Log24

Sunday, November 11, 2012

Professor Lavery’s Sunday School–

Filed under: General — m759 @ 8:00 AM

Saving an Appearance

(Click images for background.)

IMAGE- Owen Barfield on Israel, Christ, and 'participation'

See also Isaiah

IMAGE- Isaiah Sheffer, paid death notice, first paragraph

For a founder of Symphony Space

"To assuage this space…"

IMAGE- Weblog post on Barfield, 'To assuage this space...'

Friday, August 13, 2010

For David Lavery

Filed under: General — m759 @ 2:22 PM

Now online— Lavery's "God, Death, and Pizza"

http://www.log24.com/log/pix10B/100813-ChicagoPizza.jpg

This suggests a look at Ivan Illich, at Mother Jerome, at a note from the date of death of the former, and at an image from the date of death of the latter.

http://www.log24.com/log/pix10B/100813-IvanIllichAndMotherJerome.jpg

Note from December 2, 2002— Pilate's Question

Image from June 27, 2006

http://www.log24.com/log/pix10B/100813-NewLight.gif

Saturday, September 3, 2016

Phenomenology*

Filed under: General — m759 @ 8:30 PM

For the Church of Synchronology, a correction of
a recent New York Times  obituary by Daniel Lewis —

Actor Gene Wilder died early Monday, Aug. 29, not, as 
earlier reported, late Sunday, Aug. 28.

NY Times correction: Gene Wilder died early on Mon. Aug. 29, not on Sun. Aug. 28.

See also the last Log24 post of Sunday night, Aug. 28 (Angles of Vision)
and the first post of Monday morning, Aug. 29, 2016 (Roll Credits).

* For some reading related to the title, see an Evil Genius page
by the late David Lavery mentioning Colin Wilson's novel
The Mind Parasites .  Great entertainment for the tinfoil-hat crowd —

"More and more I feel like the narrator of Colin Wilson's 
The Mind Parasites , a phenomenologist who, along with
a dedicated group of compatriots, struggles clandestinely
to overthrow alien invaders that have secretly
taken captive the 'deep structure' of the human mind." 

Friday, September 2, 2016

Raiders of the Lost Birthday

Filed under: General — Tags: , — m759 @ 10:00 AM

Some images from the posts of last July 13
(Harrison Ford's birthday) may serve as funeral
ornaments for the late Prof. David Lavery.

IMAGE- Massimo Vignelli, his wife Lella, and cube

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

See as well posts on "Silent Snow" and "Starlight Like Intuition."

Thursday, September 1, 2016

Requiem for a Professor

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

The professor of the title is David Lavery,
who reportedly died Tuesday, August 30.

Lavery is the author of, among other things, the website
Evil Genius, which contains notes toward a fiction based
on a concept by Descartes.

In memoriam

Monday, January 25, 2016

A Hateful Eight

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

In memory of physicist David Ritz Finkelstein,
who reportedly died yesterday —

"His sense of irony and precision was appreciated" ….

Precision

Irony

An illustration of the song "Stuck in the Middle with You"
(from the Tarantino film "Reservoir Dogs") was posted by
an academic at Christmas 2015 —

See also, in this  journal,
The Jewel in the Lotus Meets the Kernel in the Nutshell 
(December 16, 2015).

Monday, December 21, 2015

Oral-Aural

Filed under: General — m759 @ 12:00 PM

http://www.log24.com/log/pix11C/111127-Ong-PresenceOfTheWord.jpg

See also the Eve of Devil's Night, 2015

Related material from an academic's weblog —

Happy birthday to a star of Tarantino's Yuletide offering.

Wednesday, May 6, 2015

Narrative Metaphysics

Filed under: General — m759 @ 11:01 PM

(Continued from Dec. 13, 2014.)

David Lavery's enthusiasm today for the Marvel Comics
"Infinity Stones" suggests a review of The Foundation Stone
mentioned in the post Narrative Metaphysics of 12/13/2014.

See as well "Many Dimensions" in this journal.

Saturday, April 25, 2015

Faustian Merry-Go-Round

Filed under: General — m759 @ 11:01 PM

Thanks to David Lavery for the following:

"Voilà! Stevens has managed to create out of nothing a palpable imaginative space, an interiority without material dimensions, replete with its own achieved and accomplished music. And in truth, in a world of Heisenbergian uncertainties and shifting star masses, it may be enough for the dizzying, ever-shifting merry-go-round of the Faustian mind simply to slow down and let itself come to rest, at least for the moment."

