Log24

Saturday, February 16, 2019

Bunker Bingo Continues.

Filed under: General — Tags: , — m759 @ 2:27 PM

From a post of October 16, 2017, "Halloween Meditation" —

Friday, December 28, 2018

Blackline Master

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

From a Log24 post of September 4, 2018, "Identity Crisis" —

http://www.log24.com/log/pix18/180903-Womens_Night_Bingo-at48.41-The_Net.jpg

From the 2011 Spanish film "Verbo" — (Click to enlarge) —

From a  Blackline Master

Friday, September 7, 2018

A Square for Sims

Filed under: General — m759 @ 3:00 AM

The American Mathematical Society on Wednesday, September 5,
reported a death from October 23 last year

AMS obituary for mathematician Charles C. Sims

See also Higman-Sims and 5×5 in this  journal.

Tuesday, September 4, 2018

Identity Crisis

Filed under: General — m759 @ 12:00 AM

http://www.log24.com/log/pix18/180903-Womens_Night_Bingo-at48.41-The_Net.jpg

http://www.log24.com/log/pix18/180903-Menand-MBTI-NYer-Sept-10-1018-500w.jpg

See also 5×5  in this  journal.

Monday, June 25, 2018

The Trials of Device

Filed under: General — Tags: — m759 @ 9:34 AM

"A blank underlies the trials of device."

Wallace Stevens

"Designing with just a blank piece of paper is very quiet."

Kate Cullinane

Related material —

An image posted at 12 AM ET December 25, 2014:

The image stands for the
phrase "five by five,"
meaning "loud and clear."

Other posts featuring the above 5×5 square with some added structure:

Friday, May 25, 2018

Grid Design

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

Click the grid for the tag 5×5 in this journal.

A related book —

See also the previous post, Bucharest Semiotics.

Wednesday, October 18, 2017

Dürer for St. Luke’s Day

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

Structure of the Dürer magic square 

16   3   2  13
 5  10  11   8   decreased by 1 is …
 9   6   7  12
 4  15  14   1

15   2   1  12
 4   9  10   7
 8   5   6  11
 3  14  13   0 .

Base 4 —

33  02  01  30
10  21  22  13
20  11  12  23 
03  32  31  00 .

Two-part decomposition of base-4 array
as two (non-Latin) orthogonal arrays

3 0 0 3     3 2 1 0
1 2 2 1     0 1 2 3
2 1 1 2     0 1 2 3
0 3 3 0     3 2 1 0 .

Base 2 –

1111  0010  0001  1100
0100  1001  1010  0111
1000  0101  0110  1011
0011  1110  1101  0000 .

Four-part decomposition of base-2 array
as four affine hyperplanes over GF(2) —

1001  1001  1100  1010
0110  1001  0011  0101
1001  0110  0011  0101
0110  0110  1100  1010 .

— Steven H. Cullinane,
  October 18, 2017

See also recent related analyses of
noted 3×3 and 5×5 magic squares.

Monday, October 16, 2017

Highway 61 Revisited

Filed under: G-Notes,General,Geometry — Tags: , , — m759 @ 10:13 AM

"God said to Abraham …." — Bob Dylan, "Highway 61 Revisited"

Related material — 

See as well Charles Small, Harvard '64, 
"Magic Squares over Fields" —

— and Conway-Norton-Ryba in this  journal.

Some remarks on an order-five  magic square over GF(52):

"Ultra Super Magic Square"

on the numbers 0 to 24:

22   5   18   1  14
  3  11  24   7  15
  9  17   0  13  21
10  23   6  19   2
16   4  12  20   8

Base-5:

42  10  33  01  24 
03  21  44  12  30 
14  32  00  23  41
20  43  11  34  02
31  04  22  40  13 

Regarding the above digits as representing
elements of the vector 2-space over GF(5)
(or the vector 1-space over GF(52)) 

All vector row sums = (0, 0)  (or 0, over GF(52)).
All vector column sums = same.

