Log24

Friday, September 30, 2011

Primordiality

Filed under: General — m759 @ 3:48 pm

"A Phenomenological Perspective,"
Ch. 2 in The Star and the Whole:
Gian-Carlo Rota on Mathematics and Phenomenology 
,
by Fabrizio Palombi, A K Peters/CRC Press, 2011—

"Rota is convinced that one of the fundamental tasks of phenomenology is that of highlighting the primordiality of sense. In his words, if 'many disputes among philosophers are disputes about primordiality' then 'phenomenology is yet another dispute about what is most primordial' (Rota, 1991a,* p. 54). In this way he evidently does not intend to deny the existence of matter, of objects, or of that objective dimension proper to science, in favor of a spiritualist option, but rather to posit as primordial another dimension of the world connected with contexts and with roles, which is considered primordial because each one of us is confronted with it primordially."

* The End of Objectivity: The Legacy of Phenomenology ,
Lectures by Rota at MIT 1974-1991, 457 pages,
MIT Mathematics Department, Cambridge, MA

"The Ultimate, Apocalyptic Laptop"
by George Johnson
Published: September 5, 2000, by The New York Times

"In a paper in the current issue of Nature , Dr. Lloyd describes the ultimate laptop— a computer as powerful as the laws of physics will allow. So energetic is this imaginary machine that using it would be like harnessing a thermonuclear reaction. In the most extreme version of this computer supreme, so much computational circuitry would be packed into so small a space that the whole thing would collapse and form a tiny black hole, an object so dense that not even light can escape its gravity."

Related material: Rota and "Black Hole" in this journal, as well as the Sator Square.

Thursday, September 29, 2011

Michaelmas Moonshine

Filed under: General — m759 @ 11:48 pm

Lottery hermeneutics for Michaelmas—

New York Lottery the evening of Thursday, Sept. 29, 2011—

499 and 6985.

For 499, see post  499 in this journal ("Angel Night," Sept. 29, 2002).

For 6985, see a Sunday, 6/9/85, review of Amy's Eyes , a children's book by Richard Kennedy.

"Especially for the adult reader, the narrator's musings comprise many of the book's great pleasures. He discusses the seductiveness of numerology, the 'Wayward Daughter of Mathematics'….''

Edwin J. Kenney Jr.

Wednesday, September 28, 2011

Mathieu Moonshine

Filed under: General — m759 @ 2:56 pm

The properties of the Mathieu group M 24 have recently interested some physicists

(Click to enlarge.)

IMAGE- July 2011 conference on Mathieu moonshine

For some related papers, see Mendeley.com.

Tuesday, September 27, 2011

The Lost Plot

Filed under: General — m759 @ 8:00 pm

Daredevil work—

http://www.log24.com/log/pix11B/110927-DaredevilWork.jpg

For Dan Brown, author of The Lost Symbol

http://www.log24.com/log/pix10B/101031-PacinoReeves300w.jpg

Al Pacino and Keanu Reeves in Devil's Advocate
(Syfy channel, 9 PM tonight)

"Klaatu barada nikto."

Monday, September 26, 2011

Inner and Outer

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

For T.S. Eliot's Birthday

Last night's post "Transformation" was suggested in part
by the title of a Sunday New York Times  article on
George Harrison, "Within Him, Without Him," and by
the song title "Within You Without You" in the post
Death and the Apple Tree.

Related material— "Hamlet's Transformation"—

Hamlet, 2.2:

Something have you heard
Of Hamlet’s transformation; so call it,
Sith nor the exterior nor the inward man
Resembles that it was….”

A transformation:

The image “http://www.log24.com/theory/images/DTinscapes4-Trans.gif” cannot be displayed, because it contains errors.

Click on picture for details.

See also, from this year's Feast of the Transfiguration,
Correspondences and Happy Web Day.

For those who prefer the paganism of Yeats to
the Christianity of Eliot, there is the sequel to
"Death and the Apple Tree," "Dancers and the Dance."