— Paul Mariani, "God and the Imagination," Aug. 10, 1996

http://imagejournal.org/page/journal/articles/issue-18/mariani-essays

Sunday, April 5, 2015

Documenting the Academy’s Victims*

Filed under: General — m759 @ 11:00 PM

This post was suggested by today's 
Easter message from academic David Lavery —

For a reply, see

"Horus Manure: Debunking the Jesus/Horus Connection," 
a post from the weblog  Jon Sorensen: Blogging on
Catholic Apologetics 
, dated October 25, 2012.

The phrase "blood libel" also comes to mind.

* "Documenting Victims" was the title of a post in this  journal
   from the same date as Sorensen's post— Oct. 25, 2012. 

Friday, November 22, 2013

Fiction

Filed under: General — Tags: — m759 @ 7:59 AM

From David Lavery's weblog today—

IMAGE- '...final belief must be in a fiction.'- Wallace Stevens

It is?  Then a check of the rest of the poem seems in order.

In the poem, Stevens speaks of

The impossible possible philosophers' man,
The man who has had the time to think enough,
The central man, the human globe, responsive
As a mirror with a voice, the man of glass,
Who in a million diamonds sums us up.

Compare and contrast with a rather silly recent music video—

Perhaps Stevens's "human globe" could be portrayed by the
versatile Philip Seymour Hoffman, who stars in a new film directed
by Anton Corbijn, the perpetrator of the above Arcade Fire video.

See also Log24 posts on and just before the video's upload date.

Wednesday, July 17, 2013

Backward

Filed under: General — m759 @ 9:48 AM

(Continued)

For Brad Leithauser, some of whose remarks
on "Reading Poems Backward" were quoted
here on July 13

A brief review of the life of artist Marc Simont,
who died on that day.

(Click for a larger and clearer image.)

Tell it slant .

Sunday, November 11, 2012

Lincoln Porn

Filed under: General — m759 @ 2:56 PM

Tablet  magazine, November 9th, 2012,
on Spielberg's Lincoln :

"… the movie’s lone Rocky moment
of ecstatic self-congratulation
is reserved for the amendment’s climactic
passage with the victorious congressmen
spontaneously bursting into
'The Battle Hymn of the Republic.' "

IMAGE- From Wikipedia, Venn diagram for NAND operator (cf. 'Mandorla')

"Mine eyes have seen the glory…"

IMAGE- Chris Pirillo, T-Mobile ad, 'Life Without Limits'

Both images above refer to this morning's post
 Professor Lavery's Sunday School.

For other porn from Tablet  magazine, see
Minimalist Whirl.

For other porn from Lincoln's seat of government, see
Physical Poetry and All In .

For further blasphemy, see The Apotheosis of Washington:

IMAGE- Blasphemous interior of the U.S. Capitol Dome

Tuesday, July 17, 2012

Putting the X in…

Filed under: General — m759 @ 12:00 PM
 

Éxito

Or: The Death of Ivan Illich

See For David Lavery and the prequel Art Isn't Easy

"Time for you to see the field."

Tuesday, May 10, 2011

Groups Acting

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

The LA Times  on last weekend's film "Thor"—

"… the film… attempts to bridge director Kenneth Branagh's high-minded Shakespearean intentions with Marvel Entertainment's bottom-line-oriented need to crank out entertainment product."

Those averse to Nordic religion may contemplate a different approach to entertainment (such as Taymor's recent approach to Spider-Man).

A high-minded— if not Shakespearean— non-Nordic approach to groups acting—

"What was wrong? I had taken almost four semesters of algebra in college. I had read every page of Herstein, tried every exercise. Somehow, a message had been lost on me. Groups act . The elements of a group do not have to just sit there, abstract and implacable; they can do  things, they can 'produce changes.' In particular, groups arise naturally as the symmetries of a set with structure. And if a group is given abstractly, such as the fundamental group of a simplical complex or a presentation in terms of generators and relators, then it might be a good idea to find something for the group to act on, such as the universal covering space or a graph."

