Log24

Monday, October 16, 2017

Highway 61 Revisited

Filed under: 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

Thursday, June 4, 2015

Foundations

Filed under: Uncategorized — 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

Sunday, December 28, 2014

A Christmas Carol

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

Click image for some related posts.

Wednesday, December 17, 2014

Launched from Cuber

Filed under: Uncategorized — 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:

 

 

 

 

Saturday, October 25, 2014

Foundation Square

Filed under: Uncategorized — 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).)

Sunday, January 26, 2014

A Midnight Exorcism

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

Click image for a meditation.

Sunday, December 2, 2012

Knight’s Labyrinth

Filed under: Uncategorized — 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.

Thursday, October 14, 2010

Diamond Theory and Magic Squares

Filed under: Uncategorized — 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: Uncategorized — 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

Friday, June 6, 2008

Friday June 6, 2008

Filed under: Uncategorized — 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

Saturday, February 4, 2006

Saturday February 4, 2006

Filed under: Uncategorized — 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: Uncategorized — 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.

Tuesday, July 1, 2003

Tuesday July 1, 2003

Filed under: Uncategorized — 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: Uncategorized — 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.

Friday, October 25, 2002

Friday October 25, 2002

Filed under: Uncategorized — 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 

 

The image “http://www.log24.com/log/images/021025-AddsUp.jpg” cannot be displayed, because it contains errors.

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