Sunday, September 25, 2011

Transformation

Filed under: General — m759 @ 11:01 pm

Random thoughts from A Story (September 13th)—

797

April 24, 2003
A Terrible Beauty

451

August 26, 2002
Round Lights

1734

April 24, 2005
Today's Sermon

3276

March 24, 2008
Death and the Apple Tree

A September 24th story from The Washington Post

"James R. Adams was author or co-author of seven books,
beginning in 1971 with 'The Sting of Death.'"

Adams, an Episcopal priest, died on September 13th.

The September 13th Log24 post from which the above numbered links were
taken was in memory of film producer John Calley, who also died on that day.

A quote from Adams on the resurrected body of Christ:

"This new body had peculiar powers."

A quote from Calley:

"Let me put you in this unit."

Saturday, September 24, 2011

Live from New York, It’s…

Filed under: General — m759 @ 11:29 pm

http://www.log24.com/log/pix11B/110924-RadioheadAndPhilosophy131.jpg

For instance…

Click to enlarge

http://www.log24.com/log/pix11B/110924-ArchetypalArchitecture-500w.jpg

See also Plato's Ghost.

Kernels of Being

Filed under: General,Geometry — Tags: — m759 @ 10:29 pm

For the Pope in Germany

"We wish to see Jesus. For somehow we know, we suspect, we intuit, that if we see Jesus we will see what Meister Eckhart might call “The Divine Kernel of Being”— that Divine Spark of God’s essence, God’s imago Dei, the image in which we are created. We seem to know that in seeing Jesus we just might find something essential about ourselves."

—The Reverend Kirk Alan Kubicek, St. Peter’s at Ellicott Mills, Maryland, weblog post of Saturday, March 28, 2009, on a sermon for Sunday, March 29, 2009

See also this journal in March 2009.

Related non-theology—

Weyl on coordinate systems, Cassirer on the kernel of being, and A Study in Art Education.

Ariadne and the Exorcist

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

The title describes two philosophical events (one major, one minor) from the same day— Thursday, July 5, 2007. Some background from 2001:

"Are the finite simple groups, like the prime numbers, jewels strung on an as-yet invisible thread? And will this thread lead us out of the current labyrinthine proof to a radically new proof of the Classification Theorem?" (p. 345)

— Ronald Solomon,  "A Brief History of the Classification of Finite Simple Groups," Bulletin of the American Mathematical Society , Vol. 38 No. 3 (July 2001), pp. 315-352

The major event— On July 5, 2007, Cambridge University Press published Robert T. Curtis's Symmetric Generation of Groups.*

Curtis's book does not purport to lead us out of Solomon's labyrinth, but its publication date may furnish a Jungian synchronistic clue to help in exiting another  nightmare labyrinth— that of postmodernist nominalism.

The minor event— The posting of Their Name is Legion in this journal on July 5, 2007.

* This is the date given by Amazon.co.uk and by BookDepository.com. Other sources give a later July date, perhaps applicable to the book's publication in the U.S. rather than Britain.

Friday, September 23, 2011

Kali’s Thunder

Filed under: General — m759 @ 9:00 pm

NY Lottery this evening—

http://www.log24.com/log/pix11B/110923-NYlotteryEvening-747-3695.jpg

Continued from Themes of Sept. 17—

"And I heard, as it were, the noise of thunder."

Lottery hermeneutics for this evening—

747 — Source of the sound effect in a post of April 28, 2009:

"And Kali, ‘The Dark One,’ addressed him with the voice of a cloud of thunder…"
The King and the Corpse , by Heinrich Zimmer

3695 — Number of a post on Steps Toward Salvation  (Dec. 14, 2008)

Bingo

Filed under: General — m759 @ 3:01 pm

NY Lottery this afternoon—

http://www.log24.com/log/pix11B/110923-NYlotteryMidday-314-1115.jpg
 

See also post 1115.

Pallbearer

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

For those who prefer Nick Stahl (star of "The Speed of Thought"— see previous post)
to Keanu Reeves as a savior figure, here is a still from another film with Stahl as savior—

IMAGE- Schwarzenegger carries coffin in 'Terminator 3: Rise of the Machines'

Backstory —

IMAGE- NY Times obits for Julius Blank and A. Richard Turner

See also a Log24 post from the day of Blank's death, The Uploading.