— Thomas W. Tucker, review of Lyndon's Groups and Geometry  in The American Mathematical Monthly , Vol. 94, No. 4 (April 1987), pp. 392-394

"Groups act "… For some examples, see

Related entertainment—

High-minded— Many Dimensions

Not so high-minded— The Cosmic Cube

http://www.log24.com/log/pix11A/110509-SpideySuperStories39Sm.jpg

One way of blending high and low—

The high-minded Charles Williams tells a story
in his novel Many Dimensions about a cosmically
significant cube inscribed with the Tetragrammaton—
the name, in Hebrew, of God.

The following figure can be interpreted as
the Hebrew letter Aleph inscribed in a 3×3 square—

http://www.log24.com/log/pix11A/110510-GaloisAleph.GIF

The above illustration is from undated software by Ed Pegg Jr.

For mathematical background, see a 1985 note, "Visualizing GL(2,p)."

For entertainment purposes, that note can be generalized from square to cube
(as Pegg does with his "GL(3,3)" software button).

For the Nordic-averse, some background on the Hebrew connection—

Monday, January 3, 2011

New Critical Art

Filed under: General — m759 @ 9:00 PM

From a scholar quoted in this morning's post

"Both Vico and Joyce, each in his own way, practice what Vico calls a nuov'arte critica , a 'new critical art'…"

From Hugh Grant's birthday, 2003 (found in a search for whiteness  in this morning's post) —

Tara Fitzgerald and Hugh Grant
in "Sirens" (1994)

PATRICK’S RUNE

At Tara, in this fateful hour,
I place all heaven with its power.
And the sun with its brightness,
And the snow with its whiteness,
And the fire with all the strength it hath,
And the lightning with its rapid wrath,
And the winds with their swiftness along their path,
And the sea with its deepness,
And the rocks with their steepness,
And the earth with its starkness;
All these I place
By God’s almighty help and grace
Between myself and the powers of darkness.

From A Swiftly Tilting Planet
by Madeleine L’Engle

The cover of yesterday's Sunday New York Times Book Review
features stylized letters by artist Leonardo Sonnoli that include black
circles and triangles —

IMAGE- NY Times Book Review cover art by Leonardo Sonnoli

The stylized Sonnoli letters spell out "WORDS ABOUT WORDS ABOUT WORDS."
This phrase is used to introduce essays on criticism by "six accomplished critics."

A less accomplished critic might note that in the picture above, Tara is modeling
a new fashion by Sonnoli — namely, the word OOV.  A search for this word yields…

"OOV in text processing stands for 'out-of-vocabulary,' i.e., a word
 that is not known in the computer's online dictionary."

It should be.

Addendum (from a link in the same search for whiteness ) in memory of a great beauty who died on Sunday —
      http://www.log24.com/log10/saved/100613-WhiteBySchwartz.gif

Wednesday, November 17, 2010

Church Narrative

Filed under: General,Geometry — m759 @ 2:22 AM

Thanks to David Lavery for the following dialogue on the word "narrative" in politics—

"It's like – does this fit into narrative?
It's like, wait, wait, what about a platform? What about, like, ideas?
What about, you know, these truths we hold to be self-evident?
No, it's the narrative."

"Is narrative a fancy word for spin?"

Related material —

Church Logic (Log24, October 29) —

  What sort of geometry
    is the following?

IMAGE- The four-point, six-line geometry

 

"What about, you know, these truths we hold to be self-evident?"

Some background from Cambridge University Press in 1976 —

http://www.log24.com/log/pix10B/101117-CameronIntro2.jpg

Commentary —

The Church Logic post argues that Cameron's implicit definition of "non-Euclidean" is incorrect.

The four-point, six-line geometry has as lines "all subsets of the point set" which have cardinality 2.

It clearly satisfies Euclid's parallel postulate.  Is it, then, not  non-Euclidean?

That would, according to the principle of the excluded middle (cf. Church), make it Euclidean.

A definition from Wikipedia that is still essentially the same as it was when written on July 14, 2003

"Finite geometry describes any geometric system that has only a finite number of points. Euclidean geometry, for example, is not finite, because a Euclidean line contains infinitely many points…."

This definition would seem to imply that a finite geometry (such as the four-point geometry above) should be called non -Euclidean whether or not  it violates Euclid's parallel postulate. (The definition's author, unlike many at Wikipedia, is not  anonymous.)

See also the rest  of Little Gidding.

