Chaos theory was first developed in the 1960's, but one can see in the way Nietzsche tries to explain eternal recurrence that he seems to have had an intuitive understanding of it. This would make sense in light of Nietzsche’s connection of time to ascent and descent and Fraser’s observation that lower umwelts have effects on higher ones. Fractals are images of eotemporal systems where the lower prototemporal and atemporal levels are most pronounced – creating the fractal image, such as the Mandelbrot set, one of finite space encompassed by an infinite border, which repeats the created image an infinite number of times as one descends through the details of the crooked border, creating an eternal recurrence of the same form over time as one goes deeper into (magnifies) the eternal border of the form. Nietzsche says, in describing the eternal return, that “since between every combination and its next recurrence all other possible combinations would have to take place, and each of those combinations conditions the entire sequences of combinations in the same series, a circular movement of absolutely identical series is thus demonstrated” (WP, 1066). We will remember that Zarathustra chastises the dwarf for oversimplifying the eternal return by calling it circular, so this note by Nietzsche should be moderated by Nietzsche himself having Zarathustra make this comment, showing us there is a more dynamic element to the eternal return than mere circularity. This description matches Fraser’s description of fractals:
The repeating regularity [of formal chaos] makes for an infinite depth of self-similarity. This may involve exact replication, it may be statistical or random; it may even consist of continuously emerging new patterns mixed with continuously reemerging old patterns. An infinite depth of self-similarity means that, no matter how much the details are magnified, self-similarity remains. (TOC, 6)
The fractal’s image is created by what is called a strange attractor. “A master trajectory toward which nearby trajectories of a system evolve is called an attractor” (TOC, 4), though “attractors themselves are models. They are metaphors for processes” (5). A strange attractor has the property of not being there, yet simultaneously having the ability to attract a system into creating an image of its becoming around it. This is perhaps what Nietzsche could mean when he says “There stands the boat – over there is perhaps the way to the great Nothingness. But who wants to step into this ‘perhaps’?” (TSZ, 224). If we extrapolate the idea of strange attractors up the umwelts from our understanding of them as working on the eotemporal level, we can see it acting to help create the biological forms and, if we extrapolate it up to the noetic level, helping to create ideas, concepts, goals, and values. We can now see something like the Lorenz attractor with apparent opposites. If we see one strange attractor as “good” and the other as “evil” (or pick any pair of opposites Nietzsche or Heraclitus affirm as constituting the world, through their agon – the Lorenz attractor makes an image of this very agon), what we see is that there is no pure good or evil, since the strange attractors are in one sense not there, though they do have an effect. Nonetheless, these strange attractors create a system of morals which pull our actions toward either the “good” or “evil” attractors – it is this system which can be said to be beyond good and evil, and is a more accurate vision of morals than are the strange attractors themselves, since the attractors are in a real sense not there, though they do affect everything. We can never be good or evil, since neither good nor evil have Being – we can only become better or worse in our actions. Or, as Ludwig von Mises says “The act of choosing is always a decision among various opportunities open to the choosing individual. Man never chooses between virtue and vice, but only between two modes of actions which we call from an adopted point of view virtuous or vicious” (45). The very choices of an individual are a complex dynamic system, making all of our actions, in this sense, beyond good and evil. This is, of course, a highly simplified metaphor. The “good” attractor is likely itself a set of agonal games set in opposition to the threat of destruction – to evil. The “good” attractor is a much more interesting attractor than is the “evil” attractor, though it seems this attractor is necessary for the “good” attractor to exist at all.
One could perhaps object that I have merely replaced the metaphor of the eternal return with another metaphor, the fractal. I do not deny that I am doing precisely that. The history of philosophy is a record of changing metaphors to fit philosophy to contemporary thought. The reason I am doing it in this particular case is because the metaphor of the fractal has the benefit of coming with a clear visual image which can help us understand the meaning of the metaphor. Also, it seems to me that any time one is using almost identical language to describe two seemingly different things, then those two things are probably the same thing. I have already given a few examples of places where Nietzsche seems to be using the same language to describe eternal return as I have for fractals, but are these the only ones?
