Log24

Friday, January 13, 2017

Elsewhere …

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

Embarcadero

Filed under: General — Tags: — m759 @ 9:45 AM

For the title, see Wiktionary.

Thursday, January 12, 2017

The Cherished Gift

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

From "Solomon's Cube" —

Related material —

"Is this a dagger I see before me?

"No." (A line suggested by Polanski's 2010 "The Ghost Writer")

Changes

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

Despite a remark at ichingpsychics.com, the I Ching's underlying group actually has 1,290,157,424,640 permutations.

Saturday, November 12, 2016

Good Questions

Filed under: General — Tags: — m759 @ 7:13 AM

1 Corinthians 15:55

Wednesday, July 27, 2016

Deathly Hallows

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

The previous post, on the July 13 death of computer scientist Robert Fano,
suggests a review of "Deathly Hallows" posts in this journal. From that review —

Mathematics

http://www.log24.com/log/pix11A/110505-WikipediaFanoPlane.jpg

The Fano plane block design

Magic

http://www.log24.com/log/pix11A/110505-DeathlyHallows.jpg

The Deathly Hallows symbol—
Two blocks short of  a design.

For further information, click the image below —

 .

Tuesday, July 26, 2016

In Nomine Patris

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

"Robert Fano, an electrical engineer who was instrumental
in creating a world of instantly responsive computers, died
on July 13 in Naples, Fla. He was 98."

John Markoff in this evening's online New York Times

Wikipedia on Robert Fano

"Fano's father was the mathematician Gino Fano . . . .

A mnemonic I associate with the Fano plane — "Seven is Heaven . . . .

Log24 on the date of Robert Fano's death —

Wednesday, July 13, 2016

Luminosity

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

"At CERN the LHC has reached design luminosity,
and is breaking records with a fast pace of new
collisions. This may have something to do with the
report that the LHC is also about to tear open
a portal to another dimension
."

— Peter Woit, Thursday, June 30, 2016,
    at 1:01 PM ET 

Another sort of design luminosity —

IMAGE- Massimo Vignelli, his wife Lella, and cube

Claves

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

For one meaning of the title, see The Faustian Merry-Go-Round.

Look Busters

Filed under: General,Geometry — Tags: — m759 @ 8:48 PM

See a search in this journal for "Look, Buster."

Fritz Leiber's 'Spider' symbol

Block That Metaphor

Filed under: General — Tags: , — m759 @ 8:38 PM

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points (The 6 cube faces are mapped to the 6 hexagram lines.)

Happy dies natalis  to the late Frida Kahlo.

Art Wars

Filed under: General — Tags: — m759 @ 10:45 AM

Wil S. Hylton today in the online New York Times

"It seems to me now, with greater reflection,
that the value of experiencing another person’s art
is not merely the work itself, but the opportunity
it presents to connect with the interior impulse of another.
The arts occupy a vanishing space in modern life:
They offer one of the last lingering places to seek out
empathy for its own sake, and to the extent that
an artist’s work is frustrating or difficult or awful,
you could say this allows greater opportunity to try to
meet it. I am not saying there is no room for discriminating 
taste and judgment, just that there is also, I think,
this other portal through which to experience creative work
and to access a different kind of beauty, which might be
called communion."

Or damnation.

Always Nice to See You

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

“It is always
Nice to see you”
Says the man
Behind the counter

— Suzanne Vega. "Tom's Diner"

Thursday, February 13, 2014

Plan 9

Filed under: General — Tags: , — m759 @ 6:29 PM

(Continued)

The final link in today's previous post leads to
a post whose own final link leads to

Thursday, December 13, 2012

Space

Filed under: Uncategorized — m759 @ 12:00 PM                

 The sequel to Vibrations

Charles Taylor, "Epiphanies of Modernism,"
Chapter 24 of Sources of the Self
(Cambridge U. Press, 1989, p. 477) — 

“… the object sets up a kind of 
 frame or space or field 
 within which there can be epiphany.”

Or place.

See  A Prince of Darkness 
and "A Clean, Well-Lighted Place."

Fashion Week — The Conclusion

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

Frank Langella as Dracula 
(opened on Broadway in October, 1977)

Related material: Bat Signal.

Winter’s Game*

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

Part I:  Continued from January 20 — "Arising Heaven" —

Part II:  The Stars My Destination  in this journal

'The Stars My Destination,' current edition (with cover slightly changed)

Part III:  Ender's Game  —

* The title refers to a character, Rogue Winter, in Alfred Bester's
  1981 novel The Deceivers .

Wednesday, December 25, 2013

A Midnight Clear

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

Click image for a meditation.

Tuesday, December 24, 2013

Through a Mirror, Darkly

Filed under: General — Tags: — m759 @ 12:26 PM

Review of a book first published in 1989—

Reality's Mirror: Exploring the Mathematics of Symmetry —

"Here is a book that explains in laymen language
what symmetry is all about, from the lowliest snowflake
and flounder to the lofty group structures whose
astonishing applications to the Old One are winning
Nobel prizes. Bunch's book is a marvel of clear, witty
science writing, as delightful to read as it is informative
and up-to-date. The author is to be congratulated on
a job well done." — Martin Gardner

A completely different person whose name
mirrors that of the Mathematics of Symmetry  author —

IMAGE- Daily Princetonian, Dec. 23, 2013

See also this  journal on the date mentioned in the Princetonian .

"Always with a little humor." — Yen Lo

Wednesday, December 18, 2013

Bing Bang Theory

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

Microsoft in 2009 on its new search engine name—

"We like Bing because it sounds off in our heads
when we think about that moment of discovery
and decision making— when you resolve those
important tasks."

A search on Bing today —

IMAGE- Top search result on Bing for 'diamond space' on Dec. 18, 2013

A colorful tale —

IMAGE- The Diamond 16 Puzzle, with commentary

"Bing bang, I saw the whole gang
Bobby Darin, 1958

Saturday, December 14, 2013

Beautiful Mathematics

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

The title, which I dislike, is taken from a 2011 publication
of the MAA, also sold by Cambridge University Press.

Some material relevant to the title adjective:

"For those who have learned something of higher mathematics, nothing could be more natural than to use the word 'beautiful' in connection with it. Mathematical beauty, like the beauty of, say, a late Beethoven quartet, arises from a combination of strangeness and inevitability. Simply defined abstractions disclose hidden quirks and complexities. Seemingly unrelated structures turn out to have mysterious correspondences. Uncanny patterns emerge, and they remain uncanny even after being underwritten by the rigor of logic."— Jim Holt, opening of a book review in the Dec. 5, 2013, issue of The New York Review of Books

Some relevant links—

The above list was updated on Jan. 31, 2014, to include the
"Strangeness" and "Hidden quirks" links.  See also a post of
​Jan. 31, 2014.

Update of March 9, 2014 —

The link "Simply defined abstractions" is to the construction of the Steiner
system S(5, 8, 24) described by R. T. Curtis in his 1976 paper defining the
Miracle Octad Generator. It should be noted that this construction is due
to Richard J. Turyn, in a 1967 Sylvania research report. (See Emily Jennings's
talk of 1 Nov. 2012.) Compare  the Curtis construction, written in 1974,
with the Turyn construction of 1967 as described in Sphere Packings, Lattices
and Groups , by J. H. Conway and N. J. A. Sloane (first published in 1988).

