sometimes dumber is gooder

Laura lent me The Visual Mind: Art and Mathematics (1995), which I’ve been thumbing through, in between struggling to develop a homespun 3D engine for my book. I’ve been working on the same stupid back face culling problem for what seems like 2 weeks now, and well, I’m not feeling too much love for my a-analytical brain lately. (Perhaps the problem could be due to a faulty basal ganglia).
I think the book (The Visual Mind, not mine) is significant as an historical landmark, documenting a relatively early period of development in computer graphics. I don’t think the book actually deals very much with art and mathematics though. The book does deal with interesting mathematical ideas and the problems (especially pre-CGI) of visualizing them, and it presents the math in an inspiring way, which is, I guess, its connection to art. However, I’d challenge the idea that a beautiful bronze cast of some 4D math function is a synthesis of math and art. Rather, I’d place the work solidly within mathematics, its “newness” perhaps extending the rendering/drafting medium (pencil, compass…casting, graphing calculator, etc) I don’t mean to devalue the beautiful works discussed in the book, generated by equally beautiful mathematical ideas. But, I think the rational framework underlying the work/process imposes itself too pragmatically–precluding the process from getting too “out of control” for unexpected a-rational “stuff” to be found.
I think a true fusion between math and art would lead to work that wouldn’t necessarily illustrate the math/art connection, or at least not as didactically as many of the book’s examples. Some good arguments could be made for the contemplative and aesthetic aspects of the processes/works in the book as justification for their signification as “Art”. However, I would argue back (not too forcefully) that the term “craft” encompasses notions of both the contemplative and aesthetic. For mathematical work to approach art, for me, it needs to transcend the rational. I think Escher, albeit very didactically, illustrated this in his work. It is the impossibility of his seemingly mathematically created and precise worlds that is fascinating (beautiful.) Of course many artists throughout history have created transcendent mathematically inspired/based art: Piero Della Francesca’s Resurrection immediately comes to mind. I remember seeing the piece in Sansepolcro and being overwhelmed, and I assure you I wasn’t thinking about perspective or any other mathematical idea at the time. The raw human emotional drama of the piece subsumed any of the (not trivial) math underlying it.
Ironically, it seems through the development of powerful applied mathematical tools (computation) that new math/art integration struggles ensue, which will make another interesting thing to consider in a future post (preferably not by me.)
Back to obsessing about my basal ganglia.