Friday, July 31, 2009

Fractal Sky


I was pleased to see fractals, especially the Sierpinski gasket, mentioned recently over at infinitesummer.org. But I was disappointed that insufficient discussion was dedicated to explicating what it might mean for a printed text of finite length to implement, or approximate, or whatever, a fractal structure. So here’s my stab.

The Sierpinski gasket is infinitely decomposable into microstructures each of which mirrors the macrostructure above it--a triangular arrangement of one negative and three positive triangles each of which, the positives, consist of such an arrangement. So, one thing to look for in reading the text of IJ, is not just repeating structures, but repetitions that constitute the mirroring of the macro in the micro.

Of course, in a literal fractal there's an infinite decomposability that can be directly implemented in a literary fractal only if, for example, the text is printed in an infinite number of infinitely small characters.

Now, DFW is well aware of the various proposed solutions to the problem of literal infinities that have arisen in the history of math and philosophy. One way of conceiving of a finite entity as sufficing to represent an infinity is by conceiving it as a recipe that, if followed infinitely, has an infinite result. Infinite suds from just three words: "lather, rinse, repeat." Of course, the kind of infinity generated by the shampoo instruction isn’t fractal. To achieve that, it helps to have some sort of self-reference, as in, “Rewrite this very instruction with itself included as a terminating parenthetical remark.”


To wrap this up: my take on what's fractal-ish about IJ is that it, the text itself, presents a finite number of results of the implementation of a procedure which itself is represented in the text. The infinitely decomposable self-similar structure that is thereby represented is only approximated via the activity of reading (that is, following the procedure), and re-reading, and re-re-reading, the text.