Sunday, June 13, 2010

Today’s Sermon

Filed under: General — m759 @ 10:30 AM

 

    Whiteness    


Thursday, June 10, 2010

Brightness at Noon (continued)

Filed under: General — m759 @ 12:00 PM

"By groping toward the light we are made to realize
 how deep the darkness is around us."
  — Arthur Koestler, The Call Girls: A Tragi-Comedy,
      Random House, 1973, page 118

Continued from Christmas 2009 and from last Sunday

The serious reflection is composed
Neither of comic nor tragic but of commonplace."

Wallace Stevens

Tuesday, March 16, 2010

Gameplayers of the Academy

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

New Game

In memory of a Jesuit who died on February 22 (see yesterday's "For the Ides of March")–

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

— M. A. Foster, The Gameplayers of Zan

"… for Othello, no less than his creator Shakespeare, death without speechmaking is almost unthinkable."

"Walter Ong," by Jeet Heer (Book & Culture, July/August 2004)

"This Jack, joke, poor potsherd, patch, matchwood…."

— Jesuit quote at David Lavery's weblog today

See also this journal on February 22, the date of the Jesuit death. A post on that date mentions Ong and his teacher McLuhan, and displays a McLuhan figure related to the "joke" quote above–

McLuhan 'tetrad' figure with four diamonds surrounding a fifth, the medium

Click figure for background.

Ong discussed "agonistic" culture.
See "Sunday's Theater" and a film
based on the novel discussed there–

Menin... First line, in Greek, of the Iliad

Classics 101

IMAGE- Anthony Hopkins in 'The Human Stain'

Prof. Coleman Silk introduces
freshmen to academic values

For academic gameplayers who prefer
less emotionally challenging subjects,
there is Othello Online —

http://www.log24.com/log/pix10/100316-NewGame.jpg

"New Game. You May Pass for White to Start."

Saturday, March 13, 2010

Ideas of Reference

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

Thanks to David Lavery for the following–

http://www.log24.com/log/pix10/100313-Memorabilia.jpg

See also references in Log24 to "Hitler Plans Burning Man," as well as…

"Imagine a multidimensional spider's web…."
— Alan Watts in Wikipedia article on Indra's Net.

and

"the Burning Man Evolution of
 Spider Robinson's Cross-Time Saloon."

The paranoid schizophrenics among us might also enjoy what they may, if they like, view as a coded reference to today's date, 3/13–

Page 313 in Robert Stone's classic novel
A Flag for Sunrise  (Knopf hardcover, 1981).

Thursday, August 20, 2009

Thursday August 20, 2009

Filed under: General,Geometry — m759 @ 4:00 PM

Sophists

From David Lavery’s weblog today

Kierkegaard on Sophists:

“If the natural sciences had been developed in Socrates’ day as they are now, all the sophists would have been scientists. One would have hung a microscope outside his shop in order to attract customers, and then would have had a sign painted saying: Learn and see through a giant microscope how a man thinks (and on reading the advertisement Socrates would have said: that is how men who do not think behave).”

— Søren Kierkegaard, Journals, edited and translated by Alexander Dru

To anyone familiar with Pirsig’s classic Zen and the Art of Motorcycle Maintenance, the above remarks of Kierkegaard ring false. Actually, the sophists as described by Pirsig are not at all like scientists, but rather like relativist purveyors of postmodern literary “theory.” According to Pirsig, the scientists are like Plato (and hence Socrates)– defenders of objective truth.

Pirsig on Sophists:

“The pre-Socratic philosophers mentioned so far all sought to establish a universal Immortal Principle in the external world they found around them. Their common effort united them into a group that may be called Cosmologists. They all agreed that such a principle existed but their disagreements as to what it was seemed irresolvable. The followers of Heraclitus insisted the Immortal Principle was change and motion. But Parmenides’ disciple, Zeno, proved through a series of paradoxes that any perception of motion and change is illusory. Reality had to be motionless.

The resolution of the arguments of the Cosmologists came from a new direction entirely, from a group Phædrus seemed to feel were early humanists. They were teachers, but what they sought to teach was not principles, but beliefs of men. Their object was not any single absolute truth, but the improvement of men. All principles, all truths, are relative, they said. ‘Man is the measure of all things.’ These were the famous teachers of ‘wisdom,’ the Sophists of ancient Greece.

