Log24

Friday, August 20, 2021

Space Note

Filed under: General — Tags: — m759 @ 7:50 pm

"Consider the six-dimensional vector space ( 𝔽2 )6
over the two-element field 𝔽2 ."

— Page 23 of "The Universal Kummer Threefold,"
arXiv:1208.1229v3, 12 June 2013, by Qingchun Ren,
Steven V. Sam, Gus Schrader, and Bernd Sturmfels.

An illustration of that space from 1981 —

IMAGE- 'Solid Symmetry' by Steven H. Cullinane, Dec. 24, 1981

The above recollection of the Kummer Threefold  remark was suggested by
recent posts now tagged Smallfield . . .

"Third Man – an elderly American railway bum,
a schizophrenic, speaks with a Southern drawl"

"Art to which I fix my celebrated signature."

— "Third Man" in Victor Snaith's play "Changing Stations"

If we read the above "art" as  a scythe blade to which the "signature" —
Snaith ("the crooked handle or shaft of a scythe") — is attached,
an image of the late art critic Robert Hughes comes to mind:

That image of Hughes appeared here in a post of June 17, 2015 —
"Slow Art, Continued" — that also referenced the Kummer Threefold
paper above.

Monday, August 17, 2020

The Silence at the Core

Filed under: General — Tags: — m759 @ 10:19 pm

The title is a phrase by Robert Hughes from the previous post.

Sunday, January 1, 2017

The Unhurried Curve

Filed under: General — Tags: , , — m759 @ 3:33 pm

From today's previous post —

"The unhurried curve got me. 
It was like the horizon of a world
that made a non-world of
all of the space outside it."

— Peter Schjeldahl, "Postscript: Ellsworth Kelly,"
The New Yorker , December 30, 2015

Related figures —

Art critic Robert Hughes in "The Space of Horizons,"
a Log24 post of August 7, 2012:

Religion writer Huston Smith, who reportedly died
on December 30, 2016:

Wednesday, June 17, 2015

Slow Art, Continued

Filed under: General,Geometry — Tags: , , — m759 @ 10:01 am

The title of the previous post, "Slow Art," is a phrase
of the late art critic Robert Hughes.

Example from mathematics:

  • Göpel tetrads as subsets of a 4×4 square in the classic
    1905 book Kummer's Quartic Surface  by R. W. H. T. Hudson.
    These subsets were constructed as helpful schematic diagrams,
    without any reference to the concept of finite  geometry they
    were later to embody.
     
  • Göpel tetrads (not named as such), again as subsets of
    a 4×4 square, that form the 15 isotropic projective lines of the
    finite projective 3-space PG(3,2) in a note on finite geometry
    from 1986 —

    Göpel tetrads in an inscape, April 1986

  • Göpel tetrads as these figures of finite  geometry in a 1990
    foreword to the reissued 1905 book of Hudson:

IMAGE- Galois geometry in Wolf Barth's 1990 foreword to Hudson's 1905 'Kummer's Quartic Surface'

Click the Barth passage to see it with its surrounding text.

Related material:

Wednesday, May 13, 2015

Space

Filed under: General,Geometry — Tags: , — m759 @ 2:00 pm

Notes on space for day 13 of May, 2015 —

The 13 symmetry axes of the cube may be viewed as
the 13 points of the Galois projective space PG(2,3).
This space (a plane) may also be viewed as the nine points
of the Galois affine space AG(2,3) plus the four points on
an added "line at infinity."

Related poetic material:

The ninefold square and Apollo, as well as …

http://www.log24.com/log/pix11A/110426-ApolloAndDionysus.jpg

Wednesday, June 19, 2013

Midnight in the Garden

Filed under: General — Tags: — m759 @ 12:00 am

(Continued)

See Robert Hughes in this journal.

Wednesday, April 10, 2013

Caution: Slow Art

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

"Of course, DeLillo being DeLillo,
it’s the deeper implications of the piece —
what it reveals about the nature of
film, perception and time — that detain him."

— Geoff Dyer, review of Point Omega

Related material:

A phrase of critic Robert Hughes,
"slow art," in this journal.

