As detailed throughout his constructed mythology, William Blake's theories in particular, though dating from two centuries ago, seem to suggest "universal" truths only now being supported by scientific observations. While Blake decries Newton's mechanistic laws--to him they are as limiting as the empirical tools of the Urizenic senses--he might very well have seen chaos theory as liberating, justifying his personal conceptions of certain aspects of reality. Specifically, Blake's treatment of Urizen and others in "The Book of Urizen" ("BU") and "The Book of Ahania" ("BA") suggests quite strongly that systems recognizable today as "chaotic" underlie much of the basis of his conceived material reality, Ulro. In other words, the fallen world Blake constructs (which is quite reflective of his political, social and religious views) is only apparently chaotic and entropic in its many surges of destruction and decay; it only seems to tend toward homogeneity and heat-death. I intend to prove that the narrative of Blake's mythology fits within a pattern provided by chaos theory; much of Blake will be clarified and reconciled by viewing Ulro and the process of its creation--initiated by the supposedly "orderly" god Urizen--as an archetypal chaotic system.

Generally, chaos theory implies that many systems in the physical world (such as water turbulence) which seem chaotic in fact demonstrate complex and subtle levels of order once they are closely analyzed. Ilya Prigogine, a Nobel prize-winning chemist, describes certain types of chemical processes which behave "chaotically," terming these processes "dissipative structures."

Prigogine posits several conditions a system must fulfill in order for it to organize itself "chaotically," identifying characteristics universal to any chaotic system. Using what we will learn about the behavior of dissipative structures and other chaotic systems, we may observe the processes undergone in "BU" and "BA" as signifying both more than simple, mechanistic, Newtonian action-reaction, and more than traditionally-defined, "disorganized" chaos.

We will see that the creation process which takes place in Blake's mythology indeed meets all of the conditions of a chaotic system. Chaos theory dictates that any given system meeting a certain number of preconditions will tend toward an ordered "chaotic" state, which will be seen to correspond to the periodic repetitiveness of the Orc cycle. Though he appropriates chaos theory for his own poststructuralist ends, David Porush helpfully distills Prigogine's descriptions of these conditions into six characteristics which may be said to be fundamental to all chaotic systems. By understanding these conditions and then comparing them to the initial conditions of Urizen's world and the first events in its history, we will be able to discern the Blakean depiction of Urizen's creation and domination of the fallen world as fitting closely within the pattern of a chaotic system.

Before we proceed to examine Blake in light of chaos theory and Prigogine's conditions for a chaotic system, we will first briefly examine the process by which an originally stable system lapses into "chaos." In differential calculus, such systems can represented by nonlinear differential equations, which by definition involve "real world" elements of unpredictability (such as friction, or the effects of an environment on the growth of a population) and require repeated guessing when attempting to solve them. They describe systems that therefore "change abruptly or discontinuously," and, as explained by John Briggs and David Peat in Turbulent Mirror, "[i]n a nonlinear equation a small change in one variable can have a disproportional, even catastrophic impact on other variables. . . . plots of nonlinear equations show breaks, loops, recursions--all kinds of turbulence" (qtd. in Argyros 237). When the nonlinear elements, or parameters (figures representing a system's degree of unpredictability) of such equations are of low value, the equations may tend to produce few or single solutions. In the case of chaotic systems, however, an equation's outputs instead "bifurcate" repeatedly, becoming more and more numerous until they enter a state of complete unpredictability or randomness--a graph of this equation would enter a "region of chaos"--though it is precisely during this shift of an equation's equilibrium into chaos that periodic "islands of stability" appear. Chaotic systems are therefore fundamentally unpredictable yet ordered; this is the definition of "chaotic" order, chaos theory thus demonstrating that there is a "deeper" order within the apparent randomness of a chaotic system.2

