Math is more clever than chance.

Another two-dimensional diagram is animated. I let math determine the initial orientation of the image in each cell, as always. Then random number generation takes over during the animation, determining which adjacent cell to move into empty cells. The total set is processed serially.

Peter Schjeldahl, writing for The New Yorker, quoted Gerhard Richter: "Chance is 'more clever than I'". ("Many-colored Glass, Gerhard Richter and Sigmar Polke do windows.", by Peter Schjeldahl, The New Yorker, May 12, 2008.) I think math is more clever than chance, which is more clever than I. Chance, when using a random number generator, is after all math.

Jacob's Ladder

Another animated, greatest common divisor, arc:

The diagram below is a necessary part of the programming process. There are four possible orientations for images in a single grid cell. There are sixteen possible transformations from an image cell to an empty cell.

Entropy

Here's another new animated GCD image. I think the animated versions have something to do with entropy. They each start in a very ordered state, having been plotted according to mathematical formulas. Then they change, randomly, so they no longer represent the original formula(s), and it's almost impossible to return to the ordered state.

New Animated GCD Arcs

Here are a couple of new animated GCD images: 1 and 2. These are based on the GCD Arcs Project, requiring minor modifications to a similar animation with quarter-circles.

Technology and Art

“Bird in the Wood #2” was painted in 1964 by Walter Darby Bannard, before he quit minimalist painting. Currently it hangs high on a wall of the Portland Museum of Art opposite Frank Stella’s “Eskimo Curlew”, done in 1976. Besides the bird titles, I believe they share a common method of development. In the Stella, three of the shapes are enlarged tracings of draftsman’s templates — French curves. The shapes are not used as draftsmen or technical illustrators would use them, to create smooth complex curves out of ellipses, hyperbolas, and parabolas. They’re simply traced, in whole. The Bannard painting is three abutting shapes on a large flat field, or one shape segmented into three. I am almost certain that Bannard came up with his design by tracing around a protractor. The outer shape on two sides is the inner tracing of a protractor. Like Stella, he didn’t use the tool as it was intended; he simply traced a piece of it.

If I’m correct about “Bird in the Wood #2”, Stella and Bannard both used technical illustration tools in non-technical ways. There’s nothing particularly interesting about the shapes. There are really interesting things you can do with the templates if you use them as they’re intended. Stella and Bannard just picked up what was lying around, and traced them.

In 1966, Bannard wrote an article for Artforum, “Color, Paint, and Present-Day Painting” [Artforum, Vol. 4, (April 1966) pp. 35 - 37.]. This may be as close as Bannard ever got in his writing to anything technical. After describing the Munsell color system, Bannard says he has his paint mixed at a commercial paint store.

“Bird in the Wood #2” shows that at least Bannard owned a protractor, though he apparently didn’t care to use it as it’s intended. Sometime between 1965 and 1980 Bannard changed styles, and was able to put his technical drawing tools away for good. Based on his paintings and a few of his articles, I’d guess Bannard was averse to things technical.

In 1968, Bannard slammed Jack Burnham in Art Forum for Burnham’s article in a previous issue, “Systems Aesthetics”.

Bannard says:

“What’s wrong is expressed by the notion that pervades every sentence: there’s a good new modern revolutionary systems esthetic way to make art and it is beating the dickens out of the bad old outmoded establishment formalist way to make art.” [See Letter to the Editor (1968). Artforum, Vol. 7, (November, 1968) p. 4.]

In 1969, Bannard reviewed Burnham’s book, Beyond Modern Sculpture.

Bannard says:

“Every page exudes the notion that certain forms, materials and processes guarantee art quality and conversely certain other forms, materials and processes guarantee artistic failure, that old methods and materials are no longer suitable for good art and that good sculpture from now on must consist only of the particular materials, organizations, couplings, successions, formal variety, arrangements and appearances described in Beyond Modern Sculpture.” [See “Beyond Modern Sculpture” by Jack Burnham (1969), in Artforum, Vol. 7, (May 1969) pp. 70 - 71.]

Donald Judd also slammed Burnham. [See Judd, “Complaints: part I”, (1975) Complete Writings. Halifax: The Press of the Nova Scotia College of Art and Design, ISBN-10: 0919616429. ISBN-13: 978-0919616424. Page 198.]

Judd wrote:

“A good example of baloney and of silly futurism is this:

[quoting Burnham] ‘The shifting psychology of sculpture invention closely parallels the inversion taking place between technics and man: as the craftsman slowly withdraws his personal feelings from the constructed object, the object gradually gains its independence from its human maker; in time it seeks a life of its own through self-reproduction.’ (Burnham’s italics.)

[back to Judd.] “I dislike very much this sort of sloppy correlation of such highly different activities as science and art, the careless and general history and the mystical projection of the future.”

James Croak summarized 20^th century art history in these four words: “Duchamp won, Picasso lost.” (I'm sure Picasso cried all the way to the bank.) In my very limited little art world, Jack Burnham also won, and Walter Darby Bannard lost. I'm almost certainly in the minority on this, but not necessarily alone. See “All Systems Go: Recovering Jack Burnham’s ‘Systems Aesthetics’”, by Luke Skrebowski, Tate Papers Spring 2006.

