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Web Journal of
Steven H.
Cullinane
Music for Pegasus

m759
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Name: Steven
Country: United States
State: Pennsylvania
Gender: Male


Interests: Mathematics, literature.
Occupation: Retired
Industry: Computers (Software)


Message: message me
Website: visit my website


Member Since: 7/20/2002

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Archived Entries:
See log24.com.

Selected Past Entries:

Three Days
of the
Saint, 2002

12/6:
Santa vs.
the Volcano


12/7:
Satori at
Pearl Harbor


12/8:
Architecture
of Eternity


Some may feel that the Saint in question is Philip Berrigan, who joined Saburo Ienaga and Ivan Illich on Dec. 6, 2002.

Others may feel that the Saint is Don Ameche, who died on Dec. 6, 1993.

"Things change."

— SHC 12/9/02

Sequel

Stan Rice died on Dec. 9, 2002. A poem of his tells what happened next.

Eight is a Gate

Hollywood producer dies Dec. 14, meets Bach at Heaven's Gate. Realistic comedy.

The Diamond Project

Notes on dance, mortality, and "the still point" on the date of Irene Diamond's death.

Immortal Diamond,
or
NASA Meets Jesus

Thoughts on John O'Hara and G. M. Hopkins for James Joyce's birthday.

Blackbird Singing

The Fred Rogers memorial koan.

Art Wars

LeWitt vs. Witt

Stone, not Wood

best describes St. Peter

The Word

in the Desert

Art Wars:

Fahne Hoch

and

Thorny Crown


O'Hara's Crucifixion


Unity and Reciprocity

in mathematics

The Quality of Diamond


Da Vinci Code ,

Crimson Passion,

Cubist Crucifixion.

Truth and Style


The Line


Bush Mutiny


Symmetry and Change


A Shot at Redemption


Mathematics and Narrative


The Judas Seat


My math sites:

Finitegeometry.org

Finitegeometry.org/sc

The Diamond 16 Puzzle

Notes on Finite Geometry

The Diamond Theorem

The Geometry of Qubits

Diamond Theory

Diamond Theory
in 1937


Galois Geometry

A Four-Color Theorem

Latin-Square Geometry

Walsh Functions

The Fano Plane Revisualized

Knight Moves

The MOG

Inscapes

The Diamond Theory of Truth

Logos and Logic

Literary-Philosophical
Puzzle Notes


A Mathematician's Aesthetics

Reflection Groups in Finite Geometry

A Reflection Group of Order 168

Reflection Groups: The Missing Link

Geometry of
the I Ching


The Diamond Archetype

Modal Theology

The Eightfold Way and Solomon's Seal

Crystal and Dragon in Diamond Theory

Poetry's Bones

Time Fold

War of Ideas

The Proof
and the Lie


Lemniscate
to Langlands


Symmetry Groups

Block Designs

Finite Relativity

Cognitive Blending

Geometry of the 4x4 Square

Visualizing GL(2,p)

Pattern Groups

Ideas and Art

Jung's Imago

Theme and Variations

The Geometry of Logic

Space-Time and a Finite Model

Quilt Geometry

Duality and Symmetry

Polster on Pictures

Kaleidoscope

The Dharwadker Files

Certified Crank

Dharwadker at Wikipedia

Coset Representatives

Archived Journal


Radio I Like

Plano TX KHYI

WAMU 88.5FM

WHRB Harvard

BBC 3

Live365.com


Favorite Books

The Practical Cogitator

Style

The Reader Over Your Shoulder

The Oxford Book of English Prose

Fancies and Goodnights


Other Online Commonplace Books

David Lavery

Peter J. Cameron

A. M. Kuchling

Constant Reader

Identity Theory

J. Jacobs

M. Magnus

ChrisNet

Anonymous

Sites I Read:

Bloglines list

Ping form

SubscriptionsSites I Read

Blogrings
: : : HARVARD : : :
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Sunday, May 11, 2008

Annals of Poetry:

May and Zan

May Swenson, left, and Zan Knudson, right

May Swenson (left)
and Zan Knudson (right)


In memory of poet May Swenson and sports novelist Rozanne Ruth "Zan" Knudson:

Maureen Dowd in today's New York Times:
"It's a similar syndrome to the one Katharine Hepburn's star athlete and her supercilious fiancé have in 'Pat and Mike.'

The fiancé is always belittling Hepburn, so whenever he's in the stands, her tennis and golf go kerflooey. Finally, her manager, played by Spencer Tracy, asks the fiancé to stay away from big matches, explaining, 'You are the wrong jockey for this chick.'

'You know, except when you're around, we got a very valuable piece of property here,' he says, later adding, 'When you're around, she's no good, she's dead, see?'"

Girl in tesseract on cover of  'The Gameplayers of Zan'

Summary of M. A. Foster's
The Gameplayers of Zan:

"Then she has a vision of herself,
enclosed by an unfolded hypercube,
and then an immense screen
behind it covered by complex,
     ever-shifting patterns...."