Times Square Church

Filed under: General — Tags: , — m759 @ 2:56 am

Continued from April 29, 2011
 

http://www.log24.com/log/pix11B/110923-ReleaseDate.jpg


Related material— Inception and Feed Them on Your Dreams.

Thursday, September 22, 2011

Product Placement

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

And the Irving Thalberg Award goes to…

http://www.log24.com/log/pix11B/110922-DeNiro-LastTycoon.jpg

Robert De Niro as Irving Thalberg in "The Last Tycoon"

Text and Context—

Text:

http://www.log24.com/log/pix11B/110922-JerkyTreats.jpg

Jerky Treats  for dogs

Context:

http://www.log24.com/log/pix11B/110922-MadDogAndGlory.jpg

"Mad Dog and Glory" (March 5, 1993)

http://www.log24.com/log/pix11B/110922-NewDayNina-300w.jpg

"Point of No Return" (March 19, 1993) —
Note Jerky Treats  in background.

A possible acceptance speech for the Thalberg Award—

"Let me put you in this unit." — John Calley, via Buck Henry

Sicilian Reflections

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

http://www.log24.com/log/pix11B/110922-Weyl-Palermo.gif

Related material—

http://www.log24.com/log/pix11B/110922-TriquetrumCube.jpg

See also yesterday's Symmetric Generation.

New Day Nina

Filed under: General — Tags: — m759 @ 1:06 am

In memoriam
http://www.log24.com/log/pix11B/110922-NYTobit-WilliamFMay.jpg

http://www.log24.com/log/pix11B/110922-NewDayNina-500w.jpg

Bridget Fonda in "Point of No Return."  This is a 1993 remake of 1990's "La Femme Nikita ,"
virtually the same scene-by-scene, but with two nice new touches: the young assassin's code name
is Nina, after Nina Simone, and she happily shops as Simone sings "new day" in the soundtrack.

Wednesday, September 21, 2011

The Forking

Filed under: General — m759 @ 10:16 pm

"When you come to a fork in the road, take it." — Yogi Berra

http://www.log24.com/log/pix11B/110921-NYlotteryEvening.jpg

This evening's NY Lottery numbers were 375 and 3141.

Subjective interpretations—

There seems to be only one relevant result of a Google search for "375 Log24"—

http://www.log24.com/log/pix11B/110921-Search-375-Log24.jpg

There are, however, two  relevant interpretations of the number 3141—

1. The Saturday Evening Post  3/1/41 article by Jack Alexander on AA—

"The members of Alcoholics Anonymous do not pursue or coddle
a malingering prospect, and they know the strange tricks of the alcoholic
as a reformed swindler knows the art of bamboozling."

2. Post number 3141 in this  journal— Aesthetics for Jesuits.

The Gleaming (continued)

Filed under: General — m759 @ 3:33 pm

Happy Birthday to Bill Murray (61) and Stephen King (64).

Symmetric Generation

Suggested by yesterday's Relativity Problem Revisited and by Cassirer on Objectivity

From Symmetric Generation of Groups , by R.T. Curtis (Cambridge U. Press, 2007)—

"… we are saying much more than that G M 24 is generated by
some set of seven involutions, which would be a very weak
requirement. We are asserting that M 24 is generated by a set
of seven involutions which possesses all the symmetries of L3(2)
acting on the points of the 7-point projective plane…."
Symmetric Generation , p. 41

"It turns out that this approach is particularly revealing and that
many simple groups, both sporadic and classical, have surprisingly
simple definitions of this type."
Symmetric Generation , p. 42

See also (click to enlarge)—

http://www.log24.com/log/pix11B/110921-CassirerOnObjectivity-400w.jpg

Cassirer's remarks connect the concept of objectivity  with that of object .

The above quotations perhaps indicate how the Mathieu group M 24 may be viewed as an object.

"This is the moment which I call epiphany. First we recognise that the object is one  integral thing, then we recognise that it is an organised composite structure, a thing  in fact: finally, when the relation of the parts is exquisite, when the parts are adjusted to the special point, we recognise that it is that  thing which it is. Its soul, its whatness, leaps to us from the vestment of its appearance. The soul of the commonest object, the structure of which is so adjusted, seems to us radiant. The object achieves its epiphany."