Bend Sinister

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

I Ching hexagram 14, box style

Click image for background.
See also related posts.

American Beauty

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

Or: Blackboard Jungle, Continued

  Click image for
  a related story.

Sacred and Profane

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

(Continued from yesterday afternoon)

This journal on December 12th, 2009

Rothstein's 'Emblems of Mind,' 1995, cover illustrations by Pinturicchio from Vatican

Cover illustration— Arithmetic and Music,
Borgia Apartments, The Vatican

Compare and contrast with Frenkel at the Fields Institute

Thursday, December 12, 2013

Outsider Art

Filed under: General,Geometry — Tags: — m759 @ 4:10 PM

"… Galois was a mathematical outsider…."

— Tony Mann, "head of the department of mathematical sciences,
University of Greenwich, and president, British Society for the
History of Mathematics," in a May 6, 2010, review of Duel at Dawn
in Times Higher Education.

Related art: 

(Click for a larger image.)

IMAGE- Google search for 'Diamond Space' + Galois

For a less outside  version of the central image
above, see Kunstkritikk  on Oct. 15, 2013.

Thursday, December 5, 2013

Blackboard Jungle

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

Continued from Field of Dreams, Jan. 20, 2013.

IMAGE- Richard Kiley in 'Blackboard Jungle,' with grids and broken records

That post mentioned the March 2011 AMS Notices ,
an issue on mathematics education.

In that issue was an interview with Abel Prize winner
John Tate done in Oslo on May 25, 2010, the day
he was awarded the prize. From the interview—

Research Contributions

Raussen and Skau: This brings us to the next
topic: Your Ph.D. thesis from 1950, when you were
twenty-five years old. It has been extensively cited
in the literature under the sobriquet “Tate’s thesis”.
Several mathematicians have described your thesis
as unsurpassable in conciseness and lucidity and as
representing a watershed in the study of number
fields. Could you tell us what was so novel and fruitful
in your thesis?

Tate: Well, first of all, it was not a new result, except
perhaps for some local aspects. The big global
theorem had been proved around 1920 by the
great German mathematician Erich Hecke, namely
​the fact that all L -functions of number fields,
abelian -functions, generalizations of Dirichlet’s
L -functions, have an analytic continuation
throughout the plane with a functional equation
of the expected type. In the course of proving
it Hecke saw that his proof even applied to a new
kind of L -function, the so-called L -functions with
Grössencharacter. Artin suggested to me that one
might prove Hecke’s theorem using abstract
harmonic analysis on what is now called the adele
ring, treating all places of the field equally, instead
of using classical Fourier analysis at the archimedian 
places and finite Fourier analysis with congruences 
at the p -adic places as Hecke had done. I think I did
a good job —it might even have been lucid and
concise!—but in a way it was just a wonderful 
exercise to carry out this idea. And it was also in the
air. So often there is a time in mathematics for 
something to be done. My thesis is an example. 
Iwasawa would have done it had I not.

[For a different perspective on the highlighted areas of
mathematics, see recent remarks by Edward Frenkel.]

"So often there is a time in mathematics for something to be done."

— John Tate in Oslo on May 25, 2010.

See also this journal on May 25, 2010, as well as
Galois Groups and Harmonic Analysis on Nov. 24, 2013.

Fields

Filed under: General,Geometry — Tags: , , — m759 @ 1:20 AM

Edward Frenkel recently claimed for Robert Langlands
the discovery of a link between two "totally different"
fields of mathematics— number theory and harmonic analysis.
He implied that before Langlands, no relationship between
these fields was known.

See his recent book, and his lecture at the Fields Institute
in Toronto on October 24, 2013.

Meanwhile, in this journal on that date, two math-related
quotations for Stephen King, author of Doctor Sleep

"Danvers is a town in Essex County, Massachusetts, 
United States, located on the Danvers River near the
northeastern coast of Massachusetts. Originally known
as Salem Village, the town is most widely known for its
association with the 1692 Salem witch trials. It is also
known for the Danvers State Hospital, one of the state's
19th-century psychiatric hospitals, which was located here." 

"The summer's gone and all the roses fallin' "

For those who prefer their mathematics presented as fact, not fiction—

(Click for a larger image.)

The arrows in the figure at the right are an attempt to say visually that 
the diamond theorem is related to various fields of mathematics.
There is no claim that prior to the theorem, these fields were not  related.

See also Scott Carnahan on arrow diagrams, and Mathematical Imagery.

Tuesday, December 3, 2013

Diamond Space

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

A new website illustrates its URL.
See DiamondSpace.net.

IMAGE- Site with keywords 'Galois space, Galois geometry, finite geometry' at DiamondSpace.net

Thursday, November 21, 2013

ART WARS:

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

The Mitgang Menu

Related material: This morning's 6 AM post and Wiener News.

Update of 3:29 PM:

From Herbert Mitgang's New York Times  
obituary of Cleanth Brooks

"The New Critics advocated close reading of literary texts
and detailed analysis, concentrating on semantics, meter,
imagery, metaphor and symbol as well as references to
history, biography and cultural background."

Twelfth Step

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

Continued from 24 hours ago.

From this morning's 6 AM (ET) post

"… you never made a Twelfth Step
call on an active alcoholic by yourself,
unless the alkie in question was safely
incarcerated in a hospital, detox, or the
local bughouse."

— Stephen King, Doctor Sleep

Related material from a math addict, a likely victim
of a professor's misleading rhetoric —

"Frenkel is the real deal, a professor at Berkeley…."

— "Math Porn Update" by David Justice,
       Nov. 20, 2013

The rhetoric link above leads to remarks by Frenkel.
For a similar professor's earlier misleading remarks,
see Barry Mazur in this journal.

But It Rings…

Filed under: General — Tags: — m759 @ 6:29 AM

"The shaving razor's cold and it stings."

The above image is from Ulysses “Seen,”   adapted
by Robert Berry from the novel by James Joyce.

Quad Rants

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

Continued from 24 hours ago.

"AA had no rules but many traditions (that were, in fact, rules).
One of the most ironclad was that you never made a Twelfth Step
call on an active alcoholic by yourself, unless the alkie in question
was safely incarcerated in a hospital, detox, or the local bughouse.
If you did, you were apt to end up matching him drink for drink and
line for line."

— King, Stephen (2013-09-24). Doctor Sleep: A Novel
     (p. 272). Scribner. Kindle Edition.

 

" Aus 'It' wurde 'Es', und King sprach es so aus,
dass man sich alleine vom Klang des Titels
gruselte: 'Essssss!' " 

— Last night's online
Hamburger Abendblatt 

"You want Frye's with that?"

Tuesday, November 12, 2013

The X-Men Tree

Filed under: General — Tags: — m759 @ 11:01 PM

Related material:

The comments on a Log24 post of Nov. 6, 2013,
remarks by Michael Worton on the tree in 
"Waiting for Godot," images from the film
"The Tree of Life," and, in memory of Robert
de Marrais, an image search from this evening:
"Spelling the Tree" + "de Marrais," 2 MB.