"Christ! What are
 patterns for?"
-- Amy Lowell   

"Does the word 'tesseract'
mean anything to you?
"
-- Robert A. Heinlein


Saturday, May 10, 2008

ART WARS continued:

MoMA Goes to
Kindergarten

"... the startling thesis of Mr. Brosterman's new book, 'Inventing Kindergarten' (Harry N. Abrams, $39.95): that everything the giants of modern art and architecture knew about abstraction they learned in kindergarten, thanks to building blocks and other educational toys designed by Friedrich Froebel, a German educator, who coined the term 'kindergarten' in the 1830's."

-- "Was Modernism Born
     in Toddler Toolboxes?"
     by Trip Gabriel, New York Times,
     April 10, 1997

RELATED MATERIAL

Figure 1 --
Concept from 1819:

Cubic crystal system
(Footnotes 1 and 2)

Figure 2 --
The Third Gift, 1837:


Froebel's third gift

Froebel's Third Gift

Froebel, the inventor of
kindergarten, worked as
an assistant to the
crystallographer Weiss
mentioned in Fig. 1.

(Footnote 3)

Figure 3 --
The Third Gift, 1906:

Seven partitions of the eightfold cube in a book from 1906

Figure 4 --
Solomon's Cube,
1981 and 1983:


Solomon's Cube - A 1981 design by Steven H. Cullinane

Figure 5 --
Design Cube, 2006:


Design Cube 4x4x4 by Steven H. Cullinane

The above screenshot shows a
moveable JavaScript display
of a space of six dimensions
(over the two-element field).

(To see how the display works,
try the Kaleidoscope Puzzle first.)

For some mathematical background, see
Footnotes:

1. Image said to be after Holden and Morrison, Crystals and Crystal Growing, 1982
2. Curtis Schuh, "The Library: Biobibliography of Mineralogy," article on Mohs
3. Bart Kahr, "Crystal Engineering in Kindergarten" (pdf), Crystal Growth & Design, Vol. 4 No. 1, 2004, 3-9


Friday, May 09, 2008

Mathematics and Narrative, continued:

Cubist Language Game

"Philosophers ponder the idea
 of identity: what it is to give
 something a name on Monday
 and have it respond to 
  that name on Friday...."

-- Bernard Holland 


Monday:

From Log24 on
August 19, 2003
and on
Ash Wednesday, 2004:
a reviewer on
An Instance of the Fingerpost::

"Perhaps we are meant to
 see the story as a cubist
 retelling of the crucifixion."

Related material
for today's anniversay
of the birth of philosopher
Jose Ortega y Gasset:

Cubism as Multispeech

and
Halloween Meditations
(illustrated below)

Cover of 'The Gameplayers of Zan,' by M.A. Foster


"Modern art...
will always have
the masses against it."
-- Ortega y Gasset, 1925   


ART WARS continued:

Kernel of Eternity
continued from April 29

 
The Klein Group: The four elements in four colors, with black points representing the identity

Wikipedia on the Klein group (denoted V, for Vierergruppe):
In this representation, V is a normal subgroup of the alternating group A4 (and also the symmetric group S4) on 4 letters. In fact, it is the kernel of a surjective map from S4 to S3. According to Galois theory, the existence of the Klein four-group (and in particular, this representation of it) explains the existence of the formula for calculating the roots of quartic equations in terms of radicals.
For radicals of another sort, see A Logocentric Meditation, A Mass for Lucero, and Steven Erlanger in The New York Times-- "France Still Divided Over Lessons of 1968 Unrest."

The Klein Group as Kernel
of a Map from S4 to S3:

Portrait of O:  The Klein Group as Kernel in  the Symmetric Group of Degree Four

Click to enlarge.

For those who prefer Galois's
politics to his mathematics,
there is
MAY 68: STREET POSTERS
FROM THE PARIS REBELLION

at London's Southbank Centre
 (May 1 - June 1, 2008).


Thursday, May 08, 2008

ART WARS continued:

Synchronicity,
Part Deux


Footprints at Log24 on the afternoon of May 8, 2008, including two from France

From
"On the Holy Trinity,"
the entry in the 3:20 PM
French footprint:

"...while the scientist sees
everything that happens
in one point of space,
the poet feels
everything that happens
in one point of time...
all forming an
instantaneous and transparent
organism of events...."

-- Vladimir Nabokov

From
"Angel in the Details,"
 the entry in the 3:59 PM
French footprint:

"I dwell in Possibility -
A fairer House than Prose"

-- Emily Dickinson


These, along with this afternoon's
earlier entry, suggest a review
of a third Log24 item, Windmills,
with an actress from France as...

Changing Woman:

"Kaleidoscope turning...

Juliette Binoche in 'Blue'  The 24 2x2 Cullinane Kaleidoscope animated images

Shifting pattern
within unalterable structure..."
-- Roger Zelazny, Eye of Cat  

"When life itself seems lunatic,
who knows where madness lies?"

-- For the source, see 
Joyce's Nightmare Continues.



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