A search for that phrase yields the following
figure from a post on DeLillo of Oct. 12, 2011:

The 3x3 square

The above 3×3 grid is embedded in a 
somewhat more sophisticated example
of conceptual art from April 1, 2013:

IMAGE- A Galois-geometry key to Desargues' theorem

Update of April 12, 2013

The above key uses labels from the frontispiece
to Baker's 1922 Principles of Geometry, Vol. I ,
that shows a three-triangle version of Desargues's theorem.

A different figure, from a site at National Tsing Hua University,
shows the three triangles of Baker's figure more clearly:

IMAGE- Desargues' theorem with three triangles (the large Desargues configuration) and Galois-geometry version

Wednesday, April 3, 2013

Museum Piece

Filed under: General,Geometry — Tags: — m759 @ 3:01 pm

Roberta Smith in 2011 on the American Folk Art Museum (see previous post):

"It could be argued that we need a museum of folk art
the way we need a museum of modern art,
to shine a very strong, undiluted light on
a very important achievement."

Some other aesthetic remarks:

"We have had a gutful of fast art and fast food.
What we need more of is slow art: art that holds time
as a vase holds water: art that grows out of modes
of perception and whose skill and doggedness
make you think and feel; art that isn't merely sensational,
that doesn't get its message across in 10 seconds,
that isn't falsely iconic, that hooks onto something
deep-running in our natures. In a word, art that is
the very opposite of mass media. For no spiritually
authentic art can beat mass media at their own game."

— Robert Hughes, speech of June 2, 2004,
     quoted here June 15, 2007.

Perhaps, as well as museums of modern art and of folk art,
we need a Museum of Slow Art. 

One possible exhibit, from this journal Monday:

The diagram on the left is from 1922.  The 20 small squares at right
that each have 4 subsquares darkened were discussed, in a different
context, in 1905. They were re-illustrated, in a new context
(Galois geometry), in 1986. The "key" square, and the combined
illustration, is from April 1, 2013. For deeper background, see
Classical Geometry in Light of Galois Geometry.

Those who prefer faster art may consult Ten Years After.

Thursday, March 7, 2013

Ten Years After

Filed under: General,Geometry — m759 @ 8:00 am

Rock guitarist Alvin Lee, a founder of
the band Ten Years After , died
on March 6, 2013 (Michelangelo's
birthday). In his memory, a figure
from a post Ten Years Before —

Plato's reported motto for his Academy:
"Let no one ignorant of geometry enter."

For visual commentary by an artist ignorant
of geometry, see a work by Sol LeWitt.

For verbal commentary by an art critic  ignorant
of geometry, see a review of LeWitt by
Robert Hughes—

"A Beauty Really Bare" (TIME, Feb. 6, 2001).

See also Ten Years Group and Four Gods.

Monday, August 13, 2012

Something Between

Filed under: General — m759 @ 6:07 pm

"I am a skeptic to whom the idea that a benign God 
created us and watches over us is something between
a fairy story and a bad joke." 

— The late art critic Robert Hughes in Things I Didn't Know*

A followup to this afternoon's previous Amy Adams post—

"Here was finality indeed, and cleavage!" 

             — Under the Volcano

     * Vintage paperback, December 2007, page 7

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.

Tuesday, October 11, 2011

24 Hour DeLillo

Filed under: General — m759 @ 12:00 pm

Review of DeLillo's novel Point Omega—

"One difference between art and entertainment has to do with the speed of perception. Art deliberately slows and complicates reading, hearing, and/or viewing so that you’re challenged to re-think and re-feel form and experience. Entertainment deliberately accelerates and simplifies them so that you don’t have to think about or feel very much of anything at all except, perhaps, the adrenalin rush before dazzling spectacle. Although, of course, there can be myriad gradations between the former and latter, in their starkest articulation we’re talking about the distance between, say, David Foster Wallace’s Infinite Jest  and Dan Brown’s The Lost Symbol…."

— Lance Olsen, March 1, 2010, in The Quarterly Conversation

Robert Hughes on fast and slow art—

"We have had a gutful of fast art and fast food. What we need more of is slow art: art that holds time as a vase holds water: art that grows out of modes of perception and whose skill and doggedness make you think and feel; art that isn't merely sensational, that doesn't get its message across in 10 seconds, that isn't falsely iconic, that hooks onto something deep-running in our natures. In a word, art that is the very opposite of mass media. For no spiritually authentic art can beat mass media at their own game."

