Log24

Saturday, May 30, 2009

Saturday May 30, 2009

Filed under: Uncategorized — m759 @ 9:29 AM
Saturday Mourning

Part I:

From  'Diamond-Theory.com'-- 'Welcome to the Frontpage'

Part II:

Front page of New York Daily News, Saturday morning, May 30, 2009: Omar Edwards with Yankees baseball cap

Click on images for details.

Thursday, May 28, 2009

Thursday May 28, 2009

Filed under: Uncategorized — m759 @ 9:00 PM
Spelling

At right below, an image from the opening of Fox Studios Australia in Sydney on November 7, 1999.  The Fox ceremonies included, notably, Kylie Minogue singing “Diamonds are a Girl’s Best Friend.”

Red Windmill

Windmill image from diamond theory

Kylie Minogue

Kylie Minogue

For the mathematical properties of the red windmill (moulin rouge) figure at left, see Diamond Theory.

“There comes a time when you have
  learned enough to decide whether
  the way of the Craft is for you….

 First you will need to 
   prepare your sacred space….

 Calling the Corners (or Quarters)
  is something you will always do.”

— “Becoming a Witch” webpage

In related news:

CBS Evening News-- 'New York's Newest  Ballpark'

Happy birthday, Kylie.

Tuesday, May 26, 2009

Tuesday May 26, 2009

Filed under: Uncategorized — m759 @ 12:00 PM
For Daedalus
“Some writers describe the
first draft as ‘making clay’….”– Janet Burroway

Quoted here
a year ago today:

“… she explores
the nature of identity
in a structure of
crystalline complexity.”

 — Janet Burroway
(See ART WARS.)

For Stevie Nicks on her birthday: ART WARS: THE CRAFT

Related material:

Amy Adams in 'Doubt'

Amy Adams in Doubt

Stars of 'Doubt,' Amy Adams and Meryl Streep

Amy Adams and Meryl Streep
at premiere of Doubt

Janet Burroway's 'Writing Fiction: A Guide to Narrative Craft,' fifth edition, with I Ching coins on cover

Above:
Craft, 1999

“The matron had given her
leave to go out as soon as
the women’s tea was over….”

— James Joyce, “Clay

Ite, missa est.”

Sunday, May 24, 2009

Sunday May 24, 2009

Filed under: Uncategorized — m759 @ 2:45 AM

One More for the Road

“Angel eyes that old Devil sent,
they glow unbearably bright….”

Sinatra

Saturday, May 23, 2009

Saturday May 23, 2009

Filed under: Uncategorized — m759 @ 1:00 PM
Indiana Jones and the
Temple of Doom


'Indiana Jones and the Temple of Doom' poster

25 years ago today–

 Release Date:
23 May 1984 (USA)

Plot:
“After arriving in India,
Indiana Jones is asked
by a desperate village
      to find a mystical stone….”

Friday, May 22, 2009

Friday May 22, 2009

Filed under: Uncategorized — Tags: — m759 @ 9:29 AM
Steiner System

New York Times
banner this morning:

NYT banner, 9:21 AM Friday, May 22, 2009-- Ears are ads for HSBC.

Click to enlarge.

Related material from
July 11, 2008:

HSBC logo with framed version

The HSBC Logo Designer —

Henry Steiner

Henry Steiner, designerHe is an internationally recognized corporate identity consultant. Based in Hong Kong, his work for clients such as HongkongBank, IBM and Unilever is a major influence in Pacific Rim design.

Born in Austria and raised in New York, Steiner was educated at Yale under Paul Rand and attended the Sorbonne as a Fulbright Fellow. He is a past President of Alliance Graphique Internationale. Other professional affiliations include the American Institute of Graphic Arts, Chartered Society of Designers, Design Austria, and the New York Art Directors' Club.

His Cross-Cultural Design: Communicating in the Global Marketplace was published by Thames and Hudson (1995).

Yaneff.com

 

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."

 

Related material suggested by
an ad last night on
ABC's Ugly Betty season finale:

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

Credit for 'Diamonds' miniseries poster: Diane Robertson Design, London

Diamond from last night's
Log24 entry, with
four colored pencils from
Diane Robertson Design:

Diamond-shaped face of Durer's 'Melencolia I' solid, with  four colored pencils from Diane Robertson Design
 
See also
A Four-Color Theorem.

Thursday, May 21, 2009

Thursday May 21, 2009

Filed under: Uncategorized — m759 @ 8:14 PM
Diamonds

http://www.log24.com/log/pix09/090521-Plato-Durer.jpg

Thursday May 21, 2009

Filed under: Uncategorized — m759 @ 8:28 AM
Die
 
 Cast:

'Die,' by Tony Smith Die (Tony Smith)

Episcopal Bishop Paul Moore, Jr.