Before we can apply this theory to Blake we must first establish a "chaotic" framework for the narrative of his creation process. It is particularly important to understand Blake's conception of an original God-like eternity which exists in perfect order before the splitting of the four zoas and Urizen's self-imposed isolation, which he details in his commentary on "A Vision of the Last Judgment" (563). For Blake, any who envision the primal universe as chaotic (including Milton) are merely submitting to the faulty perceptions of their material, "Vegetative" bodies, and are being inauthentic to their true divine nature. Beings in Blake's Eternity do not exist in "Solitude" as Urizen desires, nor is Eternity chaotic. Instead, Blake maintains, "In Eternity one Thing never Changes into another Thing Each Identity is Eternal . . . " (556). Blake's vision of the universe from which Urizen attempts to isolate himself is one of perfect organization where each being exists in harmony with each other being; thus Urizen's new world, which attempts to discount the influence of any of the other Eternals or of Eternity itself, is incomplete and fractured from its very beginnings, a world which is "Disorganiz'd" ("BU" 10:27).

Urizen attempts to create his universe by ordering it strictly--like the Miltonic God, parceling it out with compasses. However, Urizen does not understand that his "creative" action refutes the highest form of Eternal order, for even before he begins creating he is alone, contrary to the state of Eternal unity; as he separates himself, he is "Self clos'd, all repelling." "[U]nknown, abstracted / Brooding secret, the dark power hid" ("BU" 3:3, 6-7). Urizen hopes "for a joy without pain, / For a solid without fluctuation" (4:10-11), insecurely seeking to escape the threatening pain of the presence of Others, to establish a complete universe separate from the "completeness" of Eternal unity; this of course proves to be impossible. The only result of his solipsistic hubris can be disarray. Ironically, in trying to escape from "fluctuation," Urizen's creation attempt immediately results in traditionally-defined chaos as he strives "in battles dire / In unseen conflictions with shapes / Bred from his forsaken wilderness" (3:13-15) and indeed, from the perspective of the Eternals, Ulro appears as "The petrific abominable chaos" (3:26). It is worthwhile to note that Blake describes the narcissistic retreat of Urizen similarly in the first few lines of the poem, asking "what Demon / Hath form'd this abominable void" (3:3-4). For Blake, the solipsistic, necessarily chaotic retreat from ordered Eternity and others is virulently "abominable" to the supra-Urizenic laws of this divine state.

Urizen reacts to this perceived chaos by promulgating his sexually and morally repressive decree in the style of the stern God of the Old Testament, establishing "One command, one joy, one desire, / One curse, one weight, one measure / One King, one God, one Law" (4:38-40). As it is impossible to permanently restrain the Eternal fires that burn within his creations, his Law will be unable to forever control them. Fittingly, in response to this Law, the Eternals rain their fire upon Urizen, spurring on the narrative of "BU." This urge of man to return to an unfallen state of Eternal order is heralded by Cramer as central to Blake, who states in his discussion of "A Vision of the Last Judgment" that "Eternity Exists and All things in Eternity Independent of Creation" (Blake 563) (Cramer 523). This concept will be quite useful in explaining the drive toward Orcish energetic rebellion as an attempt to reestablish contact with the Eternal self, and why the momentary instances of Orc's overthrow of Urizen correspond to "moments of stability" in chaotic systems.

Now that this framework for "BU" is established, we can more easily see these and subsequent events in "BU" and "BA" as falling within the characteristics of a chaotic system. As we will be looking at Prigogine's definitions of these characteristics, we must first note that the dissipative structures he discusses are indeed recognizable as chaotic systems.

According to Prigogine, like any chaotic system, a dissipative structure originates "spontaneously" in systems that are "far from equilibrium" (12).
Once this structure appears, order usurps formerly chaotic conditions. The "chaotic" process of this system is dependent on the its interaction with its surroundings; this influence on the ensuing chaos of a system is precisely what nonlinear parameters try to describe. As with other chaotic systems, dissipative structures derive an internal order from their instability, and it is by means of their constant lapsing into disorder and rebounding into organization that they "evolve," proceeding toward some unimaginably complicated yet structured end, despite the efforts of the supposedly-dominant force of entropy.

