Flatland

I just finished reading Flatland, by Edwin A. Abbott. First published in 1884, this story of a two-dimensional world provides a subtle introduction to the concept of worlds with four or more dimensions. Beings in Flatland are lines, polygons, and spheres. I don't recall reading anything about the natural Flatland world. If Flatland could have Bézier curves the landscape might look like this —

Observer Effect

An image created with a Flash ActionScript program is different each time it's created. It almost demonstrates an observer effect. Not really, but that's the idea.

Jeffry Mitchell talks with Denise Patry Leidy

Last Sunday at the Portland Art Museum, Denise Patry Leidy, Curator of Chinese Art at the Metropolitan Museum of Art, spoke on perfection and form in Asian art. As she explained, it's a huge topic covering a vast part of art history both in time and space.

After her talk, she and Jeffry Mitchell presented an equally interesting one-on-one presentation of Mitchell's three contributions to the museum's Contemporary Northwest Art Awards exhibit. Mitchell and Leidy complement each other because Mitchell has an abiding interest in Asian art. He often draws on images and concepts with strong Asian influences. I still have difficulty with some of Mitchell's work. I disparaged it in a previous blog. I don't connect with what I read as his storybook imagery. However, two of the three Mitchell pieces in this exhibit interest me.

Of the three pieces Mitchell has in the show, "Sphinx" has been described by critics almost to the exclusion of the other two pieces, "From a Muddy Pond: Like an Elephant in a (Plexi) Box" and the black-on-black painting, "Black Star". "Sphinx" shares some of the same imagery that I criticized when Mitchell showed at Pulliam Deffenbaugh. I prefer "From a Muddy Pond" and the black-on-black painting — they're atypical for Mitchell. There's an aspect of "From a Muddy Pond" that I can relate to. Mitchell created a sort of wallpaper group from lithograph prints on transparent paper. Because the paper is transparent, he can achieve the reflection of a plane symmetry or wallpaper group by flipping the image over.

In the black-on-black painting Mitchell uses a highly geometric process to develop a remarkable image. In the center of the painting is a pentagon. Toward the edges are five circles. Concentric pentagonal shapes radiate from the center and morph into concentric circles radiating from the five outer shapes. This is all accomplished with black drawn on black oil paint. The entire painting is meant to be the image his "Sphinx" (self-portrait) contemplates from across the room, and therefore seems to me to be the real focus of his exhibit, not the "Sphinx".

Math Ideas, Art Ideas

I've posted several quotes (and here) on the relationship of art to math. I found a good one in the excellent monograph, Robert Mangold. Mangold ended his "Statement for a Panel on Abstract Art, 'The Geometric Tradition in America Art 1930-1990', Whitney Museum of American Art, New York, 1993" with the following:

"Whatever role geometry plays in my work I see as incidental. I have used circles, squares, ellipses, and all manner of four- and many-sided forms and combine forms. I see no difference between this and the way a writer or poet would use words and made-up words to express an idea: the key is to express an idea.

Abstraction is an idea. Geometry is not." [Robert Mangold by Richard Shiff, Robert Starr, Arthur C. Danto, and Nancy Princenthal. New York, Phaidon Press Inc., ISBN 0 7148 4448 9. page 164]

There's disagreement among artists about whether art or math is based on ideas. Compare Mangold's statement with this one from Mel Bochner's:

"Happily there seems to be little or no connection between art and mathematics (math deals with abstractions, art deals with tangibilities)." [Bochner, Solar System & Rest Rooms, Writings and Interviews, 1965-2007, Cambridge, MA: The MIT Press, ISBN 978-0-262-02631-4, page 39-43]

Once again, here's my favorite quote from mathematician 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)

Below, I include one of the latest prints from my Plane Symmetry series. Disclosure: to make this print I used programming, simple math, elementary algebra, the number PI, trigonometry, Bezier curves, and Euclidean geometry.