Funeral Canticle

Filed under: General — Tags: — m759 @ 8:02 PM

For and by composer Sir John Tavener, 69,
who reportedly died today.

Update of 8:28 PM ET Nov. 12—
The obituary link above is to The Telegraph.
Here is a link to the version in The New York Times

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.

Wednesday, October 9, 2013

Sign in

Filed under: General — Tags: — m759 @ 7:20 PM

From the upper right of the Google search screen —

For related religious remarks, see "The Ninth."

According to Hoyle

Filed under: General — Tags: — m759 @ 1:13 PM

IMAGE- Quote from Hoyle's 'October the First is Too Late'

See also the previous post.

"Some like it in the pot, nine days old."

To Apollo*

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

From Log24

From Josefine Lyche's website —

* For the title, see Apollo + Outram in this journal.

 

Friday, October 4, 2013

Christian’s Question

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

"Now, who's the master?"

— Christian Bale in "American Hustle," a film
     scheduled for limited release on St. Lucy's Day
     and wide release on Christmas Day, 2013

See also this journal on November 26, 2012.

Walter’s Wake

Filed under: General — Tags: , — m759 @ 8:12 PM

(Continued from October First)

"It gets to the end
We get to run it again"

— James Taylor,
    "One More Go Round" from
    New Moon Shine  album

For the Feast of St. Francis

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

"According to Vladimir Nabokov, Salvador Dalí
 was 'really Norman Rockwell’s  twin brother
 kidnapped by gypsies in babyhood.'
 But actually there were triplets: the third one is
 Stephen King."

 — Margaret Atwood, "Shine On,"  
      online Sept. 19, 2013

"The metaphor for metamorphosis
  no keys unlock."

 — Steven H. Cullinane, Nov. 7, 1986

Color News

Filed under: General — Tags: , — m759 @ 12:48 PM

(Continued from yesterday's STEM and Truman Show.)

Old Soldier

Filed under: General — Tags: — m759 @ 12:20 PM

Roll Credits

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

See also Howl in this journal.

Related material from a June 22, 2013, post

Kitty in Uncanny X-Men #168 (April 1983)

Inceptions

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

From Inception  (2010) :

From Diamonds Studio Generative Identity (2013) :

Sunday, September 22, 2013

Incarnation, Part 2

Filed under: General,Geometry — Tags: , , — m759 @ 10:18 AM

From yesterday —

"…  a list of group theoretic invariants
and their geometric incarnation…"

David Lehavi on the Kummer 166 configuration in 2007

Related material —

IMAGE- 'This is not mathematics; this is theology.' - Paul Gordan

"The hint half guessed, the gift half understood, is Incarnation."

T. S. Eliot in Four Quartets

"This is not theology; this is mathematics."

— Steven H. Cullinane on  four quartets

To wit:


Click to enlarge.

Saturday, September 21, 2013

Geometric Incarnation

The  Kummer 166  configuration  is the configuration of sixteen
6-sets within a 4×4 square array of points in which each 6-set
is determined by one of the 16 points of the array and
consists of the 3 other points in that point's row and the
3 other points in that point's column.

See Configurations and Squares.

The Wikipedia article Kummer surface  uses a rather poetic
phrase* to describe the relationship of the 166 to a number
of other mathematical concepts — "geometric incarnation."

Geometric Incarnation in the Galois Tesseract

Related material from finitegeometry.org —

IMAGE- 4x4 Geometry: Rosenhain and Göpel Tetrads and the Kummer Configuration

* Apparently from David Lehavi on March 18, 2007, at Citizendium .

Mathematics and Narrative (continued)

Filed under: General,Geometry — Tags: , — m759 @ 1:00 AM

Mathematics:

A review of posts from earlier this month —

Wednesday, September 4, 2013

Moonshine

Filed under: Uncategorized — m759 @ 4:00 PM

Unexpected connections between areas of mathematics
previously thought to be unrelated are sometimes referred
to as "moonshine."  An example—  the apparent connections
between parts of complex analysis and groups related to the
large Mathieu group M24. Some recent work on such apparent
connections, by Anne Taormina and Katrin Wendland, among
others (for instance, Miranda C.N. Cheng and John F.R. Duncan),
involves structures related to Kummer surfaces .
In a classic book, Kummer's Quartic Surface  (1905),
R.W.H.T. Hudson pictured a set of 140 structures, the 80
Rosenhain tetrads and the 60 Göpel tetrads, as 4-element
subsets of a 16-element 4×4 array.  It turns out that these
140 structures are the planes of the finite affine geometry
AG(4,2) of four dimensions over the two-element Galois field.
(See Diamond Theory in 1937.)

Thursday, September 5, 2013

Moonshine II

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

(Continued from yesterday)

The foreword by Wolf Barth in the 1990 Cambridge U. Press
reissue of Hudson's 1905 classic Kummer's Quartic Surface
covers some of the material in yesterday's post Moonshine.

The distinction that Barth described in 1990 was also described, and illustrated,
in my 1986 note "Picturing the smallest projective 3-space."  The affine 4-space
over the the finite Galois field GF(2) that Barth describes was earlier described—
within a 4×4 array like that pictured by Hudson in 1905— in a 1979 American
Mathematical Society abstract, "Symmetry invariance in a diamond ring."

"The distinction between Rosenhain and Goepel tetrads
is nothing but the distinction between isotropic and
non-isotropic planes in this affine space over the finite field."

The 1990 paragraph of Barth quoted above may be viewed as a summary
of these facts, and also of my March 17, 2013, note "Rosenhain and Göpel
Tetrads in PG(3,2)
."

Narrative:

Aooo.

Happy birthday to Stephen King.

Monday, September 9, 2013

ART WARS Midrash

Filed under: General — Tags: , — m759 @ 5:48 PM

Poster shown here last night

IMAGE- Poster for film 'MAX'- 'Art + Politics = Power'

Politics this afternoon —

IMAGE- News: Norway's center-right heads for big win.

Viking Book

Filed under: General — Tags: — m759 @ 4:00 PM

For the late Billy Wilder, director of Ace in the Hole  (1951)

IMAGE- Book by Halvor Bodin on the art of Josefine Lyche and others. See halvorbodin.com.

Click image for a larger version.

See, too, this morning's quarter-to-three post, and The Vikings  (1958)—

The art by Josefine Lyche in the Bodin book shown 
above is, as the artist notes, based on my own work.

Ace in the Hole

Filed under: General — Tags: — m759 @ 2:45 AM

Some random thoughts suggested by the Norwegian ice hole
in the opening scene of the 2012 film Kon-Tiki .

From a Log24 post of August 2, 2013

IMAGE-Kristen Wiig in 'The Secret Life of Walter Mitty'

See, too, the secret life of Marsden Hartley :

IMAGE- Two pictures by Marsden Hartley- 'The Ice Hole' and 'Portrait of a German Officer'

Winning*

Filed under: General — Tags: — m759 @ 1:09 AM

For the star of Platoon 

* Continued from July 28, 2011.

Sunday, September 8, 2013

The Importance of Being Ernst

Filed under: General — Tags: , — m759 @ 11:14 PM

For John Cusack and Menno Meyjes —

"I still haven't found what I'm looking for." — Bono

"In fact Surrealism found what it had been looking for
from the first in the 1920 collages [by Max Ernst],
which introduced an entirely original scheme of visual structure…."