Above array as two
orthogonal Latin squares:
   
4 1 3 0 2     2 0 3 1 4
0 2 4 1 3     3 1 4 2 0 
1 3 0 2 4     4 2 0 3 1         
2 4 1 3 0     0 3 1 4 2
3 0 2 4 1     1 4 2 0 3

— Steven H. Cullinane,
      October 16, 2017

Sunday, December 25, 2016

Miracle Eight Generator

Filed under: General — m759 @ 9:00 AM

Merry Xmas to Katherine Neville.

Monday, July 25, 2016

The Retinoid Self

Filed under: General,Geometry — m759 @ 1:10 PM

Trehub - 'Self as the neuronal origin of retinoid space'

"… which grounds the self" . . .

Popular Mechanics  online today

"Verizon exec Marni Walden seemed to
indicate Mayer's future may still be up in the air."

See also 5×5 in this  journal —

IMAGE- Right 3-4-5 triangle with squares on sides and hypotenuse as base

"If you have built castles in the air, 
your work need not be lost;
that is where they should be.
Now put the foundations under them.”

— Henry David Thoreau

Tuesday, February 2, 2016

Depth Haiku

Filed under: General — m759 @ 8:30 PM

From yesterday's 2 PM post

From "Inception" —

Paraphrase of remarks by "Inception" director Christopher Nolan
at Princeton on June 1, 2015 —

"If you have built castles in the air, 
your work need not be lost;
that is where they should be.
Now put the foundations under them.”

— Henry David Thoreau

Monday, January 25, 2016

High White Noon

Filed under: General — m759 @ 12:00 PM

Continued. See previous episodes and also 5×5.

Thursday, June 4, 2015

Foundations

Filed under: General,Geometry — Tags: — m759 @ 7:47 PM

Princeton University's president on June 2, 2015 —

“Dream Audaciously,” Eisgruber Urges Graduates

Related news —

Film director Christopher Nolan at Princeton on June 1, 2015:

“In these graduation speeches, generally, you have the
speaker say something along the lines of, ‘You need to
chase your dreams,’ ” Nolan said. “But I’m not going to
say that because I don’t believe it. I don’t want you to
chase your dreams. I want you to chase your realities.
And I want to say: Don’t chase your realities at the
expense of your dreams, but as the foundation of your
dreams.”

IMAGE- Right 3-4-5 triangle with squares on sides and hypotenuse as base

"If you have built castles in the air, 
your work need not be lost;
that is where they should be.
Now put the foundations under them.”

— Henry David Thoreau

Monday, December 29, 2014

Dodecahedron Model of PG(2,5)

Filed under: General,Geometry — Tags: , , — m759 @ 2:28 PM

Recent posts tagged Sagan Dodecahedron 
mention an association between that Platonic
solid and the 5×5 grid. That grid, when extended
by the six points on a "line at infinity," yields
the 31 points of the finite projective plane of
order five.  

For details of how the dodecahedron serves as
a model of this projective plane (PG(2,5)), see
Polster's A Geometrical Picture Book , p. 120:

For associations of the grid with magic rather than
with Plato, see a search for 5×5 in this journal.

Sunday, December 28, 2014

A Christmas Carol

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

See also Sagan Dodecahedron, which includes 
an image posted at 12 AM ET December 25, 2014:

The image stands for the
phrase "five by five,"
meaning "loud and clear."

Thursday, December 25, 2014

Design

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

Click image for some related posts.

Thursday, December 18, 2014

Platonic Analogy

Filed under: General,Geometry — Tags: , , — m759 @ 2:23 PM

(Five by Five continued)

As the 3×3 grid underlies the order-3 finite projective plane,
whose 13 points may be modeled by
the 13 symmetry axes of the cube,
so the 5×5 grid underlies the order-5 finite projective plane,
whose 31 points may be modeled by
the 31 symmetry axes of the dodecahedron.

See posts tagged Galois-Plane Models.

Wednesday, December 17, 2014

Launched from Cuber

Filed under: General — Tags: — m759 @ 5:55 PM

Continued from Nobel Note (Jan. 29, 2014).

IMAGE- 'Launched from Cuber' scene in 'X-Men: First Class'

From Tradition in Action , "The Missal Crisis of '62,"
remarks on the revision of the Catholic missal in that year—

"Neither can the claim that none of these changes
is heretical in content be used as an argument
in favor of its use, for neither is the employment of
hula girls, fireworks, and mariachis strictly speaking
heretical in itself, but they belong to that class of novel
and profane things that do not belong in the Mass."

