Log24

Tuesday, April 4, 2017

White Cube

Filed under: General — Tags: , — m759 @ 12:21 PM

"Inside the White Cube" —

"We have now reached
a point where we see
not the art but the space first….
An image comes to mind
of a white, ideal space
that, more than any single picture,
may be the archetypal image
of 20th-century art."

http://www.log24.com/log/pix09/090205-cube2x2x2.gif

"Space: what you
damn well have to see."

— James Joyce, Ulysses  

Thursday, February 27, 2014

Sacred Space, continued

Filed under: General — Tags: — m759 @ 11:00 AM

"An image comes to mind of a white, ideal space
‚Äčthat, more than any single picture, may be the
archetypal image of 20th-century art."

— Brian O'Doherty, "Inside the White Cube"

Cube  spaces exist also in mathematics.

Thursday, January 24, 2013

Cube Space

Filed under: General — Tags: — m759 @ 12:24 PM

For the late Cardinal Glemp of Poland,
who died yesterday, some links:

Thursday, December 27, 2012

Object Lesson

Filed under: General,Geometry — Tags: — m759 @ 3:17 AM

Yesterday's post on the current Museum of Modern Art exhibition
"Inventing Abstraction: 1910-1925" suggests a renewed look at
abstraction and a fundamental building block: the cube.

From a recent Harvard University Press philosophical treatise on symmetry—

The treatise corrects Nozick's error of not crediting Weyl's 1952 remarks
on objectivity and symmetry, but repeats Weyl's error of not crediting
Cassirer's extensive 1910 (and later) remarks on this subject.

For greater depth see Cassirer's 1910 passage on Vorstellung :

IMAGE- Ernst Cassirer on 'representation' or 'Vorstellung' in 'Substance and Function' as 'the riddle of knowledge'

This of course echoes Schopenhauer, as do discussions of "Will and Idea" in this journal.

For the relationship of all this to MoMA and abstraction, see Cube Space and Inside the White Cube.

"The sacramental nature of the space becomes clear…." — Brian O'Doherty

Thursday, November 25, 2010

Art Object, continued

Filed under: General,Geometry — m759 @ 4:00 AM

Inside the White Cube

"An image comes to mind of a white, ideal space
 that, more than any single picture, may be
 the archetypal image of 20th-century art."

"May be" —

http://www.log24.com/log/pix10B/101123-plain_cube_200x227.gif

     Image from this journal
     at noon (EST) Tuesday

"The geometry of unit cubes is a meeting point
 of several different subjects in mathematics."
                                    — Chuanming Zong

http://www.log24.com/log/pix10B/101125-ZongAMS.jpg

    (Click to enlarge.)

"A meeting point" —

http://www.log24.com/log/pix10B/101125-NYTobit-UN.jpg

  The above death reportedly occurred "early Wednesday in Beijing."

Another meeting point —

                            http://www.log24.com/log/pix10B/101125-McDonaldLogoSm.jpg

http://www.log24.com/log/pix10B/101125-DayTheEarth.jpg

(Click on logo and on meeting image for more details.)

See also "no ordinary venue."

Saturday, March 6, 2010

Deconstructing Alice

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

Alyssa is  Wonderland

Manohla Dargis in The New York Times  yesterday

"Of course the character of Carroll’s original Alice is evident in each outrageous creation she dreams up in 'Wonderland' and in the sequel, 'Through the Looking-Glass,' which means that she’s a straight man to her own imagination. (She is  Wonderland.)"

Alyssa Milano as a child, with fork

From Inside the White Cube

"The sacramental nature of the space becomes clear, and so does one of the great projective laws of modernism: as modernism gets older, context becomes content. In a peculiar reversal, the object introduced into the gallery 'frames' the gallery and its laws."

From Yogi Berra–

"When you come to a fork in the road, take it."

Related material:  For Baron Samedi and…

Symbology
Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube
Jacques Derrida on the Looking-Glass garden, 'The Time before First,' and Solomon's seal

Sunday, October 11, 2009

Sunday October 11, 2009

Filed under: General,Geometry — m759 @ 7:00 PM
Concepts of Space

Today I revised the illustrations
in Finite Geometry of the
Square and Cube

for consistency in labeling
the eightfold cube.

Related material:

Inside the White Cube:
The Ideology of
the Gallery Space

Dagger Definitions

Thursday, April 2, 2009

Thursday April 2, 2009

Filed under: General,Geometry — Tags: — m759 @ 12:25 PM

Transformative
Hermeneutics

In memory of
physics historian
Martin J. Klein,
(June 25, 1924-
March 28, 2009)

"… in physics itself, there was what appeared, briefly, to be an ending, which then very quickly gave way to a new beginning: The quest for the ultimate building-blocks of the universe had been taken down to the molecular level in nineteenth-century kinetic theory… and finally to the nuclear level in the second and third decades of the twentieth century. For a moment in the 1920s the quest appeared to have ended…. However… this paradise turned out to be, if not exactly a fool's paradise, then perhaps an Eden lost."