Rosalind Krauss quoting André Breton
    in "The Master's Bedroom"

See also tonight's 10 PM post.

"Artistic Genesis and Perspective of Surrealism" (1941),
   in Surrealism and Painting  (New York, Harper & Row, 1972, p. 
64).

Saturday, August 24, 2013

Being’s Road

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

For the late Julie Harris —

By slow and carefully modulated steps Bradford's narrative
has brought his community of separatists to the place he
calls Cape Harbor… where, face-to-face with the bleak
and wintry reduction that is his image for American space,
he finds himself stopped, able to do nothing but come to
an astonished pause. The final step, that of imaginative
crossing into the land that lies before them, remains
beyond the power of narrative to take. Narrative falters, and
finding his journey advanced to an "odd Fork in Being's Road"
and himself nothing so much as an "empty spirit / In vacant
space" (to adopt apt phrases from Dickinson and Stevens…),
Bradford requires the sublime if he is to continue moving
forward: separation becomes exaltation as it becomes
manifest that only an influx 
of "the Spirit of God and His
grace" can have permitted the community to survive its
passage to the limit depicted.

— David Laurence, "William Bradford's American Sublime,"
PMLA , Vol. 102, No. 1, 1987, pp. 55-65

Cast (continued)

Filed under: General — Tags: , — m759 @ 3:31 AM

The death yesterday of British cinematographer
Gilbert Taylor suggests an image from last evening's
Log24 search Point Omega —

.

The die in the above image (shown here Dec. 28, 2012
displays the numbers 3-6-5 in counterclockwise order.
A similar die in an earlier post served as a metaphor for
a time-jump to 365 days in the past.

For some religious remarks by Umberto Eco that may
serve as a small memorial to Taylor, see this journal 
a year before  the day he died— August 23, 2012.

"Everybody comes to Rick's."

Friday, August 23, 2013

Vacant Space

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

A passage from Wallace Stevens

The spirit and space,
The empty spirit 
In vacant space.

A frame from the film American Psycho  (2000), starring Christian Bale—

IMAGE- 'espace' sign from the film 'American Psycho'

The rest of the film is not recommended.

Related material—

"24 Hour Psycho" at the Museum of Modern Art in the novel Point Omega .

Illustration from a New York Times  review

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

Ten Years of Nothing

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

For insatiable actor Patrick Bateman (protagonist of
American Psycho) and anti-theologian Kirk Varnedoe
Pictures of Nothing, this journal ten years ago today )

Philip Rieff, The Crisis of the Officer Class,
University of Virginia Press, 2007

From page 73:

The third culture's life-style, its way, is no way: it is abandonment, 
an ethos of empty seriousness best expressed, I think, by the 
greatest of American poets in the tradition that began with 
Emerson. Wallace Stevens was the greatest American maker of 
that "fictive music" of the "unreal" by which poets "give back to us 
what you [God] gave," Creation itself, now understood, in the third
culture, as the "imagination that we spurned and crave." Stevens
understood the fictive music of faith, that intensity which

proclaims
The near, the clear …
. . . . . . . . . . . . . . . . .
… an image that is sure,
. . . . . . . . . . . . . . . . . . .
Yet not too like, yet not so like to be
Too near, too clear, saving a little to endow
Our feigning with the strange unlike…. [12]

This is masterly anti-theology. This is what no "mickey mockers" of 
the spirit can ever become: the "American sublime," the mar-

[12] Wallace Stevens, "To the One of Fictive Music," in Collected 
Poems
 (New York: Alfred A. Knopf, 1954), 87-88; all citations of 
Stevens are to this edition.

From page 74:

velous panic and emptiness of belief by which the "sublime comes 
down/To the spirit itself" and terrifies the American self:

The spirit and space,
The empty spirit 
In vacant space.
What wine does one drink?
What bread does one eat? [13]

This poet is no great character, nor temple priest. He is a virtuoso 
chef, preparing the food for the American feast of unbeliefs. This 
supreme fictionist invents bread and wine, anything that will act as 
that "act of the mind." [14] Stevens had a shrewd Emersonian idea 
of myth, or Freudian, the "sexual myth" or any other "images of 
metaphors." [15] He knew that it was in "this invented world" that "the 
death of one god is the death of all." This is the most supreme of all 
fictions, by which "He imposes orders as he thinks of them." [16]

[13] Stevens, "The American Sublime," 130-31
[14] Stevens, "Of Modern Poetry," 239-40; modern poetry, which is 
"the finding of a satisfaction," or a script for a theater– whatever 
"will suffice" for the "insatiable actor" of the third culture, even the 
script of "cuisine bourgeoise," where we may "feast on human 
heads" (240, 227).
[15] Stevens, "Men Made out of Words," 355; and "Thinking of a 
Relation between the Images of Metaphors," 356-57.
[16] Stevens, "Notes toward a Supreme Fiction," 380-81, 403.

Wednesday, July 24, 2013

Dark Humor

Filed under: General — Tags: — m759 @ 5:09 AM

Arts and Letters Daily  today links to a July 17
Washington Post  review of two books on the
occult and the enlightenment. The review, by
Michael Dirda, ends on a cheerful note:

"Happy synchronicity."

In related news, a Walpurgisnacht obituary also
ends cheerfully:

"He was still trying to get out a joke
with his final breath."

That obituary describes a life that reportedly ended
on April 21, 2013. Synchronicity involving that date—

The posts of April 21, 2013 (and related material in
this morning's previous post).

The Broken Tablet

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

This post was suggested by a search for the
Derridean phrase "necessary possibility"* that
led to web pages on a conference at Harvard
on Friday and Saturday, March 26**-27, 2010,
on Derrida and Religion .

The conference featured a talk titled
"The Poetics of the Broken Tablet."

I prefer the poetics of projective geometry.

An illustration— The restoration of the full
15-point "large" Desargues configuration in
place of the diminished 10-point Desargues
configuration that is usually discussed.

IMAGE- The proof of the converse of Desargues' theorem involves a third triangle.

Click on the image for further details.

* See a discussion of this phrase in
  the context of Brazilian religion.

** See also my own philosophical reflections
   on Friday, March 26, 2010:
   "You Can't Make This Stuff Up." 

Saturday, July 13, 2013

Wire

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

The Inner Ring

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

The title refers to Brad Leithauser's remarks
in the previous post.

This way to the egress.

Circles

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

A sort of poem
by Gauss and Weyl —

Click the circle for the context in Weyl's Symmetry .

For related remarks, see the previous post.

A literary excursus—

Brad Leithauser in a New Yorker  post of July 11, 2013:

Reading Poems Backward

If a poet determines that a poem should begin at point A and conclude at point D, say, the mystery of how to get there—how to pass felicitously through points B and C—strikes me as an artistic task both genuine and enlivening. There are fertile mysteries of transition, no less than of termination.