— Fr. Patrick Perez, posted Sept. 11, 2007 

See also this  journal on November 22, 2014

Say Bingo to my little friend

    … and on Bruce Springsteen's birthday this year —

Tuesday, September 23, 2014

Matrix

Filed under: Uncategorized — m759 @ 11:00 AM 

From AP’s Today in History:

Happy birthday.

“It all adds up.” — Saul Bellow

The Matrix:

 

 

 

 

Tuesday, November 25, 2014

Euclidean-Galois Interplay

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

For previous remarks on this topic, as it relates to
symmetry axes of the cube, see previous posts tagged Interplay.

The above posts discuss, among other things, the Galois
projective plane of order 3, with 13 points and 13 lines.

Oxley's 2004 drawing of the 13-point projective plane

These Galois points and lines may be modeled in Euclidean geometry
by the 13 symmetry axes and the 13 rotation planes
of the Euclidean cube. They may also be modeled in Galois geometry
by subsets of the 3x3x3 Galois cube (vector 3-space over GF(3)).

http://www.log24.com/log/pix11A/110427-Cube27.jpg

   The 3×3×3 Galois Cube 

Exercise: Is there any such analogy between the 31 points of the
order-5 Galois projective plane and the 31 symmetry axes of the
Euclidean dodecahedron and icosahedron? Also, how may the
31 projective points  be naturally pictured as lines  within the 
5x5x5 Galois cube (vector 3-space over GF(5))?

Update of Nov. 30, 2014 —

For background to the above exercise, see
pp. 16-17 of A Geometrical Picture Book ,
by Burkard Polster (Springer, 1998), esp.
the citation to a 1983 article by Lemay.

Saturday, October 25, 2014

Foundation Square

Filed under: General,Geometry — Tags: — m759 @ 2:56 PM

In the above illustration of the 3-4-5 Pythagorean triangle,
the grids on each side may be regarded as figures of
Euclidean  geometry or of Galois  geometry.

In Euclidean geometry, these grids illustrate a property of
the inner triangle.

In elementary Galois geometry, ignoring the connection with
the inner triangle, the grids may be regarded instead as
illustrating vector spaces over finite (i.e., Galois) fields.
Previous posts in this journal have dealt with properties of
the 3×3 and 4×4 grids.  This suggests a look at properties of
the next larger grid, the 5×5 array, viewed as a picture of the
two-dimensional vector space (or affine plane) over the finite
Galois field GF(5) (also known as ℤ5).

The 5×5 array may be coordinatized in a natural way, as illustrated
in (for instance) Matters Mathematical , by I.N. Herstein and
Irving Kaplansky, 2nd ed., Chelsea Publishing, 1978, p. 171:

See Herstein and Kaplansky for the elementary Galois geometry of
the 5×5 array.

For 5×5 geometry that is not so elementary, see…

Hafner's abstract:

We describe the Hoffman-Singleton graph geometrically, showing that
it is closely related to the incidence graph of the affine plane over ℤ5.
This allows us to construct all automorphisms of the graph.

The remarks of Brouwer on graphs connect the 5×5-related geometry discussed
by Hafner with the 4×4 geometry related to the Steiner system S(5,8,24).
(See the Miracle Octad Generator of R. T. Curtis and the related coordinatization
by Cullinane of the 4×4 array as a four-dimensional vector space over GF(2).)

Tuesday, September 23, 2014

Matrix

Filed under: General — m759 @ 11:00 AM

From AP’s Today in History:

Happy birthday.

“It all adds up.” — Saul Bellow

The Matrix:

Sunday, January 26, 2014

A Midnight Exorcism

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

The summoning of the spirit of Bertrand Russell
yesterday by Peter J. Cameron at his weblog
suggests a review of this  weblog’s posts of
Christmas Eve, December 24-25, 2013.

(Recall that Robert D. Carmichael, who, in a book
linked to at midnight last Christmas Eve discusses
some “magic” mathematical structures,
reportedly was trained as a Presbyterian minister.
See also The Presbyterian Exorcist.)

