For those who think mathematics isn't useful or can't be applied to magic, why? What exactly do you mean when you refer to mathematics?

Since magic actually has a way of testing "correctness", i.e. casting magic, it seems weird that mathematics would not apply. If it does apply, why would it not be useful?

Edit: And if you think it is useful, how would you imagine wizards using it?

 

I think Taure has mentioned something in this vein. He is the only person I can recall, since he is the only person I know who often talks about the magic system of Harry Potter. I know I've heard it from others however.

 

I didn't realize this interpretation of my post could even be made, so sorry about that.

When you say you dislike maths in Arithmancy, how are you imagining it being used?

Also, where and how would you imagine maths being used outside of Arithmancy for divination?

 

One interesting thing to add is that according to Rowling wizards do not mind using math, since they can just do calculations magically.

https://www.wizardingworld.com/writing-by-jk-rowling/measurements

Personally though, I assume that learning those spells is the extent of math being taught at Hogwarts.

 

Hogwarts teaches magical theory; Hogwarts does not teach mathematics; ergo mathematics is not a part of magical theory.

I would argue a similar logic holds for Arithmancy:

Hogwarts teaches magical theory in its core classes; Arithmancy is an elective which many people do not study; ergo Arithmancy is not necessary to understand the magical theory underpinning the magic taught in the core classes.

And of course, we know from JKR that canonical Arithmancy is basically a form of divination with numbers.

When I say that magical theory is essentially unmathematical, I mean that there is no "unreasonable effectiveness of mathematics" in the realm of magic. In the natural sciences, mathematics is so effective at modelling the behaviour of the physical universe that many consider this to evidence the fact that the universe is fundamentally mathematical in nature. Mathematics is effective because the universe is already mathematical; you're simply describing what is already there.

But I don't think this works with magic, which I consider fundamentally unmathematical. See Chapter 28 of Victoria Potter for an article on magical theory which demonstrates how