No Truth Except in the Details: Essays in Honor of Martin J. Klein, introduction by A.J. Kox and Daniel Siegel, June 25, 1994

New York Times obituary dated April 1, 2009:

"Martin J. Klein, a historian of modern physics…. died Saturday, [March 28, 2009] in Chapel Hill, N.C. He was 84 and lived in Chapel Hill."

Klein edited, among other things, Paul Ehrenfest: Collected Scientific Papers (publ. by North-Holland, Amsterdam, 1959).

"It seems, as one becomes older,
 That the past has another pattern,
 and ceases to be a mere sequence…."

— T. S. Eliot, Four Quartets

A Walsh function and a corresponding finite-geometry hyperplane

"Note that at first, you can see
 the 'arrow of time.'
 After a long period, however,
 the direction of time
 is no longer evident."

— "The Ehrenfest Chains,"
     by Kyle Siegrist, ex. 16

Related material:

"Almost every famous chess game
is a well-wrought urn
in Cleanth Brooks’ sense."

— John Holbo,
Now We See
Wherein Lies the Pleasure

"The entire sequence of moves in these… chapters reminds one– or should remind one– of a certain type of chess problem where the point is not merely the finding of a mate in so many moves, but what is termed 'retrograde analysis'…."

— Vladimir Nabokov, foreword to The Defense

Thursday, February 5, 2009

Thursday February 5, 2009

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM

Through the
Looking Glass:

A Sort of Eternity

From the new president's inaugural address:

"… in the words of Scripture, the time has come to set aside childish things."

The words of Scripture:

9 For we know in part, and we prophesy in part.
10 But when that which is perfect is come, then that which is in part shall be done away.
11 When I was a child, I spake as a child, I understood as a child, I thought as a child: but when I became a man, I put away childish things.
12 For now we see through a glass, darkly, but then face to face: now I know in part; but then shall I know even as also I am known.

 

First Corinthians 13

"through a glass"

[di’ esoptrou].
By means of
a mirror [esoptron]
.

Childish things:

Froebel's third gift, the eightfold cube
© 2005 The Institute for Figuring

 

Photo by Norman Brosterman
fom the Inventing Kindergarten
exhibit at The Institute for Figuring
(co-founded by Margaret Wertheim)

Not-so-childish:

 

Three planes through
the center of a cube
that split it into
eight subcubes:
Cube subdivided into 8 subcubes by planes through the center
Through a glass, darkly:

A group of 8 transformations is
generated by affine reflections
in the above three planes.
Shown below is a pattern on
the faces of the 2x2x2 cube
 that is symmetric under one of
these 8 transformations–
a 180-degree rotation:

Design Cube 2x2x2 for demonstrating Galois geometry

(Click on image
for further details.)

But then face to face:

A larger group of 1344,
rather than 8, transformations
of the 2x2x2 cube
is generated by a different
sort of affine reflections– not
in the infinite Euclidean 3-space
over the field of real numbers,
but rather in the finite Galois
3-space over the 2-element field.

Galois age fifteen, drawn by a classmate.

Galois age fifteen,
drawn by a classmate.

These transformations
in the Galois space with
finitely many points
produce a set of 168 patterns
like the one above.
For each such pattern,
at least one nontrivial
transformation in the group of 8
described above is a symmetry
in the Euclidean space with
infinitely many points.

For some generalizations,
see Galois Geometry.

Related material:

The central aim of Western religion–

 

 

"Each of us has something to offer the Creator...
the bridging of
 masculine and feminine,
 life and death.
It's redemption.... nothing else matters."
-- Martha Cooley in The Archivist (1998)

The central aim of Western philosophy–

 Dualities of Pythagoras
 as reconstructed by Aristotle:
  Limited Unlimited
  Odd Even
  Male Female
  Light Dark
  Straight Curved
  ... and so on ....

"Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy."

— Jamie James in The Music of the Spheres (1993)

"In the garden of Adding
live Even and Odd…
And the song of love's recision
is the music of the spheres."

— The Midrash Jazz Quartet in City of God, by E. L. Doctorow (2000)

A quotation today at art critic Carol Kino's website, slightly expanded:

"Art inherited from the old religion
the power of consecrating things
and endowing them with
a sort of eternity;
museums are our temples,
and the objects displayed in them
are beyond history."