To Phaedrus, this backlight from the conflict between the Sophists and the Cosmologists adds an entirely new dimension to the Dialogues of Plato. Socrates is not just expounding noble ideas in a vacuum. He is in the middle of a war between those who think truth is absolute and those who think truth is relative. He is fighting that war with everything he has. The Sophists are the enemy.

Now Plato’s hatred of the Sophists makes sense. He and Socrates are defending the Immortal Principle of the Cosmologists against what they consider to be the decadence of the Sophists. Truth. Knowledge. That which is independent of what anyone thinks about it. The ideal that Socrates died for. The ideal that Greece alone possesses for the first time in the history of the world. It is still a very fragile thing. It can disappear completely. Plato abhors and damns the Sophists without restraint, not because they are low and immoral people… there are obviously much lower and more immoral people in Greece he completely ignores. He damns them because they threaten mankind’s first beginning grasp of the idea of truth. That’s what it is all about.

The results of Socrates’ martyrdom and Plato’s unexcelled prose that followed are nothing less than the whole world of Western man as we know it. If the idea of truth had been allowed to perish unrediscovered by the Renaissance it’s unlikely that we would be much beyond the level of prehistoric man today. The ideas of science and technology and other systematically organized efforts of man are dead-centered on it. It is the nucleus of it all.

And yet, Phaedrus understands, what he is saying about Quality is somehow opposed to all this. It seems to agree much more closely with the Sophists.”

I agree with Plato’s (and Rebecca Goldstein’s) contempt for relativists. Yet Pirsig makes a very important point. It is not the scientists but rather the storytellers (not, mind you, the literary theorists) who sometimes seem to embody Quality.

As for hanging a sign outside the shop, I suggest (particularly to New Zealand’s Cullinane College) that either or both of the following pictures would be more suggestive of Quality than a microscope:

Alfred Bester covers showing 'primordial protomatter' (altered here) from 'Stars' and Rogue Winter from 'Deceivers'

For the “primordial protomatter”
in the picture at left, see
The Diamond Archetype.

Wednesday, July 15, 2009

Wednesday July 15, 2009

Filed under: General — Tags: — m759 @ 11:09 AM
The Plot Thickens

Thanks to David Lavery
see previous entry— the
word for today is…
 
Cover of 'Zaddik,' a novel by David Rosenbaum

"As the story develops, an
 element of magical realism
 enters the picture."
Amazon review   

Related material:

For background on magical
realism, see the update to
today's previous entry.

See also
A Year of Magical Thinking
(June 6, 2009) and
the entries of May 19-22,
featuring Judy Davis in…

Poster for 'Diamonds' miniseries on ABC starting May 24, 2009

(Cf. St. Bridget's Day, 2003)

Wednesday July 15, 2009

Filed under: General — Tags: — m759 @ 4:01 AM
DETAIL
of obituaries page,
New York Times,
Monday morning:

Detail, obits page, NY Times Monday morning, July 13, 2009

Detail of arts page,
New York Times, Wednesday morning:

(Click ad for more on the Monday night death of Dash Snow.)

Arts page detail, morning of Wednesday, July 15, 2009

Headlines collage by Dash Snow

Hurt yet?
_________________

Update of 5:01 AM:

Lavery Hits
Literary Jackpot

From the top right of
this morning's online
New York Times front page:

Christoph Niemann on witchcraft and snow

Click on voodoo doll
for further details.

See also…

1. Monday's link to a
Wallace Stevens poem,
"Snow and Stars"

2. The conclusion of this
morning's Times obituary
for artist Dash Snow, which
gives his daughter's name…
"Secret."

3. David Lavery's excellent
analysis
of the classic
 Conrad Aiken story
"Silent Snow, Secret Snow."
 

Saturday, June 27, 2009

Saturday June 27, 2009

Filed under: General — m759 @ 1:00 AM

From the weblog of David Lavery, literature, film, and television scholar/critic, now teaching at Middle Tennessee State University–

Lavery’s quote of the day (6/27/09)-

“Art is based on second love, not first love. In it we make a return to something which we had willfully alienated. The child is occupied mostly with things, but it is because he is still unfurnished with systematic ideas, not because he is a ripe citizen by nature and comes already trailing clouds of glory. Images are clouds of glory for the man who has discovered that ideas are a sort of darkness.”