Wednesday, December 25, 2013

A Midnight Clear

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

Click image for a meditation.

Sunday, December 2, 2012

Knight’s Labyrinth

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

A magic— indeed, diabolic— square:

IMAGE- 5x5 magic- in fact, diabolic- square

For the construction, see a book
by W. W. Rouse Ball, founding president
of a Cambridge University magic society.

For some related religious remarks,
see Raiders of the Lost Matrix.

Tuesday, January 25, 2011

Another Reappearing Number

Filed under: General,Geometry — m759 @ 12:25 PM

(A sequel to yesterday's reappearing number)

25 —

5x5 ultra super magic square

See "Quine, Newton, logic" in this journal.

Thursday, October 14, 2010

Diamond Theory and Magic Squares

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

"A world of made
is not a world of born— pity poor flesh
and trees, poor stars and stones, but never this
fine specimen of hypermagical
ultraomnipotence."

— e. e. cummings, 1944

For one such specimen, see The Matrix of Abraham
a 5×5 square that is hypermagical… indeed, diabolical.

Related material on the algebra and geometry underlying some smaller structures
that have also, unfortunately, become associated with the word "magic"—

  1. Finite Geometry of the Square and Cube
  2. Clifford Pickover on a 4×4 square
  3. Christopher J. Henrich on the geometry of 4×4 magic squares
    (without any mention of  [1] above or related work dating back to 1976)

" … listen: there's a hell
of a good universe next door; let's go"

— e. e. cummings

Happy birthday, e. e.

Saturday, October 25, 2008

Saturday October 25, 2008

Filed under: General — Tags: , — m759 @ 11:01 AM
Actual Being

The New York Times Book Review online today has a review by Sam Tanenhaus of a new John Updike book.

The title of the review (not the book) is "Mr. Wizard."

"John Updike is the great genial sorcerer of American letters. His output alone (60 books, almost 40 of them novels or story collections) has been supernatural. More wizardly still is the ingenuity of his prose. He has now written tens of thousands of sentences, many of them tiny miracles of transubstantiation whereby some hitherto overlooked datum of the human or natural world– from the anatomical to the zoological, the socio-economic to the spiritual– emerges, as if for the first time, in the complete­ness of its actual being."

Rolling Stone interview with Sting, February 7, 1991:

"'I was brought up in a very strong Catholic community,' Sting says. 'My parents were Catholic, and in the Fifties and Sixties, Catholicism was very strong. You know, they say, "Once a Catholic, always a Catholic." In a way I'm grateful for that background. There's a very rich imagery in Catholicism: blood, guilt, death, all that stuff.' He laughs."

http://www.log24.com/log/pix08A/081025-Sting.jpg

RS 597, Feb. 7, 1991

Last night's 12:00 AM
Log24 entry:

Midnight Bingo

From this date six years ago:


It All Adds Up.

From this morning's newspaper,
a religious meditation I had not
seen last night:

The image “http://www.log24.com/log/pix08A/081025-WizardOfIdSm.jpg” cannot be displayed, because it contains errors.

Related material:

Juneteenth through
Midsummer Night, 2007

and

Church of the Forbidden Planet

Tuesday, June 24, 2008

Tuesday June 24, 2008

Filed under: General — Tags: — m759 @ 1:00 PM
Random Walk with
X's and O's

Part I: Random Walk

NY Lottery June 23, 2008: Mid-day 322, Evening 000

Part II: X's

3/22:

Actor contemplating the Chi-rho Page of the Book of Kells

"Shakespeare, Rilke, Joyce,
Beckett and Levi-Strauss are
instances of authors for whom
chiasmus and chiastic thinking
are of central importance,
for whom chiasmus is a
generator of meaning,
tool of discovery and
  philosophical template."
 
— Chiasmus in the
Drama of Life

Part III: O's —

A Cartoon Graveyard
in honor of the late
Gene Persson

Today's Garfield

Garfield cartoon of June 24, 2008

See also
Midsummer Eve's Dream:

"The meeting is closed
with the lord's prayer
and refreshments are served."

