Prior to the 20th Century, conceptions of consistent, mathematical pattern evident within the abstract aspects of the natural world were the subjects of frustration and anguish in the discipline of mathematics. While linear, Euclidean geometry was widely known and used in defining physical and natural phenomena, the more intricate pieces of geometrical presence in nature were still inexplicably disconnected from the whole mathematical picture of the world. It wasn’t until the 1960s, while observing the same mysterious and non-concrete geometric curves and patterns in nature, that mathematician Benoit Mandelbrot began defining what is known today as “fractal geometry” (McGuire). This form of mathematics connects all of nature along with every process of growth, flow, movement, and formation into one definitive geometric pattern. The pattern centers on the concept that the iteration of one simple object leads to the construction of a larger, more intricate picture, which is present throughout all the complexities of nature. Indeed, it claims that simplicity produces complexity, and the beauty of this natural pattern is the result of many pieces coming together into the one complete, whole, and remarkable image that can be seen all around the natural world.
While this geometric concept was discovered in an attempt to define nature, its reach spans much farther than the mere world in which humanity abides; for in the same way that the “coming together” of fractal geometry produces beauty and symmetry in the natural world, its beauty manifests in the nature of humanity as well, evidenced by mankind’s value for connection over isolation. The relation of this mathematical concept to human nature intricately ties two diverse disciplines together—natural sciences and humanities—manifesting not only within the humanities’ visual arts, but also within its music, philosophy, and literature. Two contemporary authors, Tom Stoppard and John Hawkes, beautifully illustrate the literary interaction of the disciplines—the demonstration of fractals within human nature—through their works Arcadia and Travesty. By the literary interpretation of fractals, they present the symmetry, completeness, and wholeness that arise from connection (human “fractalization”) as virtue in human nature. Likewise, they expose the imbalance, incompletion, and weakness that come through isolation as vice, universally undesirable by mankind and consistently leading to dissatisfaction in the human mind and soul. By looking into the moments of connection and isolation within these works, the underlying idea of fractals in human nature becomes very evident—the presence of beauty and symmetry when humanity relationally joins together, and of anguish and disorder when they separate.
Virtue: Fractal Emphasis in Arcadia
Human connection can often be identified in individuals through visual and sensual indicators of wholeness, completeness, strength of mind and heart, and overall satisfaction in life. It is a type of order, in a sense, amidst the divisions and chaos of humanity, rendering mankind more powerful, more capable, and more internally sound in the manifestation of it. Mandelbrot expresses in his work on fractals, “fractal geometry is a workable geometric middle ground between the excessive geometric order of Euclid and the geometric chaos of general mathematics” (Mandelbrot). In the same way, the beneficial conception of human connection is not ridged, tyrannical order that inhibits individuals and keeps them in internal bondage, but an empowering joining of like minds and hearts, bringing health to the human soul and strength within life. It is balance and symmetry in humanity, displaying a beautiful and intricate picture of fractals in human nature. This image of connection is most clearly seen in Stoppard’s Arcadia. While he does provide examples of human isolation and its affects in his work, the overarching channel through which he conveys the message of beneficial human “fractalization” is through the demonstration of it.
From the very beginning, the audience is exposed to one of the most significant themes of the play: love and sexual connection. The first spoken words come from the young female protagonist, Thomasina, who curiously inquiries about the meaning of it: “Septimus, what is carnal embrace?” (Stoppard 1). As sexual relationship is one of the most profound connections that human beings are capable of experiencing, Stoppard appears to be subtly emphasizing its importance through the mind of a thirteen-year-old girl, who is isolated from the knowledge of such a connection. Similarly, throughout the story, the audience witnesses several matches of love form before their eyes, like watching the spiny arms of a snowflake develop through the patterns of fractal geometry. Chloe and Bernard share an intimate connection, although displayed as dysfunctional at times, still representing the desire—through Chloe’s character—that every human has for romantic connection with another human being. Evident through Gus’s love for Hannah, it is a desire that transcends imperfection, enabling humans to pursue it regardless of differences in relationship, and demonstrating that it is capable of empowering, inspiring, and strengthening the heart and mind of mankind. At the end of the story, the imagery of Septimus and Thomasina dancing in 1812, along with Gus and Hannah in 1993 on the same stage provides beautiful order to the chaotic scene, representing that time has no hold on the value of this human connection.
