Saturday, November 10, 2012

Descartes Field of Dreams

Filed under: General,Geometry — m759 @ 2:01 PM

(A prequel to Galois Field of Dreams)

The opening of Descartes' Dream ,
by Philip J. Davis and Reuben Hersh—

"The modern world,
our world of triumphant rationality,
began on November 10, 1619,
with a revelation and a nightmare."

For a revelation, see Battlefield Geometry.

For a nightmare, see Joyce's Nightmare.

Some later work of Descartes—

From "What Descartes knew of mathematics in 1628,"
by David Rabouin, CNRS-Univ. Paris Diderot,
Historia Mathematica , Volume 37, Issue 3,
Contexts, emergence and issues of Cartesian geometry,
August 2010, pages 428–459 —

Fig. 5. How to represent the difference between white, blue, and red
according to Rule XII [from Descartes, 1701, p. 34].

A translation —

The 4×4 array of Descartes appears also in the Battlefield Geometry posts.
For its relevance to Galois's  field of dreams, see (for instance) block designs.

Friday, June 4, 2010

ART WARS continued

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

Today's New York Times

Art Review

Painting Thin Air, Sometimes in Bright Blue

(“Yves Klein: With the Void, Full Powers”
  runs through Sept. 12 at the Hirshhorn.)

Related material—

Search this journal for klein + paris.

See also Art Space (May 22, 2010)—

Box symbol

Pictorial version
of Hexagram 20,
Contemplation (View)


Wednesday, March 11, 2009

Wednesday March 11, 2009

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM
Sein Feld
in Translation
(continued from
May 15, 1998)

The New York Times March 10–
 "Paris | A Show About Nothing"–

'Voids, a Retrospective,' at the Centre Pompidou in Paris. Photo from NY Times.

The Times describes one of the empty rooms on exhibit as…

"… Yves Klein’s 'La spécialisation de la sensibilité à l’état matière première en sensibilité picturale stabilisée, Le Vide' ('The Specialization of Sensibility in the Raw Material State Into Stabilized Pictorial Sensibility, the Void')"

This is a mistranslation. See "An Aesthetics of Matter" (pdf), by Kiyohiko Kitamura and Tomoyuki Kitamura, pp. 85-101 in International Yearbook of Aesthetics, Volume 6, 2002

"The exhibition «La spécialisation de la sensibilité à l’état matière-première en sensibilité picturale stabilisée», better known as «Le Vide» (The Void) was held at the Gallery Iris Clert in Paris from April 28th till May 5th, 1955." –p. 94

"… «Sensibility in the state of prime matter»… filled the emptiness." –p. 95

Kitamura and Kitamura translate matière première correctly as "prime matter" (the prima materia of the scholastic philosophers) rather than "raw material." (The phrase in French can mean either.)

Related material:
The Diamond Archetype and
The Illuminati Diamond.

The link above to
prima materia
is to an 1876 review
by Cardinal Manning of
a work on philosophy
by T. P. Kirkman, whose
"schoolgirl problem" is
closely related to the
finite space of the
 diamond theorem.

Friday, May 9, 2008

Friday May 9, 2008

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

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

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