And I’d like to suppose that Frost himself would recognize that any ingress into a poem is better than being locked out entirely. His little two-liner, “The Secret,” suggests as much: “We dance round in a ring and suppose / But the Secret sits in the middle and knows.” Most truly good poems might be said to contain a secret: the little sacramental miracle by which you connect, intimately, with the words of a total stranger. And whether you come at the poem frontward, or backward, or inside out—whether you approach it deliberately, word by word and line by line, or you parachute into it borne on a sudden breeze from the island of Serendip—surely isn’t the important thing. What matters is whether you achieve entrance into its inner ring, and there repose companionably beside the Secret.

One should try, of course, to avoid repose in an inner circle of Hell .

Monday, July 1, 2013

Declamation

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

Continued from Sunday's post Book Award and last
midnight's post Holding the Frame

The nineteenth-century German writer Rudolf Haym on
German romantic Hellenism—

"In the enjoyment of this fair picture-world, our nation must 
needs delude itself a moment with the dream of Greek felicity 
and Greek repose to awaken directly poorer and more restless 
than before. To Poetry such a delusion was indeed natural, and 
who would dispute it with her after she had offered to our 
enjoyment what was sweetest and most perfect! But we see 
now all at once Metaphysic seized with the same illusion. 
Turning aside from the strait path of sober inquiry and from the 
labour of deliverance through the most conscientious criticism, 
Hegel begins to expand over our spiritual world his ideal that 
was found in Hellas, that was strengthened by exhaustive 
penetration into the ultimate grounds of all religion. A dreamed-of 
and yearned-for future is treated as present. A system tricked 
out with the entire dignity of the science of truth raises itself 
beside our poetry, and with diamond net spins us into an idea 
with which the want, the incompleteness, and the unbeauty of 
our political and historical actuality is at every point in contradiction."

Rudolf Haym, Hegel und seine Zeit  (1857), 91-92, translated 
and quoted in  The Secret of Hegel , by James Hutchison Stirling
(1898 edition, p. 626)

Holding the Frame

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

High praise for a 1941 film

Major Barbara  (Gabriel Pascal, 1941) — "There are some performances
that bypass your critical faculties altogether, connecting not with your brain
but with your soul. They are desperately few, those characterisations of
such heightened sensitivity, such emotional resonance that the effect is
both exalting and suffocating. You might chance upon one every three or 
four years, if you're lucky. I don't know why, or how, but every time Wendy
Hiller utters a line or holds the frame in Major Barbara , I am on the verge
of tears." — Rick Burin

Friday, June 21, 2013

Lexicon

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

From the final pages of the new novel
Lexicon , by Max Barry:

“… a fundamental language
of the human mind—
the tongue in which the human animal
speaks to itself at the basest level.
The machine language, in essence….”

“… the questions raised by
this underlying lexicon.
What are its words?
How many are there? ….
Can we learn to speak them?
What does it sound like
when who we are is expressed
in its most fundamental form?
Something to think about.”

       R. Lowell

Related material:

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

“… the clocks were striking thirteen.” — 1984

Thirty Years Ago

Filed under: General,Geometry — Tags: — m759 @ 4:00 AM

Wednesday, June 19, 2013

Juneteenth

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

See Juneteenth in this journal.

For related meditations, see last October 27th.

R.I.P.

Filed under: General — Tags: — m759 @ 10:27 PM

Ein Eck

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

"Da hats ein Eck" —

"you've/she's (etc.) got problems there"

St. Galluskirche:

St. Gallus's Day, 2012:

Click image for a St. Gallus's Day post.

A related problem: 

Discuss the structure of the 4x4x4 "magic" cube
sent by Pierre de Fermat to Father Marin Mersenne
on April 1, 1640, in light of the above post.

Hats

Filed under: General — Tags: — m759 @ 9:10 AM

http://www.guardian.co.uk/world/2013/jun/19/obama-berlin-speech-live

Midnight in the Garden

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

(Continued)

See Robert Hughes in this journal.

Tuesday, June 18, 2013

Mise-en-Scène

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

IMAGE- 'Lexicon,' a novel by Max Barry published June 18, 2013

This journal on May 14, 2013:

IMAGE- Valéry on ornament in 'Method of Leonardo,' with Valéry's serpent-and-key emblem

"And let us finally, then, observe the
parallel progress of the formations of thought
across the species of psychical onomatopoeia
of the primitives, and elementary symmetries
and contrasts, to the ideas of substances,
to metaphors, the faltering beginnings of logic,
formalisms, entities, metaphysical existences."

— Paul Valéry, Introduction to the Method of
    Leonardo da Vinci

But first, a word from our sponsor

Multispeech

Filed under: General,Geometry — Tags: — m759 @ 4:48 PM

(Continued)

For those who prefer Trudeau's
"Story Theory" of truth to his "Diamond Theory"

IMAGE- Janet Maslin's review of Max Barry's novel 'Lexicon'

Related material: Click images below for the original posts.

See as well the novel  "Lexicon" at Amazon.com 
and the word  "lexicon" in this journal.

Friday, June 14, 2013

Amy’s Shadow

Filed under: General — Tags: , — m759 @ 2:18 PM

Why knows what evil lurks…? — The Shadow

Backstory: "Amy Adams" + Shadow in this journal.

Related material —

Amy Adams as Lois Lane:

In the new Amy Adams version, Superman's Smallville mom
is played by Diane  Lane.

Lane also played George Reeves's sugar mommy
in the 2006 film Hollywoodland .

Ben Affleck and Diane Lane at the 2006 Venice Film Festival
premiere of  Hollywoodland :

See, too, today's previous post, and Amy Adams as Lacey Yeager
in the yet-to-be-made film version of An Object of Beauty .

Object of Beauty

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

This journal on July 5, 2007 —

The Eightfold Cube and its Inner Structure

“It is not clear why MySpace China will be successful."

— The Chinese magazine Caijing  in 2007, quoted in
Asia Sentinel  on July 12, 2011

This  journal on that same date,  July 12, 2011 —

http://www.log24.com/log/pix11B/110712-ObjectOfBeauty.jpg

See also the eightfold cube and kindergarten blocks
at finitegeometry.org/sc.

Friedrich Froebel, Froebel's Chief Writings on Education ,
Part II, "The Kindergarten," Ch. III, "The Third Play":

"The little ones, who always long for novelty and change,
love this simple plaything in its unvarying form and in its
constant number, even as they love their fairy tales with
the ever-recurring dwarfs…."

This journal, Group Actions, Nov. 14, 2012:

"Those who insist on vulgarizing their mathematics
may regard linear and affine group actions on the eight
cubes as the dance of  Snow White (representing (0,0,0))
and the Seven Dwarfs—

  ."

Edwin M. Knowles Fine China Company, 1991

Sunday, May 12, 2013

Recognition

Filed under: General,Geometry — Tags: — m759 @ 7:12 PM

Western Washington University in Bellingham maintains a
website to benefit secondary-school math: MathNEXUS.

The MathNEXUS "website of the week" on April 14, 2013,
was the Diamond 16 Puzzle and its related webpages.

Click on the above image for the April 14 webpage.

Language Game

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

The above images are from a prequel (March 29, 2013)
to 'Nauts  (March 26, 2006.)

See also Spider Mother,  Gamer Post,  and Spider Tale.

Friday, April 26, 2013

Master Class

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

Philip Seymour Hoffman in "Doubt"—

and in "A Late Quartet"—

High White

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

(Continued)

For Times Square Church
Click image for a video.