— Octavio Paz,"Seeing and Using: Art and Craftsmanship," in Convergences: Essays on Art and Literature (New York: Harcourt Brace Jovanovich 1987), 52 

From Brian O'Doherty's 1976 Artforum essays– not on museums, but rather on gallery space:

"Inside the White Cube"

"We have now reached
a point where we see
not the art but the space first….
An image comes to mind
of a white, ideal space
that, more than any single picture,
may be the archetypal image
of 20th-century art."

http://www.log24.com/log/pix09/090205-cube2x2x2.gif

"Space: what you
damn well have to see."

— James Joyce, Ulysses  

Tuesday, January 6, 2009

Tuesday January 6, 2009

Filed under: General,Geometry — m759 @ 12:00 AM
Archetypes, Synchronicity,
and Dyson on Jung

The current (Feb. 2009) Notices of the American Mathematical Society has a written version of Freeman Dyson’s 2008 Einstein Lecture, which was to have been given in October but had to be canceled. Dyson paraphrases a mathematician on Carl Jung’s theory of archetypes:

“… we do not need to accept Jung’s theory as true in order to find it illuminating.”

The same is true of Jung’s remarks on synchronicity.

For example —

Yesterday’s entry, “A Wealth of Algebraic Structure,” lists two articles– each, as it happens, related to Jung’s four-diamond figure from Aion as well as to my own Notes on Finite Geometry. The articles were placed online recently by Cambridge University Press on the following dates:

R. T. Curtis’s 1974 article defining his Miracle Octad Generator (MOG) was published online on Oct. 24, 2008.

Curtis’s 1987 article on geometry and algebraic structure in the MOG was published online on Dec. 19, 2008.

On these dates, the entries in this journal discussed…

Oct. 24:
Cube Space, 1984-2003

Material related to that entry:

Dec. 19:
Art and Religion: Inside the White Cube

That entry discusses a book by Mark C. Taylor:

The Picture in Question: Mark Tansey and the Ends of Representation (U. of Chicago Press, 1999).

In Chapter 3, “Sutures of Structures,” Taylor asks —

“What, then, is a frame, and what is frame work?”

One possible answer —

Hermann Weyl on the relativity problem in the context of the 4×4 “frame of reference” found in the above Cambridge University Press articles.

“Examples are the stained-glass
windows of knowledge.”
— Vladimir Nabokov 

Thursday, May 22, 2008

Thursday May 22, 2008

Filed under: General,Geometry — m759 @ 9:00 AM
The Undertaking:
An Exercise in
Conceptual Art

I Ching hexagram 54: The Marrying Maiden

Hexagram 54:
THE JUDGMENT

Undertakings bring misfortune.
Nothing that would further.

The image “http://www.log24.com/log/pix08/080522-Irelandslide1.jpg” cannot be displayed, because it contains errors.

Brian O’Doherty, an Irish-born artist,
before the [Tuesday, May 20] wake
of his alter ego* ‘Patrick Ireland’
on the grounds of the
Irish Museum of Modern Art.”
New York Times, May 22, 2008    

THE IMAGE

Thus the superior man
understands the transitory
in the light of
the eternity of the end.

Another version of
the image:

Images of time and eternity in memory of Michelangelo
See 2/22/08
and  4/19/08.


Related material:

Michael Kimmelman in today’s New York Times

“An essay from the ’70s by Mr. O’Doherty, ‘Inside the White Cube,’ became famous in art circles for describing how modern art interacted with the gallery spaces in which it was shown.”

Brian O’Doherty, “Inside the White Cube,” 1976 Artforum essays on the gallery space and 20th-century art:

“The history of modernism is intimately framed by that space. Or rather the history of modern art can be correlated with changes in that space and in the way we see it. We have now reached a point where we see not the art but the space first…. An image comes to mind of a white, ideal space that, more than any single picture, may be the archetypal image of 20th-century art.”

An archetypal image

THE SPACE:

The Eightfold Cube: The Beauty of Klein's Simple Group

A non-archetypal image

THE ART:

Jack in the Box, by Natasha Wescoat

Natasha Wescoat, 2004
See also Epiphany 2008:

How the eightfold cube works

“Nothing that would further.”
— Hexagram 54

Lear’s fool:

 …. Now thou art an 0
without a figure. I am better
than thou art, now. I am a fool;
thou art nothing….

“…. in the last mystery of all the single figure of what is called the World goes joyously dancing in a state beyond moon and sun, and the number of the Trumps is done.  Save only for that which has no number and is called the Fool, because mankind finds it folly till it is known.  It is sovereign or it is nothing, and if it is nothing then man was born dead.”

The Greater Trumps,
by Charles Williams, Ch. 14

* For a different, Jungian, alter ego, see Irish Fourplay (Jan. 31, 2003) and “Outside the Box,” a New York Times review of O’Doherty’s art (featuring a St. Bridget’s Cross) by Bridget L. Goodbody dated April 25, 2007. See also Log24 on that date.

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