Of Prigogine's conditions for the "remarkable event" of "the spontaneous formation of a dissipative structure" (Porush 290), his first is that the system must be open. David Porush, who comments extensively on Prigogine's description of dissipative structures, clarifies this point: "That is, [to be open, a system] must be engaged in some ongoing exchange of energy, matter, and/or information with its environment . . . Dissipative structures are not really dissipative in the sense that they evaporate into degraded homogeneity and entropy. Rather, they are islands of anti-dissipation that must dissipate certain energies in order to maintain the direction of their evolution" (290). The dissipation of energy produces not entropic chaos or heat-death but order, as evolution brings life forms to a more ordered state rather than a more homogeneous one, and an influx of outside influences is required for the system to evolve. Clearly Urizen's formed world, Ulro, is an open system, much to his initial dismay. In creating his universe, Urizen's intentions are to separate himself completely from the rest of Eternity and the other zoas. Despite his attempts at isolation, his realm is invaded almost immediately by the "eternal fires" of the Eternals and the guardianship of Los, who reorders Ulro in almost Urizenic fashion as Urizen himself hibernates in fear. Thus, into Urizen's closed system there immediately comes an infusion of energy (fire), matter (Los), and information (Los's further organization of Urizen's chaotic realm); this prospective chaotic system is from the start subject to outside influences from all parts of Eternity outside of Urizen himself. Even after Urizen later awakens and tries to control the human society he has found with repressive religious, sexual, and social laws, he is never successful at quenching its energy. He is always subject to revolts instigated by those such as Fuzon, his own son,and Orc, the incarnation of another zoa (Luvah). All of this rebellion comes about because of the influence of outside sources; Orc is obviously separate from Urizen, who spontaneously gives birth to Fuzon only after Los has defined the human form.

Prigogine's second condition for a dissipative structure is that it must exist in a condition "far from equilibrium." Porush explains: "That is, it must be highly unstable . . . [i.e.,] highly unbalanced and prone to erratic, even catastrophic, swings in behavior. This also means that [such a system is] highly sensitive to initial conditions, i.e., that small changes in the beginning can have system-altering and global changes at the outset. In chaos theory, this is called the 'butterfly effect'" (290). The Ulro world, created as flawed by Urizen (and, later, Los) is governed by impossible-to-obey laws, and is thus permanently unstable and far from equilibrium. As long as the flawed world exists, it will be impossible for Urizen to quench the urge to rebel of all those within Ulro; they forever burn with the "eternal fires" reminiscent of lost Eternity, desiring to throw off the repressive yoke of Urizen. Their yearnings for rebellion and periodic surges of revolution are, of course, represented by the cyclic actions of Orc and Fuzon, thus clearly demonstrating that Urizen's world perpetually exists in a highly volatile, unstable state, bursting with ungovernable energies. The instability of the initial state of Ulro is demonstrated by the ease with which Los and the "eternal fires" invade the "hidden" Ulro. Certainly, these two intrusions have repercussions which alter hugely the development of Urizen's world; what occurs as a result is a prime example of "the butterfly effect."

Dissipative structures must also, according to Prigogine, "fluctuate nonlinearly." "That is, the amount of energy, matter, and information they contain at any future moment will be unpredictable (they follow nonlinear differential equations that are usually difficult to solve and which describe behaviors impossible to predict)" (Porush 290). Once Ulro is created, its contents are immediately perceived as chaotic, even by its creator. Like a chaotic system, we know (or at least Urizen knows) the initial conditions of the structure's creation, but it is impossible to determine (for us or Urizen) what will take place within it. Despite Urizen and Los' attempts to organize Ulro, their efforts only result in greater chaos as human forms, possessing free will, become potential rebels. People experience the world "subjectively," not according to the dictates of Urizen. In fact, as Frye puts it, "[t]he possession of the will by the natural man is the basis for the contrast in Selfhood between the tyrant and the victim" (293). The only way to achieve victory over Urizen's repressive power is to exercise the will--though not necessarily in the violent manner of Orc, as Blake suggests both in Milton and Jerusalem.