Tuesday, April 23, 2013

Say When

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

IMAGE- The author of a book on 'Solomon's Seal' in mathematics once introduced Mark Twain to George Bernard Shaw.

Beneath the word "When" above, there appears
the date of a journal post— "July 27, 2012."

A check of synchronicity for this  journal on that date
yields two posts related to this morning's remarks.

The Six-Set

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

The configurations recently discussed in
Classical Geometry in Light of Galois Geometry
are not unrelated to the 27 "Solomon's Seal Lines
extensively studied in the 19th century.

See, in particular—

IMAGE- Archibald Henderson on six-set geometry (1911)

The following figures supply the connection of Henderson's six-set
to the Galois geometry previously discussed in "Classical Geometry…"—

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

Sunday, April 21, 2013

The Grandmother Ship

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

Tina Jordan at EW.com yesterday:

"E.L. Konigsburg— the author of one of my favorite
childhood books, the brilliantly quirky mystery
From The Mixed-Up Files of Mrs. Basil E. Frankweiler
died April 19 at the age of 83."

From other mixed-up files:

Detail:

Abstraction

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

(Continued from December 31st, 2012)

"Principles before personalities." — AA saying

Art Principles

Part I:

Part II:

Baker's 1922 Principles of Geometry

IMAGE- The Large Desargues Configuration

Art Personalities

Stoppard Update

Filed under: General — Tags: — m759 @ 12:30 PM

Meanwhile

   Daily Princetonian  @princetonian

Related material:

A sermon by the man named today the new President of Princeton.
The sermon is from October 7, 2012. See also Log24 on that date.

Sermon

Filed under: General — Tags: — m759 @ 11:01 AM

"There is  such a thing as a figure in four dimensions."

Adapted from a novel

Wednesday, April 10, 2013

Caution: Slow Art

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

"Of course, DeLillo being DeLillo,
it’s the deeper implications of the piece —
what it reveals about the nature of
film, perception and time — that detain him."

— Geoff Dyer, review of Point Omega

Related material:

A phrase of critic Robert Hughes,
"slow art," in this journal.

A search for that phrase yields the following
figure from a post on DeLillo of Oct. 12, 2011:

The 3x3 square

The above 3×3 grid is embedded in a 
somewhat more sophisticated example
of conceptual art from April 1, 2013:

IMAGE- A Galois-geometry key to Desargues' theorem

Update of April 12, 2013

The above key uses labels from the frontispiece
to Baker's 1922 Principles of Geometry, Vol. I ,
that shows a three-triangle version of Desargues's theorem.

A different figure, from a site at National Tsing Hua University,
shows the three triangles of Baker's figure more clearly:

IMAGE- Desargues' theorem with three triangles (the large Desargues configuration) and Galois-geometry version

Art Wars (continued)

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

This Way to the Egress:

Click images for some background.

A Text (continued)

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

This journal on July 2, 2007:

(Click for more of the post)

IMAGE- Wallace Stevens, 'A text that is an answer, although obscure'

A text:

IMAGE- Epigraph to 'Things Fall Apart,' by Chinua Achebe

Related material from July 3, 2007:

(Click for a clearer image of the quiz below.)

For answers to the quiz, see Jonathan Langdale.

For a deeper look at Achebe, see the following quote
in the context of last night's post on Hitchcock 

— as well as Time + Eternity + Cloth in this journal.

Tuesday, April 2, 2013

Hermite

Filed under: General,Geometry — Tags: , — m759 @ 7:14 PM

A sequel to the quotation here March 8 (Pinter Play)
of Joan Aiken's novel The Shadow Guests

Supposing that one's shadow guests are
Rosenhain and Göpel (see March 18)

Hans Freudenthal at Encyclopedia.com on Charles Hermite:

"In 1855 Hermite took advantage of Göpel’s and Rosenhain’s work
when he created his transformation theory (see below)."

"One of his invariant theory subjects was the fifth-degree equation,
to which he later applied elliptic functions.

Armed with the theory of invariants, Hermite returned to
Abelian functions. Meanwhile, the badly needed theta functions
of two arguments
had been found, and Hermite could apply what
he had learned about quadratic forms to understanding the
transformation of the system of the four periods. Later, Hermite’s
1855 results became basic for the transformation theory of Abelian
functions as well as for Camille Jordan’s theory of 'Abelian' groups.
They also led to Herrnite’s own theory of the fifth-degree equation
and of the modular equations of elliptic functions. It was Hermite’s
merit to use ω rather than Jacobi’s q = eπω as an argument and to
prepare the present form of the theory of modular functions.
He again dealt with the number theory applications of his theory,
particularly with class number relations or quadratic forms.
His solution of the fifth-degree equation by elliptic functions
(analogous to that of third-degree equations by trigonometric functions)
was the basic problem of this period."

See also Hermite in The Catholic Encyclopedia.

Intercultural Whatever

Filed under: General — Tags: — m759 @ 6:29 PM

University Diaries on March 22:

"An Intercultural Whatever professor at Florida Atlantic University…" (FAU).

An obituary in this afternoon's New York Times :

Related Log24 posts:

Pinter Play (March 8, about FAU) and a post
from the reported day of Gumperz's death.

Rota in a Nutshell

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

"The proof of Desargues' theorem of projective geometry
comes as close as a proof can to the Zen ideal.
It can be summarized in two words: 'I see!' "

— Gian-Carlo Rota in Indiscrete Thoughts (1997)

Also in that book, originally from a review in Advances in Mathematics,
Vol. 84, Number 1, Nov. 1990, p. 136:

IMAGE- Rota's review of 'Sphere Packings, Lattices and Groups'-- in a word, 'best'

Related material:

Pascal and the Galois nocciolo ,
Conway and the Galois tesseract,
Gardner and Galois.

See also Rota and Psychoshop.

Baker on Configurations

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

The geometry posts of Sunday and Monday have been
placed in finitegeometry.org as

Classical Geometry in Light of Galois Geometry.

Some background:

See Baker, Principles of Geometry , Vol. II, Note I
(pp. 212-218)—

On Certain Elementary Configurations, and
on the Complete Figure for Pappus's Theorem

and Vol. II, Note II (pp. 219-236)—

On the Hexagrammum Mysticum  of Pascal.

Monday's elucidation of Baker's Desargues-theorem figure
treats the figure as a 15420configuration (15 points, 
4 lines on each, and 20 lines, 3 points on each).

Such a treatment is by no means new. See Baker's notes
referred to above, and 

"The Complete Pascal Figure Graphically Presented,"
a webpage by J. Chris Fisher and Norma Fuller.

What is new in the Monday Desargues post is the graphic
presentation of Baker's frontispiece figure using Galois geometry :
specifically, the diamond theorem square model of PG(3,2).

See also Cremona's kernel, or nocciolo :

Baker on Cremona's approach to Pascal—

"forming, in Cremona's phrase, the nocciolo  of the whole."

IMAGE- Definition of 'nocciolo' as 'kernel'

A related nocciolo :

IMAGE- 'Nocciolo': A 'kernel' for Pascal's Hexagrammum Mysticum: The 15 2-subsets of a 6-set as points in a Galois geometry.

