Log24

Saturday, May 10, 2014

Happy Birthday

Filed under: General — m759 @ 12:00 pm

To Bel Kaufman, author of
Up the Down Staircase.

IMAGE- Borofsky's 'Four Gods' and related structures

Click image for some backstory.

Tuesday, August 7, 2012

The Space of Horizons

Filed under: General,Geometry — Tags: , , — m759 @ 4:00 am

"In the space of horizons that neither love nor hate"
— Wallace Stevens, "Things of August"

Seven years ago yesterday—

IMAGE- 3x3 grid related to Borofsky's 'Four Gods'

For some context, see Rosetta Stone as a Metaphor.

Related material from the University of Western Australia

Projective plane of order 3

(The four points on the curve
at the right of the image are
the points on the line at infinity.)

Art critic Robert Hughes,  who nearly died in Western
Australia in a 1999 car crash, actually met his death
yesterday at Calvary Hospital in the Bronx.

See also Hughes on "slow art" in this journal.

Wednesday, August 1, 2012

Elementary Finite Geometry

Filed under: General,Geometry — Tags: , , , — m759 @ 7:16 pm

I. General finite geometry (without coordinates):

A finite affine plane of order has n^2 points.

A finite projective plane of order n  has n^2 + n + 1 

points because it is formed from an order-n finite affine 

plane by adding a line at infinity  that contains n + 1 points.

Examples—

Affine plane of order 3

Projective plane of order 3

II. Galois finite geometry (with coordinates over a Galois field):

A finite projective Galois plane of order n has n^2 + n + 1

points because it is formed from a finite affine Galois 3-space

of order n with n^3 points by discarding the point (0,0,0) and 

identifying the points whose coordinates are multiples of the

(n-1) nonzero scalars.

Note: The resulting Galois plane of order n has 

(n^3-1)/(n-1)= (n^2 + n + 1) points because 

(n^2 + n + 1)(n – 1) =

(n^3 + n^2 + n – n^2 – n – 1) = (n^3 – 1) .
 

III. Related art:

Another version of a 1994 picture that accompanied a New Yorker
article, "Atheists with Attitude," in the issue dated May 21, 2007:

IMAGE- 'Four Gods,' by Jonathan Borofsky

The Four Gods  of Borofsky correspond to the four axes of 
symmetry
  of a square and to the four points on a line at infinity 
in an order-3 projective plane as described in Part I above.

Those who prefer literature to mathematics may, if they like,
view the Borofsky work as depicting

"Blake's Four Zoas, which represent four aspects
of the Almighty God" —Wikipedia

Monday, May 21, 2007

Monday May 21, 2007

Filed under: General — Tags: , — m759 @ 4:48 am
Down the
Up Staircase

Commentary on a
Jonathan Borofsky
painting in the
May 21 New Yorker:

IMAGE- Borofsky's 'Four Gods' and related structures
 
Commentary

"… Mondrian and Malevich
are not discussing canvas
or pigment or graphite
or any other form of matter.
They are talking about about
Being or Mind or Spirit.
From their point of view,
the grid is a staircase
to the Universal…."

Rosalind Krauss
 

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