Sunday, May 4, 2014

A. Square and the Ainulindalë

(Alternate Title: "Damn Kids, Get Your Hyperspatial Geometry Out of My Creation Myth")

I'd like to preface this blog post by noting that this is in fact a response to Monday's class - I fell quite ill Tuesday evening, and spent the better part of the time I should have been writing this post feverish and delirious, grappling with a nasty stomach bug. Cold it was as the tide of death: almost it froze my heart; darkness took me, and I strayed out of thought and time. But I digress.

Near the end of Monday's class, someone rather aptly described the music of creation as a synesthesia-like experience. I say it is very apt because the things that go into creating a universe - events and places and the laws of nature, people and their deeds and stories - can all be thought of as rich patterns of information, and it's no new concept to us that such a patterns might be compressed and re-encoded as a single, infinitely intricate work of music (the idea that infinitely complex information can be encoded in a single sound wave - or perhaps an image or some other pattern - is certainly familiar to anyone who has closely examined some of the more exotic fractals, for although some (like the Sierpinski gasket) merely contain copies of themselves, others (such as the Mandelbrot set) are truly infinite in their variations on a theme. (And I'm going to return from this tangent lest I start nesting infinitely varied parenthetical asides within themselves - unlike Eru, I do NOT have to capture the entirely of time and space in my blog post.)). But when Tolkien describes the entire richness and complexity of the whole universe and the whole course of its history being expressed through this piece of music, I think there's something more going on than just re-encoding a pattern.

We can try to achieve a better explanation by using a different (also mathematical) comparison. In the previous paragraph, I described the music in the Ainulindalë as a fractal-like re-encoding of a complex pattern, but I think it's more apt to think of it as a projection of a very high-dimensional structure. That is to say, if one wants to construct an entire universe, one needs quite a few dimensions of data (spatial and temporal, to be sure, but then you need to express people and objects that fill those places and times, and how many axes would one need to characterize a sentient mind? But again, I digress.), whereas a piece of music, no matter how intricate and beautiful, is a low-dimensional expression of information. So in a sense, we could look at the Ainulindalë as Eru crunching down the complexity of a world into the (relative) simplicity of a piece of music. But I still don't think that's quite the right way to look at it - because one of the main characteristics of projections is that they tend to sacrifice information, in the same way image compression costs us image quality. One can hardly expect to reconstruct the original data from a very low-dimensional projection, nor can one expect to construct a universe from a compressed representation.

So for those of you who grow impatient with my analogies to mathematics, I must apologize, for my third and final proposal once again argues by analogy to mathematics. (But fear not: this time I've eschewed fractals and linear algebra for simple geometry.) If we accept the premise that the universe is an incredibly large, complicated, and high dimensional structure, then it is of course difficult to imagine that us humans (who, while often noble in reason, and possessing quite substantial if not truly infinite faculty, nonetheless occasionally struggle to visualize what we had for lunch last Thursday) can comprehend complicated things like gods or infinity or the entirety of time and space. In the same way, Mr. A. Square of Flatland could scarcely comprehend a sphere - instead, when the two dimensional being was presented with a three dimension one, he could perceive just a slice of it - a strange circle that could (from his point of view) change size in addition to moving about in flat space. So I argue that the music of creation is more than just the music that is described to us, and the music we "hear" (or imagine hearing, as the case may be) is but one facet of the actual "music" (what the full form of this music may be is beyond the scope of this blog post, though).

Now of the three theories I have advanced why do I commit more to the last one than to the first two? The attractiveness of the third for me lies in it's relevance to the Ainur, and the very Christian nature of Tolkien's creation myth. We already covered quite a lot of ground in class discussing the Ainur themselves (and I'm told we covered them even further on Wednesday), and at one point we touched upon the idea that the Ainur are all aspects or facets of Eru. This idea is reinforced by comparison to Christian theology, in which - underscored by the Hebrew naming conventions - the angels are often implicitly considered to be aspects of God. In certain stories, this is made even more explicit: there are numerous instances of angels who deliver messages from God in the first person. Or, for example, consider Jacob wresting with an angel in his dream, only to receive the epithet Israel, meaning something along the lines of "wrestles with God." Given that we see hints that Tolkien thinks of the Ainur in this way, it's not unreasonable to look at the rest of the Ainulindalë and ask whether this too represents in some sense an aspect of a greater whole.

But why reject the first two models? For those of you who will no doubt object that the previous paragraph's argument seems frail and tenuous, I offer something meatier to chew on. Ultimately, the problem with the synesthesia and projection models are that they are, in some sense, not real - at least, I doubt they would be real enough for Tolkien. With the former, you get a sensational representation of something that's beyond your comprehension. With the latter, you get a sort of "reduced complexity" image of the whole - a shadow puppet creation myth. Yet, as we see from his letter to his son (letter 96), he very much objects to viewing the Christian creation myth as a mere allegory or metaphor, and would likely feel the same way about his own. "I do not now feel either ashamed or dubious of the Eden 'myth'," he claims, and while he makes it clear that his viewpoint isn't one of complete literalism he still insists that "certainly there was an Eden on this unhappy earth." What are we to make of this? It certainly ties into Tolkien's ideas of primary and secondary reality, but I also claim that it's a strong argument for the Ainulindalë being non-metaphorical. And that's what the flatland model offers: while we as limited beings cannot comprehend the full scope and majesty of Eru and the music of creation, what we do witness in the Ainulindalë is the real deal, even if only the smallest sliver of its full scale.