– Speech of June 1, 2004

Log24 on art speeds—

A Study in Art Education (June 15, 2007)

Twenty-four (March 13, 2011)

Friday, June 15, 2007

Friday June 15, 2007

Filed under: General,Geometry — Tags: , , — m759 @ 1:00 pm
A Study in
Art Education

Rudolf Arnheim, a student of Gestalt psychology (which, an obituary notes, emphasizes "the perception of forms as organized wholes") was the first Professor of the Psychology of Art at Harvard.  He died at 102 on Saturday, June 9, 2007.

The conclusion of yesterday's New York Times obituary of Arnheim:

"… in The New York Times Book Review in 1986, Celia McGee called Professor Arnheim 'the best kind of romantic,' adding, 'His wisdom, his patient explanations and lyrical enthusiasm are those of a teacher.'"

A related quotation:

"And you are teaching them a thing or two about yourself. They are learning that you are the living embodiment of two timeless characterizations of a teacher: 'I say what I mean, and I mean what I say' and 'We are going to keep doing this until we get it right.'"

— Tools for Teaching

Here, yet again, is an illustration that has often appeared in Log24– notably, on the date of Arnheim's death:
 

The 3x3 square

Related quotations:

"We have had a gutful of fast art and fast food. What we need more of is slow art: art that holds time as a vase holds water: art that grows out of modes of perception and whose skill and doggedness make you think and feel; art that isn't merely sensational, that doesn't get its message across in 10 seconds, that isn't falsely iconic, that hooks onto something deep-running in our natures. In a word, art that is the very opposite of mass media. For no spiritually authentic art can beat mass media at their own game."

— Robert Hughes, speech of June 2, 2004

"Whether the 3×3 square grid is fast art or slow art, truly or falsely iconic, perhaps depends upon the eye of the beholder."

— Log24, June 5, 2004

If the beholder is Rudolf Arnheim, whom we may now suppose to be viewing the above figure in the afterlife, the 3×3 square is apparently slow art.  Consider the following review of his 1982 book The Power of the Center:

"Arnheim deals with the significance of two kinds of visual organization, the concentric arrangement (as exemplified in a bull's-eye target) and the grid (as exemplified in a Cartesian coordinate system)….

It is proposed that the two structures of grid and target are the symbolic vehicles par excellence for two metaphysical/psychological stances.  The concentric configuration is the visual/structural equivalent of an egocentric view of the world.  The self is the center, and all distances exist in relation to the focal spectator.  The concentric arrangement is a hermetic, impregnable pattern suited to conveying the idea of unity and other-worldly completeness.  By contrast, the grid structure has no clear center, and suggests an infinite, featureless extension…. Taking these two ideal types of structural scaffold and their symbolic potential (cosmic, egocentric vs. terrestrial, uncentered) as given, Arnheim reveals how their underlying presence organizes works of art."

— Review of Rudolf Arnheim's The Power of the Center: A Study of Composition in the Visual Arts (Univ. of Calif. Press, 1982). Review by David A. Pariser, Studies in Art Education, Vol. 24, No. 3 (1983), pp. 210-213

Arnheim himself says in this book (pp. viii-ix) that "With all its virtues, the framework of verticals and horizontals has one grave defect.  It has no center, and therefore it has no way of defining any particular location.  Taken by itself, it is an endless expanse in which no one place can be distinguished from the next.  This renders it incomplete for any mathematical, scientific, and artistic purpose.  For his geometrical analysis, Descartes had to impose a center, the point where a pair of coordinates [sic] crossed.  In doing so he borrowed from the other spatial system, the centric and cosmic one."

Students of art theory should, having read the above passages, discuss in what way the 3×3 square embodies both "ideal types of structural scaffold and their symbolic potential."

We may imagine such a discussion in an afterlife art class– in, perhaps, Purgatory rather than Heaven– that now includes Arnheim as well as Ernst Gombrich and Kirk Varnedoe.

Such a class would be one prerequisite for a more advanced course– Finite geometry of the square and cube.