Prigogine's theory also posits that dissipative structures begin with a bifurcation point, "a system-shattering moment when the previous, simpler organization can no longer support the intensity or frequency of its own fluctuations, and either disintegrates, or jumps to a new level of order and integration." Given this truth about dissipative structures, it follows that these systems are "deterministic (their initial conditions can be stipulated in mathematics) but unpredictable (you literally cannot stipulate what they will look like down the road, or across the bifurcation point)" (Porush 290-1). This information helps to clarify the above comments on the existence of subjective will in Blake despite knowledge of "initial conditions." However, Porush also further explains the concept of the bifurcation point, stating that the set of solutions for a seemingly stable nonlinear system will suddenly split given a large enough "nonlinearity parameter," breaking the stability and equilibrium of the system. The set of solutions will split, and then split again . . . until the system shifts into a "region of chaos." Such moments of "bifurcation" abound in Blake's creation myth, and they clearly come about as a result of some stressful, constraining state. Perhaps the moment of bifurcation most important to the development of Ulro is the initial division of the four zoas, in "BU" told from the point of view of Los, who agonizes over the fact that Urizen has separated himself from him: "Los wept howling around the dark Demon: / And cursing his lot; for in anguish, / Urizen was rent from his side" (6:2-4, 7:1-3). Urizen apparently perceived his position among the four zoas in Eternity as limited, and consequently retreated into a world of his own making. Los reacts violently to this separation, is "affrighted" by Urizen's deathlike state, and as a result "rouz'd his fires" and begins his task of shaping Urizen's world and creating the human form. As a result of these actions, further levels of bifurcations occur: Los spontaneously generates his emanation, Enitharmon, who in turn further "bifurcates" by giving birth to Orc and, later, to the race of humans. Witnessing Los's embrace of Enitharmon, the Eternals imagine the imminent bifurcations which will come about as a result, and perceive them as evidence of Ulro's further distancing from the primal Eternal state: "Eternity shudder'd when they saw, / Man begetting his likeness, / On his own divided image" (19:14-16). Also as a consequence of Los's actions, Urizen, upon awakening and observing the new world of humans ready to be governed by his One Law, spontaneously generates children, including Fuzon, "first begotten, last born" (23:18). Fuzon attempts a rebellion against his oppressive father in "BA," castrates him, and as a result Urizen's emanation Ahania is created--another bifurcation.

Urizen retaliates, killing and crucifying his son, but by now it is too late: his system of Ulro is wholly chaotic, out of his control. The figure of Orc (which encompasses Fuzon) will periodically and perpetually direct humanity's energies against Urizen until the events of Jerusalem. Urizen's initial actions, contrary to the nature of Eternity, thus necessarily lead to the creation of a chaotic system. The fire of the Eternals and the intrusion of Los are instrumental to the creation process of Ulro, and provide the potential energy for the eventual return of humanity to an Edenic state.

Briefly, Prigogine's final two conditions for a chaotic system are (1) that it be large enough, because "Below a certain scale, phenomena tend to behave themselves better and more classically, i.e., more in accordance with Newtonian mechanics" (Porush 291); and (2) that it display reliance on "feedback mechanisms." As Ulro is the entire material universe, it certainly seems to fall within the requirement of being large enough to be a chaotic system. Its energy also feeds back upon itself once it becomes established to spur further "chaotic" growth. All of the creations of Urizen, including his son Fuzon and his emanation Ahania, react to Urizen's oppressive dominance, challenging his authority. In fact, all of the living forms of Ulro, while formed by Los, are originally brought into existence by Urizen; thus their later interactions with him (especially as part of the Orc cycle) can be termed as feedback, contributing to the greater chaos (and thereby the higher order) of Urizen's system.

