Heraclitean Water and Koch’s Curve: Let all things change and all thoughts renew

My semester’s story began in the opening week of the course when we were introduced to Ron Eglash, a professor in the school of information and design, and his book African Fractals: Modern Computing and Indigenous Design. We moved soon into Eglash’s content of fractal concepts including Koch’s curve. The first iteration of a Koch curve informed every other text we sorted through in the days that followed. In those days, I found that as the previous iteration of movement became the input for the next, Eglash used the language regarding the repeated seed shape and the sole seed shape as “not special.” The endless yet expected result of the process was exactly what made it indistinct and he further states, “an extremely tortuous curve,” since any shape that didn’t imitate the steep slope for a plot could repeat (Eglash 11). In that process too, being able to see the end while it goes on for infinity seemed to be contradictory, but Felix Hausdorff in Eglash’s attribution to him seemed to resolve this. Hausdorff, one of the founders of modern topology, stated that we could imagine these curves as “taking up more than just one dimension” in the way circles do. In my reflection as well I looked through the files we had once studied and recalled the resemblance between what was drawn on the board on January 22, 2024 to February 16, 2024 and February 6th’s class notes as well as Koch’s curve that Freytag’s Pyramid and Aristotle’s Unified Plot Structure appear comparable. As I peered at the narrative arc that so much of Western culture implemented into the art of storytelling Dr. McCoy highlighted, I took a count of the novels I had been instructed to read in some of my most formative years. I took a big look at what we had read for this course where many of the texts seemed to reach no finality or restoration for the disorder. In that disorder I found joy in the tortuous Koch curve and relief in the literature that expanded past one dimension and interpretation, past the idea that there is only a singular mode of understanding thought and experiences. 

My understanding of the course evolved as I looked back to my essay, “Call-and Response: A Means to Resist Suffering,” for the seed shape of call-and-response that formed as resistance in the face of oppression and atrocity. I realized in my further reference how no text or any form of art can ever reach a definite end, much like the ongoing call-and-response, art exists in several dimensions closer to a circle than anything else. I wandered past shapes in this reflection to look at the natural world to tell us something greater about humanity. At the heart of the course is the principle that no great lesson ends—it is a river of thought that keeps supplying a handful of ideas, those ideas that could never be the same as the last phase of the day when we reached it last. If this sounds familiar, it’s with purpose, in staring at my reflection in the river of concepts and seed shapes, I found Heraclitus’ theory of flux in his book Fragments that within in, he suggests the ever-changing nature of the world around us makes us incapable of stepping in the same river stream twice. Heraclitus believed in change and becoming as waters touching those who go in the same river, so they coexist rather than negate the other if we compare them to a physical feature that we all recognize as constantly flowing, yet named the same body. The pre-Socratic Greek philosopher wrote in his self-named incomplete work about ancient wisdoms, “Most people do not take heed of the things they find, nor do they grasp them even when they have learned about them, although they think they do,” (Heraclitus 17). 

In the past couple of weeks, I’ve reflected on that space in between dimensions and that river analogy while we read Percival Everett’s The Water Cure. In it, Everett’s speaker Ishmael Kidder calls out these fragments imagining that Heraclitus wrote them to just be what they are and not a part of a grander work, but as fragments they are not whole by necessity (Everett 56). Before direct attribution to Heraclitus in the story, Kidder introduces fragments in a visually separated sentence that isn’t a sentence as it lacks the components of a general structure including a subject, verb, and object in that order simply. If we were to analyze instructed by the conventions of what is arbitrarily called “standard English,” we’d note the literary construction of chiasmus as well that appears throughout providing a contrast of words, for instance in one section it is nouns and names (Everett 13, 38-39, 110) and may or may not (Everett 45, 109-110). Ishmael Kidder takes over as the god of meaning as the one who gets to tell us in his art, “all sections are fragments, except for this one because it lives here, in this spot, among the fragments, and has a specified job concerning those fragments surrounding it” (Everett 24). 