Producer of plays and musicals
including Album and
The Ruling Class

Lower case in honor of
Peter O'Toole, star of
the film version of
The Ruling Class.

(This film, together with
O'Toole's My Favorite Year,
may be regarded as epitomizing
Hollywood's Jesus for Jews.)

Those who prefer
less randomness
in their religion
 may consult O'Toole's
more famous film work
involving Islam,
as well as
the following structure
discussed here on
the date of Persson's death:

5x5 ultra super magic square

"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah.
"

Friday, June 6, 2008

Friday June 6, 2008

Filed under: General,Geometry — Tags: — m759 @ 2:45 AM
The Dance of Chance

"Harvard seniors have
every right to demand a
    Harvard-calibre speaker."

— Adam Goldenberg in
The Harvard Crimson

"Look down now, Cotton Mather"

— Wallace Stevens,
Harvard College
Class of 1901

For Thursday, June 5, 2008,
commencement day for Harvard's
Class of 2008, here are the
Pennsylvania Lottery numbers:

Mid-day 025
Evening 761

Thanks to the late
Harvard professor
Willard Van Orman Quine,
the mid-day number 025
suggests the name
"Isaac Newton."

(For the logic of this suggestion,
see On Linguistic Creation
and Raiders of the Lost Matrix.)

Thanks to Google search, the
  name of Newton, combined with
  Thursday's evening number 761,
suggests the following essay:

Science 10 August 2007:
Vol. 317. no. 5839, pp. 761-762

PHILOSOPHY OF SCIENCE:
The Cha-Cha-Cha Theory
of Scientific Discovery

Daniel E. Koshland Jr.*

* D. E. Koshland Jr. passed away on 23 July 2007. He was a professor of biochemistry and molecular and cell biology at the University of California, Berkeley, since 1965. He served as Science's editor-in-chief from 1985 to 1995.
 


What can a non-scientist add?

Perhaps the Log24 entries for
the date of Koshland's death:

The Philosopher's Stone
and The Rock.

Or perhaps the following
observations:

On the figure of 25 parts
discussed in
"On Linguistic Creation"–

5x5 ultra super magic square

"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah.
"

— Clifford Pickover  

"At the still point,
there the dance is.
"

— T. S. Eliot,
Harvard College
Class of 1910

Sunday, February 19, 2006

Sunday February 19, 2006

Filed under: General — m759 @ 2:04 PM

But seriously…

Raiders of the Lost Matrix
(continued)

The Matrix:

The image “http://www.log24.com/log/pix06/060219-Bingo2.jpg” cannot be displayed, because it contains errors.

Click on pictures for details.

In memory of George T. Davis,
who died on February 4,
a Hollywood ending:

Santa Claus rides alone.”
Clint Eastwood  

Saturday, February 4, 2006

Saturday February 4, 2006

Filed under: General — Tags: , — m759 @ 10:00 AM
Raiders of
the Lost Matrix

(continued)

The Archaeologist
with a Thousand Faces

"From often humble beginnings, and often with a childhood fascination for antiquity, the archaeologist leaves familiar surroundings to undergo exacting professional training under a series of mentors and when armed, at last, with the intellectual weapons of the profession, sets off for unfamiliar or exotic realms, braving opposition and danger to solve an ancient mystery.  The lives of… real-life archaeologists… have lent themselves to this style of retelling… as have such fictional heroes as John Cullinane (Michener 1965) and Indiana Jones."

— From "Promised Lands and Chosen Peoples: The Politics and Poetics of Archaeological Narrative," by Neil Asher Silberman, pp. 249-262 in Nationalism, Politics, and the Practice of Archaeology, edited by Philip L. Kohl and Clare Fawcett, Cambridge University Press, paperback, published Feb. 8, 1996.

From Today in History,
by the Associated Press:

Thought for Today:
"Character consists of what you do
on the third and fourth tries."

James Michener,
American author (1907-1997),
attributed by
Simpson's Contemporary Quotations
to Chesapeake, Random House, 78.

