It was one of those nights when time was ticking away far faster than my homework questions were being done, when the first bout of tiredness had passed and left restlessness in its wake — in short, it was a night like so many other nights that it’s… a little concerning. But that is a topic for another day. This being my first contribution to Odyssey, it is only proper for me to begin at the beginning, with the little nudge out of the door and into the wondrous world of literature that was "Harry Potter."

On such a night as I described, in the middle of some indiscernible differential equations, I began to ponder the theory of magic and spellwork in the Wizarding World. Perhaps it was because the trailer for "Fantastic Beasts" had just come out that day, or else math was proving more stimulating than I ever gave it credit for. In any case, I put aside Picard’s theorem and put on my pointy witch’s thinking hat.

It was not spells of immense power that I started with, not Avada Kedavra or Sectumsempra. It was with the household spells that were Mrs. Weasley's mainstay throughout the seven books until the moment that Bellatrix Lestrange met her end.

For the most part, household spells that we see in the series are non-verbal. Not only are they non-verbal, they also appear to be incantation-less. That means the only thing driving the magic in that case is the concentration of the witch or wizard.

I imagined it to be almost like programming, except that you’re commanding some mysterious force instead of electrical impulses. I thought of it as visualizing the results of what the spell you’re casting. If you are a wizard, and you want to cut a bowl of potatoes, you would command in your mind that the potatoes rise and are split, while specifying the split (lengthwise, cubes, etc). Verbal household spells like Tergeo should also require some concentration — else how does the spell know what to clean? And the classic Wingardium leviosa should require concentration as well in that you ought to be able to only levitate a certain object from among a pile.

Transfiguration in general appears to be an incantation-less field of magic (off the top of my head, I can only think of Evanesco). To be able to concentrate on changing something in its essence would require an absolute understanding of the anatomy of the object and the theory of how the attempted magic works — kind of like physics. I probably wouldn’t have been very good at Transfiguration.

Concentration — that, it occurred to me, was perhaps what made bookish Hermione superior to her peers in spellcasting, first with verbal spells and then non-verbal in the sixth book. There’s nothing like copious amounts of reading to train you to calm your mind and focus it intensely on one thought or action.

From there I moved on to the function of spells. Since non-verbal magic is possible, it stands to reason that the words to the spell are simply an aid for concentration. Defense spells all have incantations; this makes sense since during the tumult of battle it is unlikely that the typical wizard will have the time or presence of mind to concentrate sufficiently. A wizard could never deliver the Killing Curse without delivering its incantation as well.

And how are spells, or rather the incantations that conjure them, invented? For obviously they were all created by someone, not just Snape’s textbook scribbles; with J.K. Rowling’s confirmation that magic-users exist all over the world, some of which do not use wands, it is not the case that a wizard who doesn’t speak a Romantic (or related) language would utter Lumos to conjure a light.

Here I returned to the analogy of programming. Perhaps a spell-inventor is like a programmer. Inventing a spell would be like creating a novel program or algorithm; the incantation is merely a label. It’s like naming an object or a function, or a global variable: it doesn’t technically matter, but it really boosts efficiency and user-friendliness if the name describes what the spell is supposed to do.

A spell-inventor imbues the words with power, which is saying spells tends to be more effective than using them non-verbally. But I figured that if the wizard was powerful enough, there should be no difference.

Perhaps it was even possible, I mused, that with enough concentration, a wizard could say one spell and cast another.

The last thing I dwelt upon before reluctantly returning to my studies was the troublesome topic of the destruction and creation of things. We know, thanks to Hermione and her memorization of Gamp’s Laws, that food cannot be created, but clearly many other things can, though Transformed objects tend to be insubstantial compared with non-Transformed versions. And McGonagall herself said in Book 7 that Vanished objects go “into nonbeing, which is to say, everything.” Then perhaps the creation of things is merely a matter of the conservation of matter. If Vanished objects disappear into, say, some sort of void, where they disintegrate into formless matter, it is possible that when a wizard creates an object “out of thin air,” they are in fact drawing up matter from that void.

There are certainly many holes in my “theorems of magic,” as one would expect when trying to figure out that which does not exist. But fantastical imagination must exist for a purpose other than entertainment of the masses, else why would we have evolved to be capable of it? I look forward to many more journeys of magic, from this summer’s play, "The Cursed Child," to "Fantastic Beasts," its sequels (take my money, I don’t care), and beyond.