Paul Moore, Jr., retired Episcopal Bishop of New York, who died at home at 83 on the First of May, 2003

From “Secondary Structures,” by Tom Moody, Sculpture Magazine, June 2000:

“By the early ’90s, the perception of Minimalism as a ‘pure’ art untouched by history lay in tatters. The coup de grâce against the movement came not from an artwork, however, but from a text. Shortly after the removal of Richard Serra’s Tilted Arc from New York City’s Federal Plaza, Harvard art historian Anna Chave published ‘Minimalism and the Rhetoric of Power’ (Arts Magazine, January 1990), a rousing attack on the boys’ club that stops just short of a full-blown ad hominem rant. Analyzing artworks (Walter de Maria’s aluminum swastika, Morris’s ‘carceral images,’ Flavin’s phallic ‘hot rods’), critical vocabulary (Morris’s use of ‘intimacy’ as a negative, Judd’s incantatory use of the word ‘powerful’), even titles (Frank Stella’s National Socialist-tinged Arbeit Macht Frei and Reichstag), Chave highlights the disturbing undercurrents of hypermasculinity and social control beneath Minimalism’s bland exterior.  Seeing it through the eyes of the ordinary viewer, she concludes that ‘what [most] disturbs [the public at large] about Minimalist art may be what disturbs them about their own lives and times, as the face it projects is society’s blankest, steeliest face; the impersonal face of technology, industry and commerce; the unyielding face of the father: a face that is usually far more attractively masked.'”

For a more attractively masked father figure, see the Terminator series:

Father figure from the Terminator series

For further religious background,
see “Jesus and the Terminator
in Christianity Today.

Wednesday, May 20, 2009

Wednesday May 20, 2009

Filed under: Uncategorized — Tags: — m759 @ 4:00 PM
From Quilt Blocks to the
Mathieu Group
M24

Diamonds

(a traditional
quilt block):

Illustration of a diamond-theorem pattern

Octads:

Octads formed by a 23-cycle in the MOG of R.T. Curtis

 

Click on illustrations for details.

The connection:

The four-diamond figure is related to the finite geometry PG(3,2). (See "Symmetry Invariance in a Diamond Ring," AMS Notices, February 1979, A193-194.) PG(3,2) is in turn related to the 759 octads of the Steiner system S(5,8,24). (See "Generating the Octad Generator," expository note, 1985.)

The relationship of S(5,8,24) to the finite geometry PG(3,2) has also been discussed in–
  • "A Geometric Construction of the Steiner System S(4,7,23)," by Alphonse Baartmans, Walter Wallis, and Joseph Yucas, Discrete Mathematics 102 (1992) 177-186.

Abstract: "The Steiner system S(4,7,23) is constructed from the geometry of PG(3,2)."

  • "A Geometric Construction of the Steiner System S(5,8,24)," by R. Mandrell and J. Yucas, Journal of Statistical Planning and Inference 56 (1996), 223-228.

Abstract: "The Steiner system S(5,8,24) is constructed from the geometry of PG(3,2)."

For the connection of S(5,8,24) with the Mathieu group M24, see the references in The Miracle Octad Generator.

Tuesday, May 19, 2009

Tuesday May 19, 2009

Filed under: Uncategorized — Tags: , — m759 @ 7:20 PM
Exquisite Geometries

"By far the most important structure in design theory is the Steiner system S(5, 8, 24)."

"Block Designs," 1995, by Andries E. Brouwer

"The Steiner system S(5, 8, 24) is a set S of 759 eight-element subsets ('octads') of a twenty-four-element set T such that any five-element subset of T is contained in exactly one of the 759 octads. Its automorphism group is the large Mathieu group M24."

The Miracle Octad Generator (MOG) of R.T. Curtis (webpage)

"… in 1861 Mathieu… discovered five multiply transitive permutation groups…. In a little-known 1931 paper of Carmichael… they were first observed to be automorphism groups of exquisite finite geometries."

William M. Kantor, 1981

The 1931 paper of Carmichael is now available online from the publisher for $10.
 

Sunday, May 17, 2009

Sunday May 17, 2009

Filed under: Uncategorized — m759 @ 10:00 PM
The Sign of the
Double Cross

Scott Carnahan at Secret Blogging Seminar, December 14, 2007:

“… my advisor once told me, ‘If you ever find yourself drawing one of those meaningless diagrams with arrows connecting different areas of mathematics, it’s a good sign that you’re going senile.'”