— James Joyce, Stephen Hero

For a simpler object "which possesses all the symmetries of L3(2) acting on the points of the 7-point projective plane…." see The Eightfold Cube.

For symmetric generation of L3(2) on that cube, see A Simple Reflection Group of Order 168.

Tuesday, September 20, 2011

1949 Revisited

Filed under: General — Tags: , — m759 @ 6:18 pm

Hermann Weyl's 1949 remarks in this morning's post
were made at an event on March 19 in honor of Einstein's
70th birthday five days earlier.

Somehow the conclusion of Margaret Atwood's 1988 novel
Cat's Eye  seems appropriate:

http://www.log24.com/log/pix11B/110920-OldLight.jpg

Relativity Problem Revisited

A footnote was added to Finite Relativity

Background:

Weyl on what he calls the relativity problem

IMAGE- Weyl in 1949 on the relativity problem

"The relativity problem is one of central significance throughout geometry and algebra and has been recognized as such by the mathematicians at an early time."

– Hermann Weyl, 1949, "Relativity Theory as a Stimulus in Mathematical Research"

"This is the relativity problem: to fix objectively a class of equivalent coordinatizations and to ascertain the group of transformations S mediating between them."

– Hermann Weyl, 1946, The Classical Groups , Princeton University Press, p. 16

…. A note of Feb. 20, 1986, supplied an example of such coordinatizations in finite geometry. In that note, the group of mediating transformations acted directly on  coordinates within a 4×4 array. When the 4×4 array is embedded in a 4×6 array, a larger and more interesting group, M 24 (containing the original group), acts on the larger array.  There is no obvious solution to Weyl's relativity problem for M 24.  That is, there is no obvious way* to apply exactly 24 distinct transformable coordinate-sets (or symbol-strings ) to the 24 array elements in such a way that the natural group of mediating transformations of the 24 symbol-strings is M 24. ….

Footnote of Sept. 20, 2011:

* R.T. Curtis has, it seems, a non-obvious way that involves strings of seven symbols.  His abstract for a 1990 paper says that in his construction "The generators of M 24 are defined… as permutations of twenty-four 7-cycles in the action of PSL2(7) on seven letters…."

See "Geometric Interpretations of the ‘Natural’ Generators of the Mathieu groups," by R.T. Curtis,  Mathematical Proceedings of the Cambridge Philosophical Society  (1990), Vol. 107, Issue 01, pp. 19-26. (Rec. Jan. 3, 1989, revised Feb. 3, 1989.) This paper was published online on Oct. 24, 2008.

Some related articles by Curtis:

R.T. Curtis, "Natural Constructions of the Mathieu groups," Math. Proc. Cambridge Philos. Soc.  (1989), Vol. 106, pp. 423-429

R.T. Curtis. "Symmetric Presentations I: Introduction, with Particular Reference to the Mathieu groups M 12  and M 24" In Proceedings of 1990 LMS Durham Conference 'Groups, Combinatorics and Geometry'  (eds. M. W. Liebeck and J. Saxl),  London Math. Soc. Lecture Note Series 165, Cambridge University Press, 1992, pp. 380–396

R.T. Curtis, "A Survey of Symmetric Generation of Sporadic Simple Groups," in The Atlas of Finite Groups: Ten Years On , (eds. R.T. Curtis and R.A. Wilson), London Math. Soc. Lecture Note Series 249, Cambridge University Press, 1998, pp. 39–57

Monday, September 19, 2011

A Sunset Number

Filed under: General — m759 @ 3:33 pm

742

as indicated by Gravity's Rainbow— the end of page 742

by the New York Lottery on the evening of June 17, 2010—

http://www.log24.com/log/pix11B/110919-NYlottery100617.jpg

and by this journal on the afternoon of that day

Image-- Detail of New Yorker cover 'Finish Line,' double fiction issue of June 14 & 21, 2010

Detail from New Yorker  cover (fiction issue of June 2010)

Sunday, September 18, 2011

What Rough Beast

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

Lurching Toward Decision

http://www.log24.com/log/pix11B/110918-NYT-Lurching.jpg

"Suskind… nails, I think, Obama's intellectual blind spot. Indeed, Obama himself nails it, telling Suskind that he was too inclined to search for 'the perfect technical answer' to the myriad of complex issues coming at him."