Another present theme throughout the play is that of intellectual connection. The country house, Sidley Park, always brims with human interaction whether in the nineteenth century or the twentieth. In every scene and conversation within the manor, the characters engage in this form of connection. The most intriguing conversations are shared by Thomasina and Septimus during their tutoring sessions, in which Thomasina presents him with remarkably advanced mathematical and philosophical ideas of the natural world. “If everything from the farthest planet to the smallest atom in our brain acts according to Newton’s law of motion, what becomes of free will?” (Stoppard 5). Questions such as these and the discussions that ensue are the cause for intellectual “fractalization” in the human mind. They create order in thought and conversation, working intricate pieces of knowledge together into one beautiful image of perspective on the world. Without this form of connection—the ability to reason with another mind, sharing and listening to the thoughts of others—humanity falls quickly into disorder and confusion. Stoppard illustrates this point at the end of the play by depicting the intellect, Septimus, as an isolated hermit, living on the grounds of the manor. The death of Thomasina, the absence of his love and romantic connection, throws him into this place of isolation. Without the romantic and intellectual connection with humanity which he preciously possessed, Septimus’ life loses its order, symmetry, and sense, moving him into a state of chaos and loneliness until his own death liberates him from it. Through this imagery, Stoppard again emphasizes the value and importance of human “fractalization.”
The demonstration of human connection as a virtue in this piece is evident through its positive and universally desirable outcomes. As previously mentioned, “fractalization” in human nature is characterized by individuals experiencing wholeness throughout their being, completeness in their soul, physical and mental strength, and satisfaction with their life in general. Without human connection holding significant office in the life of an individual, it would be nearly impossible to genuinely experience these good manifestations. The Oxford Living Dictionary presents a definition of “virtue” that supports this point; “A quality considered morally good or desirable in a person” (Oxford). Applying this framework to situations as well as to individual “persons,” the evidence of virtue through Arcadia and human “fractalization,” becomes clearer, because the experience of human connection is both “good [and] desirable,” even necessary for human beings to thrive. Referring to the philosophy of Emmanuel Kant, the concept of human connection may be deemed “virtuous” as it is also capable of being upheld as a “universal law of nature,” indiscriminately desired and needed by all mankind (Kant).
Vice: Fractal Emphasis in Travesty
Human isolation becomes evident through the physical and sensual manifestation of incompletion, weakness in the human mind and heart, and overall dissatisfaction in life. No longer a joining of many intricate parts, man becomes a single piece on his own, rendering him powerless, incapable of living fully, internally unsound, and susceptible of falling into darkness and disillusionment without anyone to set him straight. King Solomon expresses the misfortune of this place of isolation in the Book of Ecclesiastes; “Two are better than one…if either of them falls down, one can help the other up. But pity anyone who falls and has no one to help them up” (Ecclesiastes 4:9-12). In a place of isolation, the strength, beauty, and fullness of human life cannot be experienced, like the intricate beauty of nature is impossible without fractal connection. This image of isolation is most clearly seen in John Hawkes’ Travesty. It is evident that, although his book centers on the idea of human isolation, he desires to convey the same message as Stoppard in Arcadia. The channel through which he presents this message, however—that human “fractalization” is good and beneficial to the human heart and mind—is through the absence of connection, or overarching presence of isolation.
The most overt depiction of isolation in this novel is the protagonist’s own mind. It is the only perspective that the audience is given to understand the events taking place within the story, and it is one-sided, giving the book an imbalanced, asymmetrical presence. Through the isolation of the speaker’s mind, chaos and disorder become very apparent within the story, and they manifest in the content of his speech. “Don’t you know that Papa loves you? Not many young women have the opportunity of passing their last minutes in the presence of lover and loving Papa both” (Hawkes 12). While the speaker presents words of ostensible human “fractalization”, the audience knows full well that his actions demonstrate the opposite. He speaks of love and connection while orchestrating death and enforcing isolation. Similarly, he tells stories of obscene and inappropriate sexual experiences, distorting the beauty of faithful, self-sacrificial sexual relationship, and leaving the audience feeling repulsed by it. “I increased my efforts and gave myself total consciousness of touch and sound and enjoyed to the fullest the agitation of her helplessness” (Hawkes 70). It becomes very clear through passages like these that Hawkes intends for the audience to feel discomfort, disapproval, and dissatisfaction in reading his novel, because they emphasize the unhealthy and undesirable state of mental isolation. Hawkes himself, when asked about the significance behind the darkness of his work, expresses “on one hand it serves to create sympathy, compassion, and on the other it’s a means for judging human failings as severely as possible; it’s a way of exposing evil” (Graham 27).
Another theme very evident in this text is that of physical and emotional isolation. In Arcadia, these types of human connection are present in every scene through constant human interaction, and conversation, through intellectual debate and relational consideration. In Travesty, however, every character demonstrates both physical and emotional separation from the others in a variety of ways. The most evident characters in this state are Henri and Chantal, the passengers in the madman’s vehicle. They are trapped within it, completely unable to reach the world outside that could offer them salvation in this moment of distress. Not only are they trapped in the car, but they are also trapped in the mind and will of the driver, forced into silence and compliance, isolating their thoughts and emotions to the confines of their own minds with no ability to express themselves. Chantal presents another layer of physical separation due to her location in the back seat of the car. The seats themselves create a barrier that she cannot cross to find comfort in someone’s arms, causing her to resort to a lonely fetal position on the floor, trying to ease the pain through her own weakening strength; “You, Chantal, burrowing down back there like some frightened animal or tearful child?” (Hawkes 53). The other character that is isolated in this story is Honorine, not included in the genocide, and left completely on her own to face a worse form of separation when she discovers the deaths of her loved ones. “Think of her now, not sleeping in that massive antique bed of hers,” both physically and emotionally disconnected from the horror occurring in her family (Hawkes 48).
