Gleick and Prigogine

I read Gleick and Prigogine both with eyes that searched for metaphors that could describe the novel, and found many, especially in Gleick. Mandelbrot's observations regarding noise in a system, creating fractal time, made me realize that narrative, too, was an example of fractal time, the words acting as the "noise" in the "system" of the novel, similar to Cantor dust. This is best seen in a rewording of Gleick's own words:

Mandelbrot saw the Cantor set as a model for the occurrence of errors in an electric transmission line. Engineers saw periods of error-free transmission, mixed with periods when errors would come in bursts. Looked at more closely, the bursts, too, contained error-free periods within them. And so on – it was an example of fractal time (93c).

which I have reworded thus:

I see the Cantor set as a model for the occurrence of words (particular words) in a novel. There are periods where a given word does not appear, mixed with periods when the word does appear, mixed with periods when the word comes in bursts. Looked at more closely, the bursts, too contain periods without that word within them. And so on – it is an example of fractal time within the novel.

These dusts occur on smaller scales, each cluster giving clusters of spaces and clusters. Naturally, in a novel one can only go down so far – to the sentence-level – but one can see the general principle holds. This is what made me think to graph several words to see if any patterns would make themselves apparent – as indeed happened with the word "friend" in my novel manuscript "Hear the Screams of the Butterfly" on the page-level. This graph is what is called a "Poincaré map," which "removes a dimension from an attractor and turns a continuous line into a collection of points" (142). "Such pictures ... [begin] to reveal the fine fractal structure" (144) of the system – in this case, the novel. Thus, we see word distribution in a novel "as a Cantor set arranged in time" (Gleick, 92), where "the degree of irregularity remains constant over different scales. ... the world displays a regular regularity" (Gleick, 98). This suggested to me that meaning in a novel is both emergent and fractaline – as one goes down, one sees ever-smaller elements of meaning – elements that finally stop at the level of words – perhaps. There is also perhaps the level of multiple interpretations of words – especially in context of the emergent properties of the phrase, sentence, paragraph, etc. Going down helps us see the fractal repetitions while going up (looking at the patterns the words make, looking at how they are functioning in a particular sentence, paragraph, scene, etc.) helps us see the emergent levels of meaning. The mere repetition of a word is not enough – it has to repeat in a chaotic pattern to create the strongest levels of meaning. Each word "repeat[s] itself, displaying familiar patterns over time. ... But the repetitions [are] never quite exact. There [is] pattern, with disturbances. An orderly disorder" (15). Thus, although the word "love" is repeated more in my text, the fact that it lacks this kind of periodic behavior 9orderly disorder) while the word "friend" does tells you the word "friend" is a stronger theme-word, having been created through the tensions in the novel. How does this happen? "Information is transmitted back from the small scales to the large... And the channel transmitting the information upward is the strange attractor, magnifying the initial randomness just as the Butterfly Effect magnifies small uncertainties into large-scale weather patterns" (261). This is why the peaks of the word "friend" correspond to major plot points in the text. So we see a novel is a particular type of fractal – it is, indeed, self-similar at lower intervals, but as one goes up, new forms are made, self-similar to what came before, but having emergent properties (meanings). What we therefore see in deconstruction is a concern only with the "infinite coastline" of the novel, to the expense of the emergent meaning of that coastline in delineating the complete form of the novel.

Since the novel is now seen to be both regular and irregular, to be, in essence, fractaline, one could perhaps see Gleick's observation on 100 as a literary judgement: "The degree of irregularity corresponded to the efficiency of the object in taking up space." Is there perhaps a correlation between a novel's degree of irregularity as a fractaline object and our finding that novel aesthetically pleasing (or, at least, long-term survival)? This would be an interesting line of research for someone to pursue. This complexity that a fractal view of the novel illuminates is also another way of judging a novel (or understanding how novels have perhaps been judged in the past) since, as Gleick says, "Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world" (116-7). Though we have to be careful when we say the word "simple," since "simple systems can do complicated things" (167), as anyone who has read Hemingway knows. Further, "as [a] system becomes chaotic ..., strictly by virtue of its unpredictability, it generates a steady stream of information" (260). This is undoubtedly why we say that both predictable stories and stories that are not retrodictable are bad stories. A chaotic story would be one that is neither predictable, but is certainly retrodictable.

Gleick also states that irregular patterns and infinitely complex shapes have "a quality of self-similarity. Above all, fractal meant self-similar" (103). Further, "self-similarity is symmetry across scale. It implies recursion, pattern inside of pattern," (103) meaning fractals are not determined by scale (107-8). The presence of meaning in a novel is also not determined by its scale. Phonemes have meaning, and so do plots, as well as every level in between. But, like eddies of air are the same as a hurricane, only at different scales, the effect of the higher levels of meaning is as different from phoneme to plot as the effects of an eddy of air are to a hurricane. All the same, an eddy of air can, building on other eddies of air, build into a hurricane over space and time in the same way as phonemes, building on other phonemes, build into a novel over space and time. This is because "each change of scale [brings] new phenomena and new kinds of behavior" (115). Therefore, the existence of meaning applies "without regard to scale" (108) in a novel. It is also natural to say that greater meaning emerges as we go up in scale, since these scales are hierarchical (116). As Gleick points out, "fractal scaling [is] not just common but universal in morphogenesis" (110). And since fractal geometry is "nature's own" (114), and a novel is a part of nature inasmuch as it is a creation by a living organism, we should not be surprised to find that novels have fractal geometry. Further, "A geometrical shape has a scale, a characteristic size. To Mandelbrot, art that satisfies lacks scale, in the sense that it contains important elements at all sizes" (117), meaning a good novel (that satisfies the reader) lacks scale, in the sense that it contains important elements at all sizes, from phonemes to plot.

On the other hand, I did not get nearly as much from Prigogine in regards to opening up new ways of understanding the novel, except in some general ways. I strengthened my belief that to really understand any text, one has to know something about its creation when Prigogine says, "these far-from-equilibrium phenomena illustrate an essential and unexpected property of matter: physics may henceforth describe structures as adapted to outside conditions" (14), with far-from-equilibrium states being those that have strong tension in them (the very definition of a story). He also makes a statement that can easily be used to describe a novel: "One of the most interesting aspects of dissipative structures is their coherence. The system behaves as a whole, as if it were the site of long-range sources. ...the system is structured as though each molecule were "informed" about the overall state of the system" (171), a dissipative system being one that has both structure and disorder in it (143), that is, chaotic. On can see a sentence as having this very structure (Turner, The Culture of Hope). One can, in a sense, see how each "molecule" of the word "friend" is "informed" about the "overall state of the system" of the novel, helping it to cohere and have meaning. Also, Prigogine does away with the postmodern view that nothing new can be created when he says, "living societies continually introduce new ways of exploiting existing resources or of discovering new ones" (193-4). This is further supported by Gleick's statement that "nonlinearity means that the act of playing the game has a way of changing the rules" (24), meaning that in the very act of writing a new story or poem, a writer changes the rules of story- or poem-writing. We therefore not only can, but always do create new forms (if you play the game of literature, you necessarily change the rules), which means that postmodernism is fundamentally wrong when it says there are not new voices or styles and therefore all literature (or any art) can do now is collage and montage. We find postmodernism in this position because it falsely believed literary change to be linear, when it is really nonlinear (it feeds back on itself, etc.).