–John Crowe Ransom

Posted by Lavery on Friday, June 26, 2009, at 9:00 PM

Saturday, June 20, 2009

Saturday June 20, 2009

Filed under: General — m759 @ 3:54 PM
Strange Bedfellows

http://www.log24.com/log/pix09/090620-ObamaNBC.jpg

The above excerpt from Google News was suggested

  1. by David Lavery’s June 19 weblog entry “Future Books,”
  2. by an example of this sort of book– “The Holy of Holies: The Constituents of Emptiness,”
  3. by the June 19 NY Lottery midday number 354 (the name of an empty page in Wallace Stevens: Collected Poetry and Prose, Library of America, 1997), and
  4. by the musical meaning of the numbers 3, 5, 4– the frequency ratios of the notes G, E, C
    The musical notes G, E, C on the piano

    and hence the numerical equivalent of the NBC chimes.
“We have heard
  the chimes at midnight.”
— William Shakespeare 
  and Orson Welles

Monday, June 1, 2009

Monday June 1, 2009

Filed under: General — m759 @ 10:31 AM

“What’s going on”

Marvin Gaye

“The action is in the plot, inaccessible to introspection, and only the characters know what’s going on.”

James Hillman, quoted at David Lavery’s weblog.

See also

Badge ID

Click on image
 for further details.

Sunday, April 12, 2009

Sunday April 12, 2009

Filed under: General — m759 @ 3:09 AM
Where Entertainment
Is God
, continued

Dialogue from the classic film Forbidden Planet

“… Which makes it a gilt-edged priority that one of us gets into that Krell lab and takes that brain boost.”

— Taken from a video (5:18-5:24 of 6:09) at David Lavery’s weblog in the entry of Tuesday, April 7.

(Cf. this journal on that date.)

Thanks to Professor Lavery for his detailed notes on his viewing experiences.

My own viewing recently included, on the night of Good Friday, April 10, the spiritually significant film Indiana Jones and the Kingdom of the Crystal Skull.

The mystic circle of 13 aliens at the end of that film, together with Leslie Nielsen’s Forbidden Planet remark quoted above, suggests the following:

“The aim of Conway’s game M13 is to get the hole at the top point and all counters in order 1,2,…,12 when moving clockwise along the circle.” —Lieven Le Bruyn

http://www.log24.com/log/pix09/090411-M13.gif

The illustration is from the weblog entry by Lieven Le Bruyn quoted below. The colored circles represent 12 of the 13 projective points described below, the 13 radial strokes represent the 13 projective lines, and the straight lines in the picture, including those that form the circle, describe which projective points are incident with which projective lines. The dot at top represents the “hole.”

From “The Mathieu Group M12 and Conway’s M13-Game” (pdf), senior honors thesis in mathematics by Jeremy L. Martin under the supervision of Professor Noam D. Elkies, Harvard University, April 1, 1996–

“Let P3 denote the projective plane of order 3. The standard construction of P3 is to remove the zero point from a three-dimensional vector space over the field F3 and then identify each point x with -x, obtaining a space with (33 – 1)/2 = 13 points. However, we will be concerned only with the geometric properties of the projective plane. The 13 points of P3 are organized into 13 lines, each line containing four points. Every point lies on four lines, any two points lie together on a unique line, and any two lines intersect at a unique point….

Conway [3] proposed the following game…. Place twelve numbered counters on the points… of P3 and leave the thirteenth point… blank. (The empty point will be referred to throughout as the “hole.”) Let the location of the hole be p; then a primitive move of the game consists of selecting one of the lines containing the hole, say {p, q, r, s}. Move the counter on q to p (thus moving the hole to q), then interchange the counters on r and s….

There is an obvious characterization of a move as a permutation in S13, operating on the points of P3. By limiting our consideration to only those moves which return the hole to its starting point…. we obtain the Conway game group. This group, which we shall denote by GC, is a subgroup of the symmetric group S12 of permutations of the twelve points…, and the group operation of GC is concatenation of paths. Conway [3] stated, but did not prove explicitly, that GC is isomorphic to the Mathieu group M12. We shall subsequently verify this isomorphism.

The set of all moves (including those not fixing the hole) is given the name M13 by Conway. It is important that M13 is not a group….”

[3] John H. Conway, “Graphs and Groups and M13,” Notes from New York Graph Theory Day XIV (1987), pp. 18–29.