Fractals show, as Nietzsche puts it, “what was and is repeated into all eternity” (BGE, 56). The repetition of the images act as a sort of “selective principle” (WP, 1058), which could help us “judge value.” What is selected? There appears to be a selection for dynamic systems with emergent properties creating greater complexity. We should judge such dynamic complex systems, and the creation of more complex systems, as valuable since they repeat regardless of scale. What Nietzsche says about how to endure eternal recurrence shows several other attributes of fractal geometry: “No longer joy in certainty but in uncertainty,” since one is uncertain which image one will encounter as one magnifies the fractal border; “no longer “cause and effect” but the continually creative.” The strange attractor does not have “cause and effect,” though the system is “continually creative”; “no longer will to preservation but to power” (WP 1059), since the image is always changing, meaning it is not preserved, though it has the power – in the strange attractors – to change; and “abolition of “knowledge-in-itself” (WP 1060). One can only see the effects of a strange attractor, one cannot know the true nature of any strange attractor, since they are all absent centers to the systems (which require time to exist) they create. In WP 1066, Nietzsche gives an excellent definition of a strange attractor: “the world may be thought of as a certain definite quantity of force and as a certain definite number of centers of force.” The world is not the Mandelbrot set, but a series of nested hierarchies like it, creating the grand system of multiple attractors we call the world, pulled into form by these “centers of force” – centers of force Nietzsche calls in WP 1067 the Will to Power. Further, Nietzsche connects the will to power to life in the same way as Stuart Kauffman connects strange attractors to life. “Life simply is will to power” (Nietzsche, BGE 259) There is a similarity too between the connection of entropy and dissipative structures to Nietzsche’s idea of discharge of strength and life: “Physiologists should think before putting down the instinct of self-preservation as the cardinal instinct of an organic being. A living thing seeks above all to discharge its strength – life itself is will to power; self-preservation is only one of the indirect and more frequent results” (BGE 13). Thus, Nietzsche asks us to suppose
we succeeded in explaining our entire instinctive life as the development and ramification of one basic form of the will—namely, of the will to power, as my proposition has it; suppose all organic functions could be traced back to this will to power and one could also find in it the solution of the problem of procreation and nourishment—it is one problem—then one would have gained the right to determine all efficient force univocally as—will to power. The world viewed from inside, the world defined and determined according to its “intelligible character”—it would be “will to power” and nothing else.— (BGE 36)
If we can connect the idea of the will to power to the idea of strange attractors and thus to dissipative structures, we can see Nietzsche arguing here – as I am arguing in this work – that everything in the universe can be understood through chaos theory and as dissipative structures. Nietzsche connects the will to power to life overall, but he also points out that the philosophers’ “will to truth is—will to power” (BGE 211). There is a connection between truth and power. Earlier, Nietzsche also said that “With the selective knowledge drive beauty again emerges as power” (PT, 26). With the connections I have made between strange attractors and both truth and beauty, the will to power could be seen as Nietzsche’s term for the world’s strange attractors – meaning the will to power is physics, not metaphysics (in the Kantian sense), as Nietzsche insists in WP 462 when he says the eternal return is the naturalization of metaphysics and religion. It can also be seen as the “will to beauty,” meaning, if the Will to Power is Nietzsche’s term for strange attractors, and strange attractors create complex fractal systems, then beauty comes from creating or seeing/hearing/etc. complex fractal systems. In light of this we can also now see what Nietzsche meant when he says in WP 522:
“Truth” is . . . not something there, that might be found or discovered – but something that must be created and that gives a name to a process, or rather to a will to overcome that has in itself no end – introducing truth, as a processus in infinitum, an active determining – not a becoming-conscious of something that is in itself firm and determined.
In WP 1067, Nietzsche describes the world again in terms that sound like he is talking about fractal geometry when he says the world is one that
does not grow bigger or smaller, that does not expend itself but only transforms itself . . . not something endlessly extended, but set in a definite space as a definite force, and not a space that might be “empty” here or there, but rather as force throughout, as a play of forces and waves of forces, at the same time one and many . . . out of the simplest forms striving toward the most complex . . . eternally self-creating, the eternally self-destroying.
In other words, the world is a dissipative structure, a fractal. And – “at the same time one any many” – beautiful, as the Will to Power is the Will to Beauty.
WP 1066 gives us this other aspect of chaos theory – Prigogine’s dissipative structures, which show how form develops out of formlessness – or form creates itself through formlessness. The “eternally self-creating, the eternally self-destroying,” the self-organized dissipative structures. Previous theories of entropy (what Nietzsche calls “the mechanistic theory”) said the world was irrevocably running down, prompting Nietzsche to say that if “the mechanistic theory cannot avoid the consequences . . . of leading to a final state, then the mechanistic theory stands refuted” (WP 1066). Prigogine’s dissipative structures solve this problem. In them we see, in Nietzsche’s formulation, that “The world exists; it is not something that passes away. Or rather: it becomes, it passes away, but it has never begun to become and never ceased from passing away – it maintains itself in both. – It lives on itself: its excrements are its food.” Entropy gives order, which itself dissipates, increasing entropy. The excrement of dissipative structures is entropy – and entropy is their food. The dissipative structure – and the fractal – both show “that everything recurs is the closest approximation of a world of becoming to a world of being” (WP 617) – in both, the world of being exists through becoming. Formlessness gives itself form through constant change. This image recurs in TSZ: “And as the world once dispersed for him, so it comes back to him again, as the evolution of good through evil, as the evolution of design from chance” (88). From what we have seen above, this means the evolution of permanence or being through transience or becoming – the very definition of a dissipative structure, which can generate spontaneous order from disorder. Fraser notes in TOC that “self-similarity signifies the presence of a pattern of behavior or structure which retains its identity in a world of pure becoming; it represents the birth of permanence from pure change” (7) and that “beneath all natural phenomena lurks chaos into which all processes and structures may collapse at any time and out of which, under certain conditions, different permanent structures and processes may arise” (9). The metaphors continue to match.
