This is the first of a three part series on mathematics, metaphysics, and magic. Check back in next Monday for part two.
I’m not ashamed to admit that I’ve thought a lot about how magic spells might work, particularly in the context of Harry Potter. In order to get magic to work, you need to be magical in the first place, point a wand, and say a specific word – unless, of course, you’re really good (Dumbledore, Voldemort) or really bad (out of control pubescent Harry), and then you need none of these to make magic happen. Couple this with the obvious fact that the objects upon which you’re casting a spell aren’t always magic – they don’t hear the words you speak and obey your commands – and it becomes clear quite quickly that the words themselves cannot be magic, but rather provide some connection between the magic within the witch or wizard and the aim of the spell.
So why say the magic words? And why in Pseudo-Latin, rather than English? And what is all of this magical theory about which so many classes are taught, anyway?
The answer, for me, lies in the metaphysical power of language. An obvious way to take this is to say that language represents knowledge, and serves as a label for an idea one might have, such that the act of saying that word focuses the mind on that idea. I’d like to take that even further, and explore the idea that language is knowledge.
I think that’s the premise for incantations – they don’t just represent what you want to do, they stand in for those thoughts. In this way, the theory of magic spells serves as an incredible allegory for the relationship between language and reason. Let’s take for an example the first spell that Harry and friends learn – levitation. Wingardium Leviosa.
Here’s how I think it works, and why it doesn’t just work right away for most students: you have to understand more than just the general idea that you want the object in front of you to float in the air. There’s a surprising amount of detail involved – you must consider how you want the thing to move, how you’ll control it’s movement, whether or not it’s floating as such, or is simply placed in the air where you demand, whether it continues to move, whether it stays where you put it, and more. These are decisions that have to be made every time you make the attempt, but if you had to think through the details (let’s see, if I want it to kind float upwards in a gentle fashion, maybe I could think of the air above the object being displaced… or maybe moved to underneath the object in just the right quantity to support the thing at the level that makes the most sense…) you’d be exhausted, and probably never do magic. You need a general concept.
Enter the magic word. “Wingardium Leviosa” is introduced to the students along with a visual demonstration, and so the senses take in the cue word while at the same time absorbing a ton of physical information that the student couldn’t possibly explain in detail. There’s a certain, unnamed understanding about how things float or levitate both along with and against the laws of physics such as they are unquantifiably comprehended, and this understanding gets associated subconsciously with the word.
That’s why young witches and wizards can’t just read the spells out of a book and expect to get them right unless they have some advanced theoretical understanding of how things move and behave. But that’s also why they need the words – the trick is to figure out how to abstract what is common to the execution of a spell and build an association between what has been abstracted and the specific incantation. The students need to see the spell in action, but the empirical experience alone would be too specific to be usefully reapplied.
It’s a bit like teaching a dog a new trick – you have to repeat the trick a number of times, letting the dog figure out what you want, and then letting the dog associate the action and the reward with the cue. If you try to change the cue at all, it’s meaningless to the dog.
After a while, though, the association becomes second nature, which is why the incantation needs to sound a little foreign – you wouldn’t want to dilute the effect the word has on your mind by making it a simple word you use thoughtlessly on a regular basis. Strong and clear repetition of the spell embeds the bundle of thoughts required to properly intend levitation into the incantation in a way that allows the spell caster to skip a bunch of steps. The word allows the witch or wizard to think without thinking, essentially.
We do the same thing with word definitions, particularly when referring to categories or concepts. Take the idea of a triangle, for example. When you first learn the word, you likely learned it by associating it with an example – a drawing on a page, a block, an example found in the real world, etc. At first, it seems like you’re learning about triangles by seeing them, but if that was the sum total of the experience of learning shapes, we’d never be able to have any idea of a triangle that went beyond that first wooden block. But we do go beyond this – we start to notice similarities between these various different things the people around we are calling triangles, and then we start to recognize them on our own by comparing new things to these memories. Without realizing it, we start to learn about the concept of triangle such that we are able to spot new ones all on our own, even if they’re different sizes, colors, textures, and different contexts than any other triangles we’ve ever seen.
Later on, we get a definition to accompany the word – a mathematical name (three sides, 180 degree, etc.) for a concept we’ve essentially learned on our own by learning simply the word “triangle”. When we see triangles in the world, we don’t run through every single memory we’ve ever had of a triangle to see if this new things matches up, and we don’t even check back in with the definition. We just know – the word replaces this process, standing in for all of the empirical data, and even some of the rational knowledge.
I take a lot of what I think on this matter from St. Augustine’s Soliloquies (for which I also owe the name of this blog). Regarding his own experience learning about shapes, he says:
In this case I have used the senses like a ship. For when they had carried me to my destination and I had left them, and I was placed, as it were, on dry land, I began to turn these things over in my thoughts, but my steps were for a long time uncertain. So it seems to me that one could sail a ship on dry land more easily than one could perceive geometry by the senses, even though they do seem to help those who are first learning.
Similarly, it seems that magic spells serve to bundle ideas abstracted from experience and then build them as intentions into a word that lets the witch or wizard skip all the complicated steps in a quick flick of a wand. Then, just as we learn words by defining them with words we already know, they can learn more complicated spells that bundle the bundles of intentions into greater and greater levels of immediacy, coming in the end to a point where they can simply act on those intentions without the middle step of using a focusing word.
In language, we come to this point when we can speak fluently, without thinking, when we can visualize things without breaking them down into their simplest components, and when we can, as it were, sight-read the music without thinking in solfege or intervals. Words, like magic spells, allow us to aggregate information we already know in a way that’s fuzzy and broad, and turn it into something we know with precision – and then from there, we can abandon our tools of precision for a knowledge that requires no mediation.
 Augustine of Hippo. Soliloquies: Augustine’s Interior Dialogue. Trans. Kim Paffenroth. Ed. John E. Rotelle, O.S.A. Hyde Park, New York: New City Press. 2006, 29