Another exposition (adapted to Martin’s notation) by Lieven le Bruyn (see illustration above):

“Conway’s puzzle M13 involves the 13 points and 13 lines of P3. On all but one point numbered counters are placed holding the numbers 1,…,12 and a move involves interchanging one counter and the ‘hole’ (the unique point having no counter) and interchanging the counters on the two other points of the line determined by the first two points. In the picture [above] the lines are represented by dashes around the circle in between two counters and the points lying on this line are those that connect to the dash either via a direct line or directly via the circle. In the first part we saw that the group of all reachable positions in Conway’s M13 puzzle having the hole at the top position contains the sporadic simple Mathieu group M12 as a subgroup.”

For the religious significance of the circle of 13 (and the “hole”), consider Arthur and the 12 knights of the round table, et cetera.

But seriously…
 
Delmore Schwartz, 'Starlight Like Intuition Pierced the Twelve'

Sunday April 12, 2009

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

From a professor’s weblog:

Saturday, April 11, 2009

Quote of the Day (4/11/09) (Elias Canetti Week)

“The novel should not be in any hurry. Once, hurry belonged to its sphere, now the film has taken that over; measured by the film, the hasty novel must always remain inadequate. The novel, as a creature of calmer times, may carry something of that old calm into our new hastiness. It could serve many people as slow-motion; it could induce them to tarry; it could replace the empty meditations of their cults.”

–Elias Canetti, The Human Province

Posted by David Lavery at 1:00 AM

Monday, July 23, 2007

Monday July 23, 2007

Filed under: General,Geometry — Tags: , , , , — m759 @ 8:00 AM
Daniel Radcliffe
is 18 today.
Daniel Radcliffe as Harry Potter

Greetings.

“The greatest sorcerer (writes Novalis memorably)
would be the one who bewitched himself to the point of
taking his own phantasmagorias for autonomous apparitions.
Would not this be true of us?”

Jorge Luis Borges, “Avatars of the Tortoise”

El mayor hechicero (escribe memorablemente Novalis)
sería el que se hechizara hasta el punto de
tomar sus propias fantasmagorías por apariciones autónomas.
¿No sería este nuestro caso?”

Jorge Luis Borges, “Los Avatares de la Tortuga

Autonomous Apparition

At Midsummer Noon:

“In Many Dimensions (1931)
Williams sets before his reader the
mysterious Stone of King Solomon,
an image he probably drew from
a brief description in Waite’s
The Holy Kabbalah (1929) of
a supernatural cubic stone
on which was inscribed
‘the Divine Name.’”
The image “http://www.log24.com/log/pix07/070624-Waite.gif” cannot be displayed, because it contains errors.
Related material:
It is not enough to cover the rock with leaves.
We must be cured of it by a cure of the ground
Or a cure of ourselves, that is equal to a cure 

Of the ground, a cure beyond forgetfulness.
And yet the leaves, if they broke into bud,
If they broke into bloom, if they bore fruit,

And if we ate the incipient colorings
Of their fresh culls might be a cure of the ground.

– Wallace Stevens, “The Rock”

See also
as well as
Hofstadter on
his magnum opus:
“… I realized that to me,
Gödel and Escher and Bach
were only shadows
cast in different directions by
some central solid essence.
I tried to reconstruct
the central object, and
came up with this book.”
Goedel Escher Bach coverHofstadter’s cover.

Here are three patterns,
“shadows” of a sort,
derived from a different
“central object”:
Faces of Solomon's Cube, related to Escher's 'Verbum'

Click on image for details.

Saturday, March 10, 2007

Saturday March 10, 2007

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

The Logic of Dreams

From A Beautiful Mind–

“How could you,” began Mackey, “how could you, a mathematician, a man devoted to reason and logical proof…how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?”

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. “Because,” Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, “the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”

Ideas:

The image “http://www.log24.com/log/pix07/070309-NYlottery.jpg” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix07/070309-PAlottery.jpg” cannot be displayed, because it contains errors.

These numbers may, in the mad way so well portrayed by Sylvia Nasar in the above book, be regarded as telling a story… a story that should, of course, not be taken too seriously.

Friday’s New York numbers (midday 214, evening 711) suggest the dates 2/14 and 7/11.  Clicking on these dates will lead the reader to Log24 entries featuring, among others, T. S. Eliot and Stephen King– two authors not unacquainted with the bizarre logic of dreams.