The affirmation of all – everything good and bad, everything great and small – is another important part of the eternal return, as we see in “the Heaviest Burden.” In GS, Nietzsche says “What I do or do not do now is as important for everything that is yet to come as is the greatest event of the past: in this tremendous perspective of effectiveness all actions appear equally great or small” (233). This is known in chaos theory as The Butterfly Effect. Newtonian physics says small causes have small effects, and large causes have large effects. Chaos theory shows that small causes – like a butterfly flapping its wings, which barely perturbs the air – can have large effects – like a hurricane – over time. Nietzsche came upon this aspect of chaos theory too in his opposition to Newtonian linear cause and effect.
“The two most extreme modes of thought – the mechanistic and the Platonic – are reconciled in the eternal recurrence” (WP 1061). This note is what showed me that the eternal return could be visualized with the images of contemporary chaos theory. The mechanical world alone is insufficient for Nietzsche, since “an essentially mechanical world would be an essentially meaningless world” (GS, 373) – it is without ambiguity, which Nietzsche says gives the world meaning. There must be some disorder for the order to be meaningful. This coincides well with contemporary information theory, which shows that one must have noise (ambiguity) if one is to communicate information. Without noise, one cannot have information – meaning. The mechanistic view shows us a world that will get more disordered over time – it is belief in creationless destruction. But this, the 2nd Law of Thermodynamics, appears, as Dauer points out, to contradict the 1st Law of Thermodynamics, which says energy cannot be created or destroyed, but only transformed. In Dauer’s words, it shows “the inevitable recurrence of natural phenomena” (90), which she argues Nietzsche was attempting to reconcile with the eternal return. When Nietzsche points out that “The principle of the conservation of energy inevitably involves eternal recurrence” (WP 1063), we can see, as Dauer says, that he “is roughly correct from the point of view of physics” (90). At least, physics as it was known at the time Nietzsche was writing. In addition to the view of the world the physics of the time promoted, Nietzsche had a problem with the Platonic view, which he saw as metaphysical, with its Forms. One could see the Platonic (especially Platonic Christianity) as the opposite of the entropic – as belief in destructionless creation. For Nietzsche, both views lead to nihilism, the mechanistic because it shows the world as meaningless, the Platonic because Nietzsche sees nihilism coming out of seeking meaning in the meaningless and realizing one has, by doing so, wasted a lot of time and strength on something false (WP,12) – such as Plato’s Forms and other metaphysical systems (12,13). By reconciling these in eternal recurrence, we get a mechanical world with meaning – meaning derived from the will to power/strange attractors, which one could easily mistake for Platonic Forms (or a noumenal world or a Schopenhauerian Will), since, like the Forms, the world gets its form (in Nietzsche’s words, “image” – which are the only things which exist) from them. We get a world where some things have meaning, but where everything does not have to be meaningful. And we also get Nietzsche’s cycle of destruction and creation. Here we see the dissipative structure – the fractal – the eternal return.
But we are still left with a question. How can a fractal-image of creation be the heaviest burden? The answer lies in the fact that this view shows us we can never reach the truth – we can only try (the trying-to-say of the creator). The “truth” is the strange attractor, the absent center that attracts, yet is not there. It is a burden because it shows the futility of all searching after truth. It is a burden because it shows we must do it anyway (in the trying-to-say of the creator). We now know we must search after truth, knowing there is no truth to find, that there is only the search, the system of searching, pulled into form by the strange attractor of “truth.” This is the burden and the tragedy of the idea, particularly as one important aspect of tragedy is that those who speak do not themselves truly understand what they are saying. In other words, the very act of trying-to-say is tragic – meaning the creator’s life is tragic. “The search for truth appears to be a wild-goose chase, as indeed it is. There are no fixtures in nature, wrote Emerson. ‘In nature every moment is new . . . the coming only is sacred . . .’” (Fraser TCHV, 72). The fractal-image of truth shows how right Fraser is. Truth is exactly as Emerson, Nietzsche, and Fraser say it is – unattainable. With Nietzsche’s eternal return and fractal images, we can see precisely why and how this is the case.