-discipline."

"Of course it does, but it's worth it.  I watch everything, all the time.  I'm one of the lucky ones.  I've got the gift.  I knew it when I was a kid, but I didn't grasp it."  The murmur had intensified.  "This last time, when I was alone so long, I got it right.  I watch for every opportunity and I never do the soft thing.  That's why I succeed."

Avril was silent for a long time.  "It is the fashion," he said at last.  "You've been reading the Frenchmen, I suppose?  Or no, no, perhaps you haven't.  How absurd of me."

"Don't blether."  The voice, stripped of all its disguises, was harsh and naive.  "You always blethered.  You never said anything straight.  What do you know about the Science of Luck?  Go on, tell me.  You're the only one who's understood at all.  Have you ever heard of it before?"

"Not under that name."

"I don't suppose you have.  That's my name for it.  What's its real name?"

"The Pursuit of Death."

— Margery Allingham,
Chapter Seventeen,
"On the Staircase," from
The Tiger in the Smoke

Anagrams

In memory of Danny Sugerman,
late manager of The Doors:

The image “http://www.log24.com/log/pix05/050116-Sugerman.jpg” cannot be displayed, because it contains errors.
Danny Sugerman
Photo by
Frank Alan Bella, 2002

"Mr Mojo Risin" = "Jim Morrison."
"Audible Era" = "Baudelaire."
"Bad Rumi" = "Rimbaud."

From the dark jungle
as a tiger bright,
Form from the viewless Spirit
leaps to light.

— Rumi,  "Reality and Appearance,"
translated by R. A. Nicholson

(See also Death and the Spirit
from Twelfth Night, 2005, the date
of Danny Sugerman's death.)

Wednesday, January 5, 2005

Wednesday January 5, 2005

Filed under: General — Tags: — m759 @ 7:11 AM

Death and the Spirit

A meditation for Twelfth Night
on "the whirligig of time"

Today's New York Times obituaries feature two notable graphic artists: 
  • Frank Kelly Freas, who created, among other works, 400 portraits of saints for the Franciscans and the covers of Mad Magazine from 1958 through 1962. "I found it difficult to shift my artistic gears from the sublime to the ridiculous and back again," he said of his departure from Mad.
  • Will Eisner, "an innovative comic-book artist who created the Spirit, a hero without superpowers, and the first modern graphic novel."

Yesterday's entry provided an approach to The Dark Lady, Kali, that was, in Freas's apt word, "ridiculous."  The illustration below, "Mate," is an attempt to balance yesterday's entry with an approach that is, if not sublime, at least more serious.  It is based on a similar illustration from Jan. 31, 2003, with actress Judy Davis playing The Dark Lady.  Today it seems appropriate to replace Davis with another actress (anonymous here, though some may recognize her).  I once knew her (unlike Davis) personally.  One of my fondest memories of high school is reading Mad Magazine with her in the school lunch room.  Our lives diverged after high school, but I could happily have spent my life in her company.

Mate

– S. H. Cullinane, Twelfth Night, 2005

The image “http://log24.com/log/pix05/050105-Mate.jpg” cannot be displayed, because it contains errors.

A diamond and its dual "whirl" figure—
or a "jewel-box and its mate"

For details, see the five Log24 entries
ending on Feb. 1, 2003, and the
perceptive remarks of Ryan Benedetti
on Sam Spade and Brigid O'Shaughnessy.

As for Eisner and "The Spirit,"
which has been called
"the quintessential noir detective series,"
those preferring non-graphic stories
may picture Spade or his creator,
Dashiell Hammett, in the title role.

Then, of course, there are Eisner's later
  story, "A Contract With God,"
  John 4:24, and 1916 4/24.

Tuesday, October 12, 2004

Tuesday October 12, 2004

Filed under: General — Tags: , — m759 @ 4:30 PM

The Last Enemy
(See April 30)

  

"I was also impressed… by the intensity of Continental modes of literary-critical thought….

On the Continent, studies of Hölderlin and Rousseau, of Poe, Baudelaire, Mallarmé and Rilke, of Rabelais, Nietzsche, Kafka, and Joyce, challenged not only received ideas on the unity of the work of art but many aspects of western thought itself. Derrida, at the same time, who for nearly a decade found a home in Yale's Comparative Literature Department, expanded the concept of textuality to the point where nothing could be demarcated as 'hors d'œuvre' and escape the literary-critical eye. It was uncanny to feel hierarchic boundaries waver until the commentary entered the text—not literally, of course, but in the sense that the over-objectified work became a reflection on its own status, its stability as an object of cognition. The well-wrought urn contained mortal ashes."

— Geoffrey Hartman, A Life of Learning

In memory of
Jacques Derrida and James Chace,
both of whom died in Paris on
Friday, Oct. 8, 2004… continued…
(See previous three entries.)

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Orson Welles


Mate in 2
V. Nabokov, 1919

"The last enemy
that shall be destroyed is death."
— Saul of Tarsus, 1 Cor. 15:26

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Knight move,
courtesy of V. Nabokov:

Nfe5 mate

The image “http://www.log24.com/log/pix04A/041012-Kt.gif” cannot be displayed, because it contains errors.

Knight:

Sir John Falstaff
(See Chimes at Midnight.)

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