While Hawkes purposefully focuses on the human state of isolation in order to emphasize its vice, he also includes several subtle moments demonstrating human connection, in an attempt to contrast the two sides. One of these moments is a recollection by the protagonist of an elderly couple, arm-in-arm, and walking to a church. As the scene is described from the perspective of the driver’s isolated mind, it does not appear in a beautiful light. However, the audience can, in this moment, remove themselves from the dark lens of the speaker, to see one of the most beautiful and lauded pictures of human “fractalization”—the faithful, timeless love of an elderly married couple, who endured the trials of life through the strength of their relationship. Highlighting the virtue of the scene, the couple’s actions were aimed at service to one of the most popular symbols of morality and goodness: “This scowling pair progressed beyond my silent automobile…until at last the woman deposited the trim little bouquet at the feet of Christ” (Hawkes 26). Similarly, the speaker relays an encounter with a protective father and little girl whom he nearly hit with his speeding vehicle. The imagery of the father’s irate face at the scare of his daughter’s harm again enables the reader to step away from the speaker’s isolated perspective and see the proper connection a father would have with his daughter in this light.
The display of isolation as a vice in this work is evident through the horrific outcomes of its presence, the results of seclusion and separation. The effects of isolation in humanity appear through the sense of internal incompletion, weakness of heart and mind, and dissatisfaction with life; the fruit of an isolated life—body and mind—is very dark and confused, as it plays with chaos when separated from human interaction and beneficial order. Again, the Oxford Living Dictionary presents a definition of the term “vice,” which supports this understanding: “A weakness of character or behavior” (Oxford). Analyzing this definition through the lens of circumstance as well as “character” presents clear evidence for vice within Travesty and through human isolation, as isolation itself always reduces an individual or situation to a place of utter weakness. This is the case within Travesty that it appears Hawkes desires to convey—isolation is a vice that deteriorates the mind and only leads to devastation, and human connection is a virtue that can spare it all.
Through both of these works, the authors seek to convey the same message to the world, that human connection is vital for survival, satisfaction, and fulfillment in life. It is itself a virtue that results in virtuous outcomes as well. In presenting this idea, Tom Stoppard depicts scenes in which the value of human “fractalization” is clearly evident though the constant relational and intellectual interaction of his characters. John Hawkes takes the opposite approach by depicting only the harmful and disturbing outcomes of humans lacking connection. In both cases, however, the concept is clear—“fractalization” is a phenomenon that not only occurs in the natural world around mankind, but also in the human nature within them; and just as fractal geometry is necessary in the production of symmetry, beauty, and wholeness in nature, it is for producing such qualities in the heart of man as well. Remembering the initial excitement over fractal discovery, visionary mathematicians expressed “a hope that it [would] remain valid in future research and that it [would] extend, for better or for worse, to our pleasure even though perhaps also to our bafflement, to wide branches of learning” (Fleischmann). As Tom Stoppard and John Hawkes both display within their literary narratives, this has certainly become the case—a beautiful, intricate connection between natural sciences and humanities.
December 6, 2018
Works Cited
Ecclesiastes. Bible Hub, New International Version, 2018.
Fleischmann, M; Tildesley, D.J; Ball, R.C. Fractals in the Natural Sciences. Princeton University Press, Princeton, 1989.
Graham, John. “John Hawkes: An Interview.” Studies in Second Skin. Charles E. Merrill Publishing Company, Columbus, 1971.
Hawkes, John. “Travesty.” New Directions Publishing Corporation, New York, 1977.
Kant, Immanuel. Groundwork of the Metaphysics of Morals. Translated by Mary Gregor; Jenns Timmermann. Cambridge University Press, Cambridge, 2012.
Mandelbrot, B.B. “Fractal Geometry: what is it, and what does it do?” Fractals in the Natural Sciences. Edited by M. Fleischmann, D.J. Tildesley, and R.C. Ball, Princeton University Press, Princeton, 1989, pp. 3-8.
McGuire, Michael. An Eye for Fractals: A Graphic and Photographic Essay. Addison-Wesley Publishing Company Inc., Ontario, 1991.
Oxford Living Dictionaries. “Virtue; Vice.” Oxford University Press, 2018.
Stoppard, Tom. Arcadia. Faber and Faber Limited, London, 1993.