Frank Rich on Ron Suskind's new book about the White House, Confidence Men

Very distantly related material—

From "Confidence Game," an Oct. 12, 2008, post in this journal, a quasi-European perspective—

Juliette Binoche in 'Blue'  Animated 2x2 kaleidoscope figures from Diamond Theory

Kaleidoscope turning…
Shifting pattern
within unalterable structure…

– Roger Zelazny, Eye of Cat   

See also …

Gravity’s Rainbow , Penguin Classics, 1995, page 742:

"… knowing his Tarot, we would expect to look among the Humility, among the gray and preterite souls, to look for him adrift in the hostile light of the sky, the darkness of the sea….

Now there’s only a long cat’s-eye of bleak sunset left over the plain tonight, bright gray against a purple ceiling of clouds, with an iris of

   742"

Anatomy of a Cube

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

R.D. Carmichael's seminal 1931 paper on tactical configurations suggests
a search for later material relating such configurations to block designs.
Such a search yields the following

"… it seems that the relationship between
BIB [balanced incomplete block ] designs
and tactical configurations, and in particular,
the Steiner system, has been overlooked."
— D. A. Sprott, U. of Toronto, 1955

http://www.log24.com/log/pix11B/110918-SprottAndCube.jpg

The figure by Cullinane included above shows a way to visualize Sprott's remarks.

For the group actions described by Cullinane, see "The Eightfold Cube" and
"A Simple Reflection Group of Order 168."

Update of 7:42 PM Sept. 18, 2011—

From a Summer 2011 course on discrete structures at a Berlin website—

A different illustration of the eightfold cube as the Steiner system S(3, 4, 8)—

http://www.log24.com/log/pix11B/110918-Felsner.jpg

Note that only the static structure is described by Felsner, not the
168 group actions discussed (as above) by Cullinane. For remarks on
such group actions in the literature, see "Cube Space, 1984-2003."

Alpha and Omega

Filed under: General,Geometry — Tags: , — m759 @ 2:22 am

http://www.log24.com/log/pix11B/110918-AlphaAndOmega.jpg

A transcription—

"Now suppose that α  is an element of order 23 in M 24 ; we number the points of Ω
as the projective line , 0, 1, 2, … , 22 so that α : i i  + 1 (modulo 23) and fixes . In
fact there is a full L 2 (23) acting on this line and preserving the octads…."

— R. T. Curtis, "A New Combinatorial Approach to M 24 ,"
Mathematical Proceedings of the Cambridge Philosophical Society  (1976), 79: 25-42

Midnight in Dostoevsky

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

"But Thou knewest not, it seems, that no sooner would man reject
miracle than he would reject God likewise, for he seeketh less
God than 'a sign' from Him." —The Grand Inquisitor

Update of 1:44 AM—

Seek and Ye Shall Find …

(Click images for larger context)

http://www.log24.com/log/pix11B/110918-DostoevskyDetail.jpg

  The Holy Office —

http://www.log24.com/log/pix11B/110918-ThinkfreeOffice3Setup.jpg

Saturday, September 17, 2011

As It Were

Filed under: General — m759 @ 5:45 pm

Historic plane crashes at West Virginia air show

"The T-28 aircraft crashed at about 2:40 p.m.
during an acrobatic demonstration at the 2011
Thunder Over the Blue Ridge Open House & Air Show…."

See also Themes

"And I heard, as it were, the noise of thunder."

Objectivity

Filed under: General — m759 @ 12:00 pm

The previous two posts, Baggage and The Uploading, suggest
a review of Wroclaw's native son Ernst Cassirer.

The Uploading

Filed under: General — Tags: — m759 @ 11:32 am

(Continued from March 9.)

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

"Uploaded by SesameStreet on Jul 18, 2008"

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

Baggage

Filed under: General — m759 @ 10:48 am

Dateline WROCLAW

http://www.log24.com/log/pix11B/110917-NYTfront-Feist-500w.jpg

See also "Feist Sings 1, 2, 3, 4."

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