Click on the nocciolo  for some
geometric background.

Friday, March 29, 2013

Where Credit Is Due

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

Ape to Affleck:

Score by Boston Pops.

Backstory credit— Boston Moms:

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

The Dreaming Jewels (continued)

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

In Memoriam

"In the late ’60s, Williams became a friend and confidant
of science fiction writer Philip K. Dick and wrote about
the iconoclastic author in Rolling Stone  in 1974.
Williams eventually completed a biography on Dick
and became his literary executor after the writer’s death
in 1982. He also edited The Complete Stories of
Theodore Sturgeon, Vol. I-XII 
."

— Yesterday in the Hollywood Reporter —
Pioneering Rock Journalist Paul S. Williams Dies at 64
4:06 PM PDT 3/28/2013 by Mitch Myers

See also Crawdaddy Story and The Dreaming Jewels
in this journal.

Related reading: Yesterday's noon post and Puzzles.

Update of 8:20 AM Good Friday, 2013:

IMAGE- Daily Princetonian, Good Friday, 2013: James Diamond, rabbi and retired director of Princeton's University's Center for Jewish Life. Diamond was killed in a Princeton auto accident Thursday morning at about 9:42 AM ET.

Monday, March 25, 2013

Einsatz für Pessach

Filed under: General — Tags: — m759 @ 6:00 PM

Today's New York Times :

"… potential recruits with the right skills
have too often been heading for business,
and those who do choose government work
often go to the National Security Agency…."

Review: Einsatz in this journal—

IMAGE- German title of 'The Recruit' is 'Der Einsatz'; the MacGuffin is 'Ice 9.'

The German title of "The Recruit" (released Jan. 31, 2003)
is "Der Einsatz." Its MacGuffin is "'Ice 9."

Brightness at Noon

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

The two symbols on the monolith from yesterday

Images of time and eternity in a 1x4x9 black monolith

— may, if one likes, be interpreted as standing for
Damnation Morning and for the Windmill of Time
(alternately, as motifs for a ukara cloth).

The above explanation may help those confused by
knight's-move discourse like that described by
Jemima in The Eiger Sanction .

Art Wars:

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

Monolith for Maggie, continued from yesterday

"The young woman counted—
'Otu, abua, ato, ano, ise, isii, asaa'—
using what remained to her of
the secret language…."

— Opening sentence of the prologue to The Choir Boats,
a 2009 novel by Daniel A. Rabuzzi

The piano link in today's previous post suggests a review
of a post from Feb. 11, 2008. That post suggests in turn
a passage from the Trevanian classic The Eiger Sanction
that says, in part…

"Often it was unnecessary to finish a sentence…."

The Dante Prize

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

(Damnation Morning, continued)

For the late, great Bebo Valdés, who
reportedly died on Friday in Stockholm:

Trailers from Hell: Joe Dante on 'The Prize'

"Mr. Valdés never returned to Cuba. He played piano
in Stockholm hotel lounges for more than three decades."

— Ben Ratliff in this morning's New York Times

"Heaven for climate, Hell for company."

Tuesday, March 12, 2013

Michael Porter: The Great and Powerful

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

Thanks to University Diaries for her link today to an
excellent Forbes  article on management guru Michael Porter.

Related searches (click images to enlarge)—

For some background, see Diamond model in Wikipedia.

The Stewart quoted in Forbes  is Matthew Stewart, author of The Management Myth .

Smoke and Mirrors

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

Sistine Chapel Smoke

Tromso Kunsthall Mirrors

Background for the smoke  image:
A remark by Michelangelo in a 2007 post,  High Concept.

Background for the mirrors  image:
Note the publication date— Mar. 10, 2013.

See that date in this journal and related material.

Conclave

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

For the Garden of Good and Evil

(Click image for some backstory.)

Tim Robbins in 'Mystic River'

On Cambridge, Massachusetts:

"By all means accept the invitation to hell,
should it come. It will not take you far—
from Cambridge to hell is only a step;
or at most a hop, skip, and jump.
But now you are evading— you are
dodging the issue… after all,
Cambridge is hell enough."

— Great Circle , a 1933 novel by Conrad Aiken
(father of Joan Aiken, who wrote The Shadow Guests )

Thursday, February 14, 2013

Chapman’s Homer

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

(Continued from August 23, 2012)

“Good is a noun. That was it.
That was what Phaedrus had been looking for.
That was the homer over the fence
that ended the ballgame.”

Robert M. Pirsig

But perhaps not a proper  noun.
See the link to Good's Singularity
at the end of today's previous post.

Annals of Quantum Hype

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

Yesterday's link to Aaronson and Turing suggests a review
of events on August 16, 2012 in the light of Log24 on that date.

Exhibit A: New Institute for Quantum Studies at Chapman University—

Exhibit B: The Aug. 16, 2012, death of Chapman University's Indiana Jones—

Whether this Indiana Jones successfully transgressed
the boundaries of space and time, I do not know.

Exhibit C: Related quantum hype— 

Chapman Professor Lands Discover  Cover Story,
Chapman University Happenings, March 18, 2010

See also Good's Singularity.

Tuesday, January 29, 2013

Clash of the Caped Crusaders

Filed under: General — Tags: — m759 @ 2:29 PM

The New Yorker , quoted here yesterday, on a meeting in 1638 of Galileo and Milton—

"… it’s like those comic-book specials in which Superman meets Batman…."

Related news yesterday from The Hollywood Reporter

IMAGE- Producer Lloyd Phillips dies at 63

      Phillips's upcoming Superman film stars Amy Adams.

      Other entertainment:

      Log24 posts from the day of Phillips's death—

Binder

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

A sequel to last midnight's post

IMAGE- Inauguration 2013: Schumer, Binder, Beyoncé

See also Midnight Politics and On the Cusp.

Midnight in the Garden

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

(Continued)

     For a related essay, click on the image below.

    

Thursday, January 24, 2013

Moondance

Filed under: General,Geometry — Tags: — m759 @ 9:01 PM

The title was suggested by an ad for a film that opens
at 10 PM EST today: "Hansel & Gretel: Witch Hunters."

Related material: Grimm Day 2012, as well as
Amy Adams in Raiders of the Lost Tesseract
and in a Film School Rejects page today.

See also some Norwegian art in
Trish Mayo's Photostream today and in
Omega Point (Log24, Oct. 15, 2012)—

Monday, October 15, 2012

Omega Point

m759 @ 2:00 PM 

For Sergeant-Major America—

IMAGE- Art exhibition with 'Omega Point' and geometric figures related to tesseract, along with movie 'Captain America' figure

The image is from posts of Feb. 20, 2011,
and Jan. 27, 2012.

This instance of the omega point is for 
a sergeant major who died at 92 on Wednesday,
October 10, 2012.

See also posts on that date in this journal—

Midnight,  Ambiguation,  Subtitle for Odin's Day,
 and Melancholia, Depression, Ambiguity.

Object Lesson

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

Suggested by yesterday's Garden Path

Commentary by Trish Mayo on a photo at Flickr:

Gazing Globe

These beautiful garden ornaments have a long history, beginning in the 13th century when they were made in Venice, Italy of hand-blown glass. They have been called by many names: Gazing Globe, Garden Globe, Witch Ball, Butler Globe and Globe of Happiness.