The Matrix:

First try:

On Linguistic Creation
June 25, 1999

Second try:
Art Wars: Picasso's Birthday,
Oct. 25, 2002

Third try:
Matrix of the Death God,
May 25, 2003

Fourth try:
Happy Birthday,
July 26, 2004

Monday, July 26, 2004

Monday July 26, 2004

Filed under: General — Tags: , — m759 @ 11:07 PM

Happy Birthday

to Kate Beckinsale
(star of Cold Comfort Farm)

and Kevin Spacey
(star of The Usual Suspects).

From a novel,
The Footprints of God,
published August 12, 2003

A tour guide describes
stations of the cross in Jerusalem:

"Ibrahim pointed down the cobbled street to a half circle of bricks set in the street.  'There is where Jesus began to carry the cross.  Down the street is the Chapel of Flagellation, where the Roman soldiers whipped Jesus, set on him a crown of thorns, and said, "Hail, King of the Jews!" Then Pilate led him to the crowd and cried, "Ecce homo!  Behold the man!" '

Ibrahim delivered this information with the excitement of a man reading bingo numbers in a nursing home."

In keeping with this spirit of religious fervor and with the spirit of Carl Jung, expositor of the religious significance of the mandala,

Behold —

The Mandala of Abraham

For the religious significance of this mandala,
see an entry of May 25, 2003:

Matrix of the Death God.

Wednesday, July 30, 2003

Wednesday July 30, 2003

Filed under: General — m759 @ 2:45 AM

Transcendental Meditation

This week’s
 New Yorker
:

Transcendental Man
New books on
Ralph Waldo Emerson
for his bicentennial.
by John Updike

This week’s
 Time cover
:

The bicentennial of Ralph Waldo Emerson was on May 25, 2003.  For a commemoration of Emerson on that date, click on the picture below of Harvard University’s Room 305, Emerson Hall.

 

This will lead you to a discussion of the properties of a 5×5 array, or matrix, with a symbol of mystical unity at its center.  Although this symbol of mystical unity, the number “1,” is not, pace the Shema, a transcendental number, the matrix is, as perhaps a sort of Emersonian compensation, what postmodernists would call phallologocentric.  It is possible that Emerson is a saint; if so, his feast day (i.e., date of death), April 27, might reveal to us the sort of miraculous fact hoped for by Fritz Leiber in my previous entry.  A check of my April 27 notes shows us, lo and behold, another phallologocentric 5×5 array, this one starring Warren Beatty.  This rather peculiar coincidence is, perhaps, the sort of miracle appropriate to a saint who is, as this week’s politically correct New Yorker calls him, a Big Dead White Male.

 Leiber’s fiction furnishes “a behind-the-scenes view of the time change wars.”

“It’s quarter to three…” — St. Frank Sinatra

Tuesday, July 1, 2003

Tuesday July 1, 2003

Filed under: General — Tags: — m759 @ 5:37 PM

Jew’s on First

This entry is dedicated to those worshippers of Allah who have at one time or another cried
Itbah al-Yahud!” … Kill the Jew!
(See June 29 entries).

Dead at 78

Comedian Buddy Hackett died on Tuesday, July First, 2003, according to the New York Times.  According to Bloomberg.com, he died Sunday or Monday.

Associated Press

Buddy Hackett,
on the set of
“It’s a Mad, Mad,
Mad, Mad
World”
in 1962.

Whatever.  We may imagine he has now walked, leading a parade of many other stand-up saints, into a bar.


Hepburn at Chaillot

MIDRASH
for Buddy Hackett

From my May 25 entry,

Matrix of the Death God:

R. M. Abraham’s Diversions and Pastimes, published by Constable and Company, London, in 1933, has the following magic square:

The Matrix of Abraham

A summary of the religious import of the above from Princeton University Press:

“Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah.  Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.”

— Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72

Other appearances of this religious icon on the Web include:

On Linguistic Creation

Picasso’s Birthday

1991 Yearbook
Rolling Stone



Hackett

In the Picasso’s Birthday version, 22 of the 25 magic square cells are correlated with pictures on the “Class of ’91” cover of Rolling Stone magazine.  Number 7 is Rod Stewart.  In accordance with the theological rhyme “Seven is heaven, eight is a gate,” our site music for today is “Forever Young,” a tune made famous by Stewart.