And in a certain sense, I think this is how Tolkien operated as a writer as well. Though people certainly read his works as stories, and still may get something out of them from doing so, he meant for them to be more than that. When Tolkien wrote, he created histories and worlds, and his "stories" are flatlandish slices through them. Even though they are just slices, through them we can still grasp the contours of the greater whole and (as he puts in when describing Eden) "receive nourishment from both the beauty and the truth". That's what I get out of the Ainulindalë, at least: we're all just flatlanders trying to listen to the music of the spheres.

D. Kassler


  1. Of course, Tolkien was not a demigod; he was no less than us a flatlander trying to listen to the music of the spheres. I don’t think it’s quite right to say that “when Tolkien wrote, he created histories and worlds.” The histories and the worlds exist outside Tolkien and are in some sense too big for him to really have had in his head in their entirety. Certainly Tolkien himself seemed to feel this way: he describes in many letters the way he seemed to “receive” knowledge of what happened next in his stories, and in his works of fiction creative insights often come in dreams, as if from somewhere outside the creator. I think your insight here helps us make sense of how Tolkien can both be receiving the history and languages of Middle-Earth from outside himself (or, relatedly, trying to construct them in a logically determined process from our given artifacts) and still be primarily a creative agent. He didn’t make Middle-Earth: it’s our own world, and it’s been around long before Tolkien. He didn’t write the music of the spheres, nor could he even really comprehend them in their entirety, any more than we can. What he can do, however, is give us a cross-section of those spheres, which is hopefully sturdy enough to stand on its own while also giving us some idea of the beauty of the larger whole. And it is this cutting-out that is a creative act, which takes art and skill. Which is to say that of course when Tolkien wrote he was creating stories. But the creations themselves can be taken to be more than that.

  2. Dear D. Kassler,
    Great work here! I enjoyed your three models and how you carefully led your reader from one to the other without wandering and without forgetting to tie your thoughts together to express your main idea.

    What is great about the flatland model is its ability to balance the simplicity of the narrative with the great complexity (in the plan of Eä) that it surely represents but which is beyond us. But if we press this further, how could we conceptualize this relationship (i.e. we, like Mr A. Square, trying to name something beyond our experience)? Can we think of analogical language to fit this relationship?

    Secondly, I’m always reminded of Manwë’s realization, after the Dwarves’ adoption, that there were more themes and nuances to the Music than he had first heard (Quenta Sil., chapt 2, last page). Since what the Music is or represents is somehow beyond us, how does that factor into the continuing discussion of Men’s free choice to go ‘beyond’ the Music?

  3. I really appreciate this response. Your writing is delightful and I never quite considered the music of creation quite like this. Certainly the music of creation is around us constantly, as it envelops all of time and space. But what of it do we hear? Or another question-- why choose music as the carrier to all experience? I think music is a singularly potent description of how formless ideas can obtain a sensual form, from which we can detect changes, ebbs and flows. Music of course implies the universe-- as we automatically require time, space and matter.

    My point here is that music is a special "literal metaphor"-- and I think your geometrical arguments are indicative of this. However, it does pose some difficulties for the existence of Men. Is the free will granted to men another set of higher dimensions? How do they interact with the geometry differently than the Ainur who first spun the music or the immortal Elves? It would be really neat to expand this, but I'm not sure where that would take us. Cool thoughts.


  4. This is a fantastic way of looking at Tolkien’s creation myth. I don’t know if it’s necessarily what Tolkien was considering when he wrote the creation story, considering he was not a mathematician and he has never put any particular emphasis, to my knowledge, on math. However, I don’t think this invalidates your point that using music is a way to simplify the method of creation. Perhaps rather than thinking of the use of music as a tool employed by Eru to simplify creation, we can think of it as a tool employed by Tolkien to simplify to the readers the idea of creation.

    I do have an objection to your casual reference to a piece of music as data; music is not data, it is our interpretation of data, and this makes it a problem to suggest that Eru would use it to “compress” the creation of the universe. Also, perhaps this is a bit nit-picky, but I strongly object to the suggestion that a universe requires more dimensions in terms of data than a piece of music. Physically, that’s incorrect. The universe needs time, space, mass. I don’t think I’d consider people as axes but points on the graph, a culmination of time, space, and mass. You need the exact same thing with music. Music occurs when sound waves travel through the air at a particular frequency and are received by something (for example, an ear) that transmits that frequency to be interpreted as sound. You need the exact same dimensions of data for both music and the universe, but you just need greater quantity for the universe. I don’t think this model would work for your explanation. Your Mr. Square model is great!