Steven Cullinane at Log24, May 19, 2004:

Eight-point diamond-theory star, May 19, 2004

Google search, May 17, 2009:

Eight-point star of Google diamond-theorem search, May 17, 2009

Related material:

Log24, Feb. 16, 2008

Sunday May 17, 2009

Filed under: Uncategorized — m759 @ 9:49 PM
The Sign of the
Double Cross


Scott Carnahan at Secret Blogging Seminar, December 14, 2007

“… my advisor once told me, ‘If you ever find yourself drawing one of those meaningless diagrams with arrows connecting different areas of mathematics, it’s a good sign that you’re going senile.'”

Steven Cullinane at Log24.com, May 19, 2004:

Google search, May 17, 2009:

http://www.log24.com/log/pix09/090517-SearchWheel.jpg

Related material:

Log24, Feb. 16, 2008

Sunday May 17, 2009

Filed under: Uncategorized — m759 @ 9:38 PM
The Sign of the
Double Cross


Scott Carnahan at Secret Blogging Seminar, December 14, 2007

“… my advisor once told me, ‘If you ever find yourself drawing one of those meaningless diagrams with arrows connecting different areas of mathematics, it’s a good sign that you’re going senile.'”

Steven Cullinane at Log24.com, May 19, 2004:

Google search, May 17, 2009:

http://www.log24.com/log/pix09/090517-SearchWheel.jpg

Related material:

Log24, Feb. 16, 2008

Sunday May 17, 2009

Filed under: Uncategorized — m759 @ 7:59 AM
Design Theory

Laura A. Smit, Calvin College, “Towards an Aesthetic Teleology: Romantic Love, Imagination and the Beautiful in the Thought of Simone Weil and Charles Williams“–

“My work is motivated by a hope that there may be a way to recapture the ancient and medieval vision of both Beauty and purpose in a way which is relevant to our own century. I even dare to hope that the two ideas may be related, that Beauty is actually part of the meaning and purpose of life.”

Hans Ludwig de Vries, “On Orthogonal Resolutions of the Classical Steiner Quadruple System SQS(16),” Designs, Codes and Cryptography Vol. 48, No. 3 (Sept. 2008) 287-292 (DOI 10.1007/s10623-008-9207-5)–

“The Reverend T. P. Kirkman knew in 1862 that there exists a group of degree 16 and order 322560 with a normal, elementary abelian, subgroup of order 16 [1, p. 108]. Frobenius identified this group in 1904 as a subgroup of the Mathieu group M24 [4, p. 570]….”

1. Biggs N.L., “T. P. Kirkman, Mathematician,” Bulletin of the London Mathematical Society 13, 97–120 (1981).

4. Frobenius G., “Über die Charaktere der mehrfach transitiven Gruppen,” Sitzungsber. Königl. Preuss. Akad. Wiss. zu Berlin, 558–571 (1904). Reprinted in Frobenius, Gesammelte Abhandlungen III (J.-P. Serre, editor), pp. 335–348. Springer, Berlin (1968).

Olli Pottonen, “Classification of Steiner Quadruple Systems” (Master’s thesis, Helsinki, 2005)–

“The concept of group actions is very useful in the study of isomorphisms of combinatorial structures.”

Olli Pottonen,  'Classification of Steiner Quadruple Systems'

“Simplify, simplify.”
Thoreau

Beauty is bound up
with symmetry.”
Weyl

Sixteen points in a 4x4 array

Pottonen’s thesis is
 dated Nov. 16, 2005.

For some remarks on
images and theology,
see Log24 on that date.

Click on the above image
 for some further details.

Friday, May 15, 2009

Friday May 15, 2009

Filed under: Uncategorized — m759 @ 6:29 AM
Today is the opening of
Angels & Demons

Thanks to Jillian’s Specials for the following quotation:

“… faith is…. validated by individual experience and inspired by epiphanies.”

— “Where Physics Meets Faith,” by , Oct. 21, 2004

Individual Experience:

See, for instance, the link in last Sunday’s entry to a remarkable group-theoretic map.

Epiphanies:

Part I: For Jillian

Jodie Foster in 'Contact'

(with a nod to Matthew McConaughey and his films Contact and, more recently, Ghosts of Girlfriends Past).

Part II: For a mountaineer–

In this morning’s news:

News of mountaineer's death on May 13, with map of Italy showing Rome marked by graphic balloon with black dot

(with a nod to Tom Hanks and to Gian-Carlo Rota and the Black Hole of Rome (cf. Psychoshop) as well as to the mountains, both real and imagined, in last Sunday’s link “a remarkable group-theoretic map“).

