Math Systems of Watchmen

            According to John B. Fraleigh, mathematician at the University of Rhode Island, an abstraction in mathematics is “the process of extracting the underlying essence of a concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications” (37). It seems odd that this particular term would be restricted to applications of mathematics. A definition such as this begs to be employed in the graphic novel Watchmen. Through my eyes, Alan Moore used abstraction as a literary device to highlight two commonly misunderstood concepts in the physical world, open and closed systems. “Open” and “closed” systems are widely believed to sit at opposite ends of a spectrum but Moore understands where the systems overlap and wields the characters in his novel to follow the patterns of the systems to demonstrate the essential idea of Watchmen; Irregardless of which system we are each a part of, we will all reach the same place of defeat.

            To understand the connection between open and closed systems, I draw parallels between the two systems in the discipline of partial differential equations and in the graphic novel. Open and closed systems are prevalent when dealing with the diffusion of heat over a rod. The “system” of the rod stems from the length of the rod examined. “Open” refers to a rod of infinite length (0 < x < µ) and “closed” pertains to a rod of finite length, l  (0 < x  < l). The rod at the first position, x =0 is insulated to stay at a certain temperature say, 10°C while the rest of rod, either to infinity or to l, is initially at 0°C. As time passes, the rod in the closed system will still have a temperature of 10° at x =0 but along the rod, the temperature will be lower than 10° but higher than 0° as heat from the initial position is transferred to the rest of the rod. The result over time is the rod being 10° at the zero position but the rest of the rod at a temperature slightly above 0°. This outcome mimics that of the rod in the open system. The same initial conditions remain but gradually, the rest of the rod is heated to above 0° but not reaching 10° with each position warmed in succession. Eventually positions on the rod closest to x =0 have a temperature just above 0° and  positions located further out to approach infinity, will hold a temperature of 0°. Why does this happen? The energy inherent in heat is exerted when heat travels. For both systems, the energy used in traversing the rod will exceed the energy used in raising the temperature at each position. For the closed system, when the heat reaches x = l, it will reverse to span its energy over the rod back and forth to maintain the temperature of the whole rod to a small degree above 0°. In the open system situation however, the rod is infinite with no boundary to bounce off. This results in the heat not reaching a sustainable temperature but becoming 0° when a point is reached at which there is no more energy to travel or heat (Strauss 42). 

            How does Moore use these events in Watchmen? Firstly, the link to reality in both environments is gone. There is no such object as an infinite rod and there is no such person as the God-like Dr. Manhattan however, we can still form general notions about the behavior within the worlds, as Moore explicitly does. Secondly, Moore writes Rorschach as a “closed system,” having definite limits as to what is right and what is wrong and stays static within the boundary created with those views. Humanity minus Rorschach is the sum of the remaining characters.  Humanity is illustrated as an “open system,” containing an infinite array of positions on good and evil and if humanity can better itself. Additionally, Rorschach’s behavior through the novel mimics that of the rod in the explanation given above. He is constantly given energy to react to from the “accumulated filth of all [persons’] sex and murder” (ch.3, fr.3) like the constant, insulated rod. Throughout the novel, he exerts his energy in covering all “positions” of the plot to destroy the watchmen. He travels forward and backward through theories from “a [possible] old foe with a grudge” (ch.1, fr.58) to “something big [that] makes ripples” (ch.10, fr.22). In the end, his passion can no longer continue due to his moral “boundary” that leads him to be killed. Like heat, he approaches disintegration but stays above it, passing on a journal to keep the “energy” in motion with the truth of the monster. Similarly, humanity follows the path of the open system. Dr. Malcolm Long is described by his wife as the “nicest, most positive person [she] knows” (ch.6, fr.68) but even he sees his own optimism as “unfounded” (ch.6, fr.103). He ultimately speculates “in the end it is… empty, meaningless blackness” (ch.6, fr. 238). Even Dr. Manhattan, who has no faith in humans that “cannot be his concern” (ch.12, fr.236), states how “nothing ever ends” (ch.12, fr.238). The openness of humanity to a better future in turn contracts, like the heat of the rod, to be nothing despite being fed by the energy of evil to be rid of. Thus there is no consistency over time in a closed system nor in an open system, just a decrease in the “heat from the fire” in both cases.

            Moore has in effect, abstracted the concept of open and closed systems to state an outcome for our world on the page that he believes to be truth. His writing of different characters as different systems allows the characters’ opinions to follow the paths governed by the systems themselves to reach a place that is almost hopeless or devoid of hope completely. Moore is telling us that in the end, our faith will die because we are all systems approaching 0°.

Works Cited

Fraleigh, John B. A First Course in Abstract Algebra. New York, NY: Addison Wesley.

Gibbon, Dave and Alan Moore. Watchmen. New York, NY: DC Comics, 1986-1987.

Strauss, Walter A. Partial Differential Equations. Danvers, MA: John Wiley & Sons,  Inc.