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.
Incredibly insightful analysis! I guess it takes a philosopher instead of a novelist to tease this out, no disrespect to Kevin G at Infinite Summer. DFW, being both, was probably what led to the attempt to do this in the first place.
ReplyDeleteWhat's interesting to me, as neither a philosopher nor a novelist, is how the Sierpinski gasket structure is defined more by its negative space than by its positive space, which ties in thematically with the novel's being about loss, lack, and anomie. The hole left by JOI could be the center white triangle, with other losses radiating outward.
Thanks, and:
ReplyDeleteWow, very nice point about the negativity. I hadn't really focused on that before but find your remarks convincing. They have especially brutal implications in connection with the following cool factoid from the above linked mathy article: "As shown above the gasket has no area but the boundary is of infinite length." One spin to put on that is that the negativity, the loss, becomes total yet there is still a something that is there, a something that is infinite. That, to my mind, is the most important aspect of transcendence as portrayed in IJ, and ability to recognize how totally horrible things actually are while also achieving an appreciation of the beauty of it all. I realize, and perhaps DFW does too, that that is corny, when said, yet awesome, when shown.
Re Kevin G, yeah, definitely, no disrespect from me for that guy. His posts at IS in general are great and that one in particular wasn't really intended to illuminate mathy stuff.
Found your blog this a.m. via link from Ray's L,YC site. Great to see another professional philosopher who's a DFW fan taking up the IS-challenge. I like what you've done in earlier posts (esp wrt bodies)!
ReplyDeleteOver at my blog, I'm trying to do much the same, i.e. prof. philos'er's perspective without being too technical, tease out some recurring or imagined philosophical thematics, perhaps Entertain a bit along the way.
You've been linked to my blog, and I'll check back in!
Thanks for the note and the kind words. Your DFW blogging is excellent (right up there, in my mind, with infinitedetox, zombie's Daryl Houston, and Ray Gunn) and I've got you in my blogroll now. It's cool to see another philos'y prof sluggin' away at this.
ReplyDeleteI've been thinking hard, recently, about your remarks on ONANite politics ( which I enjoyed) and think mybe there's a way of conecting them to this fractal stuff by way of Prorector Thodes class. I'll post if anything comes of it.
Cheers!
Thanks, Pete. And to think, we're only half-way through!
ReplyDeleteA week ago aproximatelly I wrote a post about infinity and of course fractals, that are a great topic from it.
ReplyDelete"in the 1970s British mathematician and cosmologist Roger Penrose become the first to describe these geometric designs in the West. Quasicrystalline patterns comprise a set of interlocking units whose pattern never repeats, even when extended infinitely in all directions... they where the penrose tiles"
Penrose says people ask him 'how do you know that that tiles when the problem is noncomputable?' but that's not the point. The point is that in a particular case you may have a way of seeing the solution, but there is no systematic procedure that could be put on a machine, which requires no more thinking."
Also escher figures where inspired by this shape, made by him, such as the famous "asciending and descending" where he draws an impossible building.
And also this guy focuses on the very interesting non euclidean gemoetry (that comes next)
You can read the rest of the entry here:http://singyourownlullaby.blogspot.com/2009/07/infinity.html
enjoy
Great stuff, man. I saw this principle at play not so much in the text itself (although I have no doubt it'd be there too), but more in the dynamics of the relationships among certain sets of characters -- and I happened to see those sets as conveniently triangular sets of 3, or perhaps sets of 3 surrounding a more central character. For example, the psychological dynamics involved in the set of Joelle, Orin, and Himself -- which seemed to me to be reflected more or less in a number of other triple sets, like, say, Avril, Hal, and Wayne. And so on. By the way: Has anyone else noticed how the book proper (excluding footnotes) in every edition is exactly 981 pages, equally divisible by 9? I noticed it first as a device to break up the book pre-reading, to make it feel more readable, like a nine-part volume of 109 page novellas. (With extensive footnotes, of course.) I tried to see but didn't find enough evidence that Wallace had intentionally built key scenes in and around those nine "seams", if you will. Some evidence, but not enough to say with confidence.
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