Wednesday, May 13, 2009

Wednesday May 13, 2009

Filed under: Uncategorized — m759 @ 10:31 AM
Feds Rescue
Mathematical
 Ponzi Victims

AMS news: Feds to fund new math jobs

AMS Grad Student Blog with link to PhD Comics

PhD Comics: Ponzi Scheme (March 9, 2009)

Math grad student's blog-- AMS Grad Student Blog redundant with PhD Comics

Amen.

Sunday, May 10, 2009

Sunday May 10, 2009

Filed under: Uncategorized — m759 @ 6:29 PM
Mother’s Day
at MAA

Rick’s Tricky Six Puzzle:
S5 Sits Specially in S6
by Alex Fink and Richard Guy

Abstract. Rick Wilson identified a sliding block puzzle, the Tricky Six puzzle, in which a uniquely small fraction of the possible scrambled arrangements of the six moving pieces can be restored to the solved state. The permutations one can perform form the abstract group S5, the symmetric group on five letters, but surprisingly they aren’t any of the “obvious” copies of S5 in S6 that fix a single point and allow the other five to be permuted arbitrarily. This special S5 comes from the outer automorphism of S6, a remarkable group-theoretic map whose presence is felt in several combinatorial objects. We track down this outer automorphism in the Tricky Six puzzle as well as the projective plane of order 4, the Hoffman-Singleton graph, the Steiner system S(5,6,12), and a couple of error-correcting codes.

Meanwhile:

'Wizard of Id,' Mother's Day 2009-- Royal carriage with 'FINK ON BOARD' sign

Click to enlarge.

Background:

A pair of matronly women
gave readings of
bad mathematical poetry
on April 28 at

Carriage House Conference Center of the Mathematical Association of American in Washington, D.C

the MAA’s Carriage House
Conference Center in
Washington, D.C.

Wednesday, May 6, 2009

Wednesday May 6, 2009

Filed under: Uncategorized — m759 @ 11:07 AM
Joke

“My pursuits are a joke
in that the universe is a joke.
One has to reflect
the universe faithfully.”

John Frederick Michell
Feb. 9, 1933 –
April 24, 2009 

“I laugh because I dare not cry.
This is a crazy world and
the only way to enjoy it
is to treat it as a joke.”

— Robert A. Heinlein,
The Number of the Beast

For Marisa Tomei
  (born Dec. 4, 1964) —
on the day that
   Bob Seger turns 64 —

A Joke:
Points All Her Own

Points All Her Own,
Part I:

(For the backstory, see
the Log24 entries and links
on Marisa Tomei’s birthday
last year.)

Ad for a movie of the book 'Flatland'


Points All Her Own,

Part II:

(For the backstory, see
Galois Geometry:
The Simplest Examples
.)

Galois geometry: the simplest examples

Points All Her Own,

Part III:

(For the backstory, see
Geometry of the I Ching
and the history of
Chinese philosophy.)

Galois space of six dimensions represented in Euclidean spaces of three and of two dimensions

In simpler terms:

Smackdown!

Garfield on May 6, 2009: Smackdown!

Sunday, May 3, 2009

Sunday May 3, 2009

Filed under: Uncategorized — m759 @ 7:59 AM
Annals of
Sacred Geometry

(The phrase “sacred geometry”
is of course anathema to most
mathematicians, to whom
nothing is sacred.)

From “The Geometric
Art of John Michell
“:
John Michell rendition of  'Remember now thy Creator...'
From this morning’s
 New York Times:

John Michell, Counterculture Author Who Cherished Idiosyncrasy, Dies at 76

By DOUGLAS MARTIN 

Mr. Michell, a self-styled Merlin of the 1960s English counterculture, inspired disciples like the Rolling Stones with a deluge of writings….

Michell, who wrote on Glastonbury
(a site associated with King Arthur)
and on sacred geometry, seems to
have had a better education than
most sacred-geometry enthusiasts.
He is said to have studied at
Eton and at Trinity College,
Cambridge.

He is not to be
confused with an earlier
Trinity figure, mathematician
John Henry Michell,
who died at 76 on the third
day of February in 1940
.

Related material:

See the Log24 entry
from the date of death
 of the later Michell —

  April 24

and, in light of the later
Michell’s interest in
geometry and King Arthur,
 the Log24 remarks for
Easter Sunday this year
(April 12).

These remarks include the
following figure by
Sebastian Egner related,
if only through myth,
to Arthur’s round table —

Conway's mystic circle of 13

— and the classic Delmore Schwartz
poem “Starlight Like Intuition
Pierced the Twelve
.”

Which of the two John Michells
(each a Merlin figure of sorts)
would be more welcome in
Camelot is open to debate.

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