Roderick, actually   the name of the hero in “Madwoman of Chaillot”

Sunday, May 25, 2003

Sunday May 25, 2003

Filed under: General,Geometry — Tags: — m759 @ 7:11 PM

ART WARS

Mental Health Month, Day 25:

Matrix of the Death God

Having dealt yesterday with the Death Goddess Sarah, we turn today to the Death God Abraham.  (See Jacques Derrida, The Gift of Death, University of Chicago Press, 1996.)  For a lengthy list of pictures of this damned homicidal lunatic about to murder his son, see The Text This Week.

 

See, too, The Matrix of Abraham, illustrated below.  This is taken from a book by R. M. Abraham, Diversions and Pastimes, published by Constable and Company, London, in 1933.

The Matrix of Abraham

A summary of the religious import of the above from Princeton University Press:

“Moslems of the Middle Ages were fascinated by pandiagonal squares with 1 in the center…. The Moslems thought of the central 1 as being symbolic of the unity of Allah.  Indeed, they were so awed by that symbol that they often left blank the central cell on which the 1 should be positioned.”

— Clifford A. Pickover, The Zen of Magic Squares, Circles, and Stars, Princeton U. Press, 2002, pp. 71-72

Other appearances of this religious icon on the Web:

On Linguistic Creation

Picasso’s Birthday

A less religious approach to the icon may be found on page 393 of R. D. Carmichael’s Introduction to the Theory of Groups of Finite Order (Ginn, Boston, 1937, reprinted by Dover, 1956).

This matrix did not originate with Abraham but, unlike Neo, I have not yet found its Architect.

Sunday, April 27, 2003

Sunday April 27, 2003

Filed under: General,Geometry — m759 @ 3:24 PM

ART WARS:

Graphical Password

From a summary of “The Design and Analysis of Graphical Passwords“:

“Results from cognitive science show that people can remember pictures much better than words….

The 5×5 grid creates a good balance between security and memorability.”

 Ian Jermyn, New York University; Alain Mayer, Fabian Monrose, Michael K. Reiter, Bell Labs, Lucent Technologies; Aviel Rubin, AT&T Labs — Research

Illustration — Warren Beatty as
a graphical password:

Town & Country,”
released April 27, 2001

Those who prefer the simplicity of a 3×3 grid are referred to my entry of Jan. 9, 2003, Balanchine’s Birthday.  For material related to the “Town & Country” theme and to Balanchine, see Leadbelly Under the Volcano (Jan. 27, 2003). (“Sometimes I live in the country, sometimes I live in town…” – Huddie Ledbetter).  Those with more sophisticated tastes may prefer the work of Stephen Ledbetter on Gershwin’s piano preludes or, in view of Warren Beatty’s architectural work in “Town & Country,” the work of Stephen R. Ledbetter on window architecture.

As noted in Balanchine’s Birthday, Apollo (of the Balanchine ballet) has been associated by an architect with the 3×3, or “ninefold” grid.  The reader who wishes a deeper meditation on the number nine, related to the “Town & Country” theme and more suited to the fact that April is Poetry Month, is referred to my note of April 27 two years ago, Nine Gates to the Temple of Poetry.

Intermediate between the simplicity of the 3×3 square and the (apparent) complexity of the 5×5 square, the 4×4 square offers an introduction to geometrical concepts that appears deceptively simple, but is in reality fiendishly complex.  See Geometry for Jews.  The moral of this megilla?

32 + 42 = 52.

But that is another story.

Friday, October 25, 2002

Friday October 25, 2002

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

ART WARS:
Picasso's Birthday

From an art quotes website:

Dore Ashton's Picasso on Art —

"We all know that Art is not truth.
Art is a lie that makes us realize truth,
at least the truth that is given us
to understand." — Pablo Picasso

From "Xanadu" —

"You have to believe we are magic."
— Olivia Newton-John

The Muse
Picasso

 

Soul Kiss
Olivia
Newton-John

 

 

 

A is for Art
Cullinane

 
"A work of art has an author and yet,
when it is perfect, it has something
which is essentially anonymous about it."
Simone Weil, Gravity and Grace 

 

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