Since all of these qualifications suggested by Prigogine can be seen to apply to the system created by Urizen, we should then, if the model holds, be able to perceive the now fully-defined chaotic system as possessing a periodic order within its apparent chaos represented by "islands of stability." The momentary chaos within Urizen's world can perhaps most easily be seen to manifest itself in the straining of its populace against Urizen's repressive laws. This is symbolized in "BU" by the birth of Orc, his consecutive "burstings" of the spontaneously- forming girdles which "Opressd his bosom" (13), and his being chained upon Urizen's mountain. In other works of Blake the latter stages of the "Orc cycle" are revealed: we see Orc bursting free of his chains to rebel against Urizen, his victory, and his consequent metamorphosis into Urizen. This process then repeats itself, with the newly-deposed Urizen changing into a new Orc who sets out to rebel against the new Urizen. According to Blake, because the "original" Orc's actions are violent in nature and not "forgiving" like those of Milton in Milton and those presented in Jerusalem, Orc will always become what he originally fought against: an insecure, repressive dictator. Thus in the Orc cycle we have a world forever in a chaotic state, rebelling against control--except during those brief moments when the success of revolution, of the exercise of imaginative energy, is still fresh, before Orc has had a chance to become Urizen. At this precise instant when energy overthrows reason and before it itself decays into Urizenic tyranny--when the oppression of man's divine nature is gone--man is at this moment closest to his Eternal, perfectly ordered self. These moments, it has been said, can be seen to correspond to the periodic "islands of stability" within an otherwise random-seeming chaotic system, and according to Frye, the Orc cycles themselves indeed reoccur periodically in Blake.

These repeated moments of freedom within a larger repressive system will continue until the eventual arrival of the apocalypse envisioned by Blake in Jerusalem. At this time, once the rebellious energies have been turned toward Christ-like forgiving ends, the world will transcend its Ulro state, reuniting peacefully with the Eternity from which it sprung, forever vacillating between the paradisical states of Eden and Beulah (Bloom 433).

The chaotic system created by Urizen with the formation of Ulro can now readily be seen as resulting in the same level of complex repetitive order achieved by such systems. By the time of Jerusalem's "apocalypse," Ulro will have resolved itself toward the highest form of order--that ultimate, Eternal order from which it originated, its cyclic "islands of stability" changing from the victorious moments in the Orc cycle into the infinite cycle of Eternity.

Urizen has pushed his world to extremes by means of his repressive laws attempting to limit the creative fires that burn within the beings he has tried to create separate from Eternity. As a result, his attempt at creating a simple, deterministic, easily-governable universe has exploded. Urizen's resistance to energy and insistence on his repressive definitions of order ironically keep Blake's Edenic order from establishing itself--by attempting to order his system Urizen reinforces its chaotic state--though the cycles of Urizen's encounters with Orc reveal (to us, if not to Urizen) glimpses of a deeper order. Urizen's Ulro thus corresponds dramatically to the model of a chaotic system. Once we appropriate this metaphor for our understanding of Blake, it is much more possible to consolidate the apparent chaos of his mythology within his unified cosmic scheme; despite the often-disorienting variety of Blake's archetypal creations, we should now be able to sense within them the burning potential of Eternal order.

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Works Cited

Blake, William. The Complete Poetry and Prose of William Blake. Ed. David V. Erdman. Rev. ed. New York: Doubleday, 1988.

- - - . "The Book of Ahania." Erdman, Complete Poetry 84-90.

- - - . "The Book of Urizen." Erdman, Complete Poetry 70-83.

- - - . Jerusalem. Erdman, Complete Poetry 144-259.

- - - . Milton. Erdman, Complete Poetry 95-144.

- - - . "A Vision of the Last Judgment." Erdman, Complete Poetry 554-566.

Bloom, Harold. Blake's Apocalypse: A Study in Poetic Argument. London: Lowe & Brydone, 1963.

Cramer, Patricia. "The Role of Ahania's Lament in Blake's Book of Ahania: A Psychoanalytic Study." Journal of English and Germanic Philology 83 (1984): 522-33.

Frye, Northrop. Fearful Symmetry: A Study of William Blake. Princeton: Princeton U P, 1947.

Gleick, James. Chaos: Making a New Science. New York: Viking, 1987.

Porush, David. "Literature as Dissipative Structure: Prigogine's Theory and the Postmodern "Chaos" Machine." Literature and Technology 5 (1992): 275-306.

Prigogine, Ilya and Isabelle Stengers. Order Out of Chaos: Man's New Dialogue With Nature. New York: Bantam, 1984.