Saturday, June 26, 2004

Saturday June 26, 2004

Filed under: General — Tags: — m759 @ 3:03 am
Deep Game

The entry Ado of June 25, 2004 contains a link to an earlier entry, A Form, continued, of June 5, 2004.  This in turn contains a link to a site by Wolfgang Wildgen which contains the following:

“Historically, we may say that the consequence of Bruno’s parallel work on cosmology and artificial memory is a new model of semantic fields which was so radical in its time that the first modern followers (although ignorant of this tradition) are the Von-Neumann automata and the neural net systems of the 1980s (cf. Wildgen 1998: 39, 237f).”

Wildgen, W. 1998. Das kosmische Gedächtnis. Kosmologie, Semiotik und Gedächtniskunst im Werke von Giordano Bruno. Frankfurt/Bern: Lang.

For an applet illustrating
the above remarks, see

Gedächtniskunst:

The image “http://www.log24.com/log/pix04A/040626-Neighbors.gif” cannot be displayed, because it contains errors. 
Figure A

Neighborhood in a
Cellular Automaton
by Adam Campbell

For more of the Gedächtnis
in this Kunst, see the following
Google search on shc759:

The image “http://www.log24.com/log/pix04A/040626-Search.jpg” cannot be displayed, because it contains errors.

Figure B

Note that the reference to “forerunners” in fig. B occurs in a journal entry of June 12, 2002. See also the reference to a journal entry of the following day, June 13, 2002, in last Tuesday’s Dirty Trick.

Those who have viewed Campbell’s applet (see  fig. A) may appreciate the following observation of poet and Dante translator Robert Pinsky:

“… a grid, and a flow–
that is the essence of terza rima….”

— Poetry, Computers, and Dante’s Inferno

For some related remarks
on the muses and epic poetry,
see a paper on Walter Benjamin:

“Here the memory (Gedächtnis) means
‘the epic faculty par excellence.’ “
(Benjamin, Der Erzähler, 1936: in
Gesammelte Schriften, 1991, II.2, 453)

— Benjamin on Experience,
Narrative, and History (pdf)

One possible connection to the muses is, as noted in a link in yesterday’s Ado, via George Balanchine.

An apt link to epic poetry (aside from the reference to Dante above) is, via the June 12, 2002, entry, to the epic The Gameplayers of Zan (the third reference in fig. B above).

The applet linked below fig. A very nicely illustrates the “structured chaos” of a space described by automata theory.  For a literary approach to such a space, see the Gameplayers entry.

For the benefit of art critic Robert Hughes, who recently made a distinction between “fast art” and “slow art,” the Campbell applet has a convenient speed control.
 

Saturday, June 5, 2004

Saturday June 5, 2004

Filed under: General,Geometry — Tags: — m759 @ 11:11 am
A Form,
 continued…

Some cognitive uses
of the 3×3 square
are discussed in

From Lullus to Cognitive Semantics:
The Evolution of a Theory of Semantic Fields

by Wolfgang Wildgen and in

Another Page in the Foundation of Semiotics:
A Book Review of On the Composition of Images, Signs & Ideas, by Giordano Bruno…
by Mihai Nadin

“We have had a gutful of fast art and fast food. What we need more of is slow art: art that holds time as a vase holds water: art that grows out of modes of perception and whose skill and doggedness make you think and feel; art that isn’t merely sensational, that doesn’t get its message across in 10 seconds, that isn’t falsely iconic, that hooks onto something deep-running in our natures. In a word, art that is the very opposite of mass media. For no spiritually authentic art can beat mass media at their own game.”

— Robert Hughes, speech of June 2, 2004

Whether the 3×3 square grid is fast art or slow art, truly or falsely iconic, perhaps depends upon the eye of the beholder.

For a meditation on the related 4×4 square grid as “art that holds time,” see Time Fold.

Thursday, March 6, 2003

Thursday March 6, 2003

Filed under: General,Geometry — Tags: , — m759 @ 2:35 am

ART WARS:

Geometry for Jews

Today is Michelangelo's birthday.

Those who prefer the Sistine Chapel to the Rothko Chapel may invite their Jewish friends to answer the following essay question:

Discuss the geometry underlying the above picture.  How is this geometry related to the work of Jewish artist Sol LeWitt? How is it related to the work of Aryan artist Ernst Witt?  How is it related to the Griess "Monster" sporadic simple group whose elements number 

808 017 424 794 512 875 886 459 904 961 710 757 005 754 368 000 000 000?

Some background:

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