His references to the fragments of knowledge not just in logic, but in experience go beyond form or language as they move to his self-portraits (Everett 41, 53, 113) that refuse to affirm or even acknowledge in their creation Jefferson’s commentary in Query XIV in Notes on the State of Virginia. Jefferson professes without support, “never yet could I find that a Black had uttered a thought above the level of plain narration; never see even an elementary trait of painting or sculpture” (Jefferson 9), which Everett subverts conceptually for Ishmael Kidder’s ambivalence and fragmented sense of self are depicted in his Picasso-esque painting. In a signified conversation between Kidder and Jefferson Everett facilitates, I am reminded of another voice in James Snead’s essay, “On Repetition in Black Culture.” So I draw a line between Heraclitus, Ishmael Kidder’s story, Koch’s curves, and further back now for how no text may be uninformed by its influences and references that hide within the output as they are its input. Snead would agree as he starts off claiming a truism among people regardless of culture, “After all, men have by now had to make peace with the idea that the world is not inexhaustible in its manifold combinations, nor life in its various guises and forms” (Snead 146). Snead points us to a broader and recurring issue that Jefferson’s statement only moves past the top of, which is that Europeans during Enlightenment in particular started to define themselves over while attempting to define cultures “belonging to” Europe independently from African culture. In isolation, the “ultimate otherness,” as he calls it, declared this similar idea of being and non-being as Heraclitus of what Black culture was and what it existed as and in opposition to what. We see, however, in Ishmael Kidder’s isolation and immersion in his writings being critical of society, we are told in phases of a conflict between an individual and the collective proving an irony in many of the qualities of said society.

Adding to the handful of instances in The Water Cure that writer Ishmael Kidder discusses fragments, another happens as he unravels Thale’s story using all that he knows from Aristotle’s Metaphysics and De Anima, which allow him to land on it meaning that “Water is the essence of things. / All things have soul in them / The all is divine” (Everett 34). Aristotle, who Kidder falls back on frequently in his rumination, frames—as a critical concept we’ve returned to on many occasions as well—his thoughts of definitions of things that state their essence (Everett 190). A not so distant connection drawn to such a belief is in Kidder’s statement on art and his respective relation to it as he talks about the politics of the world being a source of disarray and atrocity, “right or wrong love it or leave it and it’s a good thing because it’s always wrong but it has taught me to torture…seek definite descriptions precise definitions clear marks of identity or identities…that might or might not exist” (Everett 191-192). So we make our way back to Heraclitus’ idea of indefinition and unity of opposites that everything is and is not at the same time with a possibility of both existence and nothingness. This is all as if to say that, to end on Everett’s novel to put a pin in the semester to come back to after a passage of time, we’ll look at the identity of the course newly and that is a natural consequence of movement of some sorts, forwards and backwards, to and fro. The iterations of this semester’s course came in full-force, but gracefully. At last I think about in Eglash’s African Fractals for the figure captions about measuring nature using fractal geometry to show how across time and space, the curves of the land change. Out of these, African fractals showed strong resemblance with Georg Cantor, who contributed a great deal to set theory and an infinite set (Figure 1.1) and looping as recursion, to create his Cantor set and fractal (Figure 13.1). This occurrence of art and its essential feature of inspiring more art using its inspiration as input to reiterate or recreate has come up significantly. Cantor’s work, according to Eglash, only became useful to the study when Benoit Mandebrot, a polymath associated with the “art of roughness,” furthered the notion of fractal dimension in scaling to measure irregularities in nature. The connection of his contribution in this dialogue between studies pulls us back to Heraclitus for Mandelbrot firstly happened upon a study of “long-term river fluctuations by British civil servant H.E. Hurst” (Eglash 208). Hurst found that the annual floods varied in their scales and couldn’t ever be grounded in an average as the only way to describe these changes was to scale annually and sketch a slope.

We’ve learned to read slopes in this way as we read Everett’s The Water Cure, which confronts a tension of power for who gets to decide the cultural aesthetics and formal narratives of literature that are deemed as canon, relevant, legitimate, worthy, and “art” and the resulting fragments of that art, and therefore people. The logic of Ishmael Kidder’s actions of making himself a god, not only to his captive, but his actual written art is interconnected with the idea of an absolute truth existing for a God and not for anyone else. There’s no truth to an order disorder restore plotline unless we are completely removed from the situation at hand, watching the river pass from above it. So I am left to meditate on the protagonist’s words that tell me about Plato’s saying, “the sense of things becomes that they are true when perceived,” (Everett 114) to believe that change and becoming can accompany one another. I believe that what we consider and value in literature as art can include movements that have kept it running forward. I believe that I can keep up even while I look back on those bends and curves and get caught in the river.

Works Cited

Eglash, Ron. African Fractals : Modern Computing and Indigenous Design. Rutgers University Press, 1999.

Everett, Percival. The Water Cure. Graywolf Press, 2007.

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