Legends formed about the mysterious powers of the globes. They were said to bring happiness, good luck and prosperity to those who owned it, known to ward off evil spirits, misfortune, illness and witches!

Some say the ball should be placed near the entrance to a house so that if a witch came by she would not be able to get past her reflection as she cannot tear herself away from her own image. Other accounts say a witch cannot bear to see her own reflection so she will not come near a "witch’s ball". A witch cannot sneak up on a person gazing into a globe as he can see if a witch approaches from behind. The smaller ball made of colored glass as opposed to the reflective kind was believed to attract and trap evil spirits.

Spiritually speaking, as one peers into the globe he can experience "oneness" with the universe.

The gazing globes practical purposes included being strategically placed on a path near the front entrance so that you could see when someone was coming for a visit. In Victorian times, the "Butler Ball" served as a mirror for servants to see when guests were needing assistance without staring at them throughout the meal. Another practical use was in the foyer of the home. Parents could keep a close eye on their daughter and her date as he bid her goodnight.

Today the globe is used ornamentally, allowing the whole garden, including the sky, to be viewed with one glance.

Under Covers

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

For Amy Adams and Trudie Styler:

http://www.log24.com/log/pix10B/101027-LangerSymbolicLogic.jpg

Click each cover for some background. See also

Cube Space

Filed under: General — Tags: — m759 @ 12:24 PM

For the late Cardinal Glemp of Poland,
who died yesterday, some links:

Wednesday, January 9, 2013

Bad Idea

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

For the 2013 Joint Mathematics Meetings in San Diego,
which start today, a cartoon by Andrew Spann—

(Click for larger image.) 

Related remarks:

This journal on the Feast of Epiphany, 2013

"The Tesseract is where it belongs: out of our reach."

The Avengers'  Nick Fury, played by Samuel L. Jackson

Today's New York Times —

"You never know what could happen.
If you have Sam, you’re going to be cool."

— The late David R. Ellis, film director

If anyone in San Diego cares about the relationship
of Spann's plane to Fury's Tesseract, he or she may
consult Finite Geometry of the Square and Cube.

Eve and Cleavage

Filed under: General — Tags: — m759 @ 11:01 AM

From a poem by Frances Frost—

"The upper peak, the shattered rock that cleaves the northward sky
remains alone untaken by the darkness"

— "From a Mountain-Top," The North American Review ,
December 1939 (Vol. 248, No. 2, page 301)

For some material related to the Frost poem,
if only by verbal coincidence, see shattered + rock in this journal.

See also rock + cleavage.

For the relationship to Eve, see New Year's Eve, 2012
and the following image by Karolin Schnoor, who also
illustrated the New York Times  op-ed piece "Catholic
Education, in Need of Salvation
" published online on
Epiphany 2013 (see last evening's Log24 post)—

For some context, see Establishment of the Talented.

Django

Filed under: General — Tags: — m759 @ 4:07 AM

"Catherine, Duchess of Cambridge, is 31."

— The Associated Press this morning, Jan. 9.

See also, in honor of the date of the Duchess's birth—
1982 Jan. 9— Django in this journal.

Tuesday, January 8, 2013

Vermont Throws Itself Together

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

"The way, when we climb a mountain,
  Vermont throws itself together"

— Wallace Stevens, "July Mountain"

For another view of reality in New Haven, see the
brief biography of Vermont poet Frances Frost
at the Yale University Library.  From that biography:

"She was survived by her son, the poet Paul Blackburn,
and by her daughter, Sister Marguerite of the Order
of St. Joseph
."

See also a figure from The New York Times  published
online on Epiphany, 2013:

Star Wars (continued)

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

The New York Times  today has an
obituary of poet Harvey Shapiro

See also the following image

'King's Moves' (eight-pointed star, viewed through bars)

  elsewhere in this journal.

Necessary Angel

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

Old Stone-Cutter

His gravestones are his everlasting children.
He loves to get his cramped left hand around
the solid faithful feeling of his chisel
and dig the names of those below the ground

or the family names of provident ones above
who cross their fingers and defy the fates
and acknowledge death their enemy and master
by ordering headstones with their birthing dates.

He carves his holy head, a solemn cherub
with granite wings and childish eyes cast down.
Those who prefer a willowed urn, disliking
angels, can go and die in another town.

FRANCES FROST

(From The North American Review , Vol. 248, No. 2,
1939, page 301)

Solemn cherub by Albrecht Dürer in 1514

Tempular

Filed under: General — Tags: — m759 @ 8:09 AM

IMAGE- Ada Louise Huxtable quotes Arthur Danto on 'tempular space'

Temporal note: The time  of this post, 8:09 AM ET, may be regarded
as a reference to the date  8/09 in the year of our Lord 2010. See also,
in this journal on that date, "Angels in the Architecture (continued)."

Friday, July 13, 2012

Through

Filed under: General — Tags: — m759 @ 5:48 PM

Oscar-winning producer
Richard Zanuck dies at 77

See also today's previous post,
Vanity Fair 's 1996 "Remains of the Dia,"
and english-for-students.com/dia.html.

Click to enlarge

Suddenly

Filed under: General — Tags: — m759 @ 10:25 AM

1940 —

2003 —

"… Conceptualism — suddenly art
could be nothing more than an idea,
a thought on a piece of paper
that played in your head."

— Michael Kimmelman,
    "The Dia Generation,"
    The New York Times Magazine ,
    Sunday, April 6, 2003


Suddenly?

Wednesday, August 31, 2011

Odin’s Day

Filed under: General — m759 @ 12:00 PM

Today is Wednesday.

O.E. Wodnesdæg  "Woden's day," a Gmc. loan-translation of L. dies Mercurii  "day of Mercury" (cf. O.N. Oðinsdagr , Swed. Onsdag , O.Fris. Wonsdei , M.Du. Wudensdach ). For Woden , see Odin  . — Online Etymology Dictionary

http://www.log24.com/log/pix11B/110831-HopkinsAsOdin.jpg

Above: Anthony Hopkins as Odin in the 2011 film "Thor"

Hugo Weaving as Johann Schmidt in the related 2011 film "Captain America"—

"The Tesseract* was the jewel of Odin's treasure room."

http://www.log24.com/log/pix11B/110831-JohannSchmidt.jpg

Weaving also played Agent Smith in The Matrix Trilogy.

The figure at the top in the circle of 13** "Thor" characters above is Agent Coulson.

"I think I'm lucky that they found out they need somebody who's connected to the real world to help bring these characters all together."

— Clark Gregg, who plays Agent Coulson in "Thor," at UGO.com

For another circle of 13, see the Crystal Skull film implicitly referenced in the Bright Star link from Abel Prize (Friday, Aug. 26, 2011)—

http://www.log24.com/log/pix11B/110831-BrightStar.jpg

Today's New York Times  has a quote about a former mathematician who died on that day (Friday, Aug. 26, 2011)—

"He treated it like a puzzle."

Sometimes that's the best you can do.

* See also tesseract  in this journal.

** For a different arrangement of 13 things, see the cube's 13 axes in this journal.

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'
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