A link in the 7/11 entry leads to a remark of Noel Gray on Plato’s Meno and “graphic austerity as the tool to bring to the surface, literally and figuratively, the inherent presence of geometry in the mind of the slave.”

Also Friday: an example of graphic austerity– indeed, Gray graphic austerity– in Log24:

Chessboard (Detail)

This illustration refers to chess rather than to geometry, and to the mind of an addict rather than to that of a slave, but chess and geometry, like addiction and slavery, are not unrelated.


Friday’s Pennsylvania numbers, midday 429 and evening 038, suggest that the story includes, appropriately enough in view of the above Beautiful Mind excerpt, Mackey himself.  The midday number suggests the date 4/29, which at Log24 leads to an entry in memory of Mackey.

(Related material: the Harvard Gazette of April 6, 2006, “Mathematician George W. Mackey, 90: Obituary“–  “A memorial service will be held at Harvard’s Memorial Church on April 29 at 2 p.m.“)

Friday’s Pennsylvania evening number 038 tells two other parts of the story involving Mackey…

As Mackey himself might hope, the number may be regarded as a reference to the 38 impressive pages of Varadarajan’s “Mackey Memorial Lecture” (pdf).

More in the spirit of Nash, 38 may also be taken as a reference to Harvard’s old postal address, Cambridge 38, and to the year, 1938, that Mackey entered graduate study at Harvard, having completed his undergraduate studies at what is now Rice University.

Returning to the concept of graphic austerity, we may further simplify the already abstract chessboard figure above to obtain an illustration that has been called both “the field of reason” and “the Garden of Apollo” by an architect, John Outram, discussing his work at Mackey’s undergraduate alma mater:

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Let us hope that Mackey,
a devotee of reason,
is now enjoying the company
of Apollo rather than that of
Tom O’Bedlam:

The image “http://www.log24.com/log/pix05A/050613-Crowe.jpg” cannot be displayed, because it contains errors.

For John Nash on his birthday:

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

Tom O’Bedlam’s Song

Wednesday, March 10, 2004

Wednesday March 10, 2004

Filed under: General — m759 @ 6:01 PM

Split

The first idea was not our own. Adam
in Eden was the father of Descartes.

— Wallace Stevens,
Notes Toward a Supreme Fiction

A very interesting web site at
Middle Tennessee State University
relates the Stevens quote
to two others:

“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. It differs from the apparently similar Cartesian crease across things in the fact that the two halves of us once were one; that we did not always stand askance like molasses and madness–logically at odds–but grew apart over the years like those husbands and wives who draw themselves into different corners of contemplation.”

— William Gass,
“The Polemical Philosopher”

“The experiment [to make rationality primary] reached the reductio ad absurdum following the attempt by Descartes to solve problems of human knowledge by giving ontological status to the dichotomy of thinking substance and extended substance, that is subject and object. Not only were God and man, sacred and secular, being and becoming, play and seriousness severed, but now also the subject which wished to unite these fragmented dichotomies was itself severed from that which it would attempt to reconcile.”

— David Miller, God and Games

“Which is it then? For Gass, the Cartesian schism is a post- lapsarian divorce-in progress, only apparently similar to the expulsion from paradise. For Stevens the fault is primordial and Descartes only its latter-day avatar. For Miller, Descartes is the historical culprit, the patriarch of the split.”

The Evil Genius Notebook,
by
David Lavery

Tuesday, February 4, 2003

Tuesday February 4, 2003

Filed under: General — m759 @ 1:15 PM

Mark Hopkins Award

From Dr. Mac’s Cultural Calendar:

  • Mark Hopkins, U.S. educator, was born on this day in 1802.  He taught at Williams College….  President Garfield, one of his students, said that all that was needed for a college was Mark Hopkins on one end of a log and a student on the other.”

I have never encountered a mentor figure capable of holding down his end of a log in the manner of Mark Hopkins.  The closest I have come to such an encounter is with a book, The Practical Cogitator, by Charles P. Curtis and Ferris Greenslet.

This year’s Mark Hopkins award for the closest approach to the log-sitting ideal goes to David Lavery, whose online commonplace book appears in the column at left.  Lavery, too, appreciates the work of Curtis and Greenslet, as his site indicates.

See also a quote from Lavery in today’s New York Times.

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