For forty years Bannard has pressed his case. See: “Artbroken: What Art Is and How We Stopped Making It”, a talk prepared for the Foundations in Art: Theory & Education (FATE) 2007 Conference, Milwaukee. In this speech, Bannard says: “When we, as artists, make our art dependent on ideas or things or theories or fashions or moral lessons or ‘truth’, or any nonvisual external, we do not enrich it, we cut it off from the deep internal sources that nourish it.”

I thoroughly enjoy reading this speech, but I disagree with that last statement, and I also find a lot of truth in Burnham’s “Systems Aesthetics”. Here’s my art, dependent on mathematical ideas, and definitely on nonvisual, external systems — programming, computers, the web. It’s most definitely not cut it off from deep internal sources, since it is also based ultimately on the grid. I use math and programming simply, paraphrasing Bannard, to do something new to make my art better. (See Bannard, Monster of Irony (1990), New York Times, October 14, 1990.)

I think Burnham is winning in that there is a lot of systems theory art around and it still shows the greatest potential to me; but I also think, and I suppose Bannard would agree, that the quality of art that has come out of systems aesthetics is usually bad. Systems aesthetics could have flourished if its practitioners were not so full of what Bannard calls “the intimidating jargon, blustering self-importance and beguiling mystique of the theories and so called ‘issues’ that are thrown, like so much trash, onto the path that art must take.”

Jess and Persian Narrative Painting

My previous blog was inspired by the exhibition, Jess, at the Cooley. Having just seen Persian Narrative Painting at the Portland Art Museum, I'm aware of similarities.

Jess produced numerous collages for books and magazines. He worked with poets and writers to produce limited-editions. Many of his collages were for these publications. The Persian paintings are, I think, entirely from manuscripts.

Jess' collages were often dense, structurally chaotic compositions. They resemble some of the Persian paintings in the way that a myriad of perspectives and sub narratives are combined in one image.

Jess appropriated the work of artists and photographers through the collage. In a sense, his collages were a group effort, with individual parts completed by a team, and with Jess taking the task of composing all the parts into a whole. Likewise, the Persian paintings were typically a group effort, with different individuals specializing in things like figures, animals, patterns, or foliage.

Jess' paintings in which he meticulously painted over prints compare in intricacy and detail with the Persian prints. The coloration is even similar.

Jess at Cooley

If you are in Portland, go see the Jess Collins exhibition at Reed College's Cooley Art Gallery (until 7/20/08). From Cooley curator and Director, Stephanie Snyder, I learned that Jess began his adult career as a chemist. He abandoned the avocation, but funneled a methodical, scientific approach into his art process. He collected and filed images and materials for his art using a highly organized system. He mixed his own paints. He appears to have regularly invented and experimented with techniques. His prior career in science obviously informed his art.

The common career path for an artist starts early, and leads without interruption through a lifelong pursuit. If they wander or train for another career, they usually settle with art early in life, certainly before thirty. Many are forced into something else to get by at least for a while (Stella). Sometimes they work in advertising or a related field (Magritte, Warhol, Wayne Thiebaud). Some are perhaps writers or educators first, and artists second (Albers, Judd, Barnett Newman, Peter Plagens). Depending on the generation, some serve in the military (Diebenkorn, Kelly, Carl Andre, Robert Smithson, and on...), but leave as soon as possible.

Jess is an exception. Of course there must be others. Kandinsky taught law until age thirty. Gauguin was a stockbroker until age thirty-five. Tony Smith started sculpting at age forty-six. I'd like to make the self-serving case that career jumping improves art by bringing in original ideas from other disciplines. Jess is a prime example of someone who brought a fresh approach to art at least partly as a result of his training outside.

GCDs of Pythagorean Triples

Euclid's formula for Pythagorean triples is used to generate triples from row and column numbers. Then the greatest common divisor (GCD) of the triple is calculated, using the Euclidean algorithm. Finally, a color is assigned the GCD.

A Mathematician's Apology

In About the Cubes and Cabtaxi Fleet Project, I quoted G. H. Hardy:

"A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas." G. H. Hardy (1877 – 1947)

This quote is from his essay, A Mathematician's Apology. The full text of that essay is here. I tacked the quote to the end of my project description just because it's a relevant and original thought. I in no way mean to imply that my projects are mathematics nor are they made with only ideas — I borrow some relatively simple math to bootstrap the creative process. Since Hardy wrote his essay, and probably before, I think we have seen artists make ideas as opposed to patterns. I doubt that the art is as permanent as most math, though. Hardy says,

"A painting may embody [an] 'idea', but the idea is usually commonplace and unimportant."

Ouch! Written in 1940, the opinions expressed might be interesting to artists for many reasons. Whether you're a young artist, an aging artist, an art critic, or simply have opinions on what constitutes a thing of beauty, the essay has something to say to you. It also has a section (28) on the relation of applied mathematics to war.

You may object to some of Hardy's other statements. For example, here out of context are a couple more:

"Statesmen despise publicists, painters despise art-critics, and physiologists, physicists, or mathematicians have usually similar feelings: there is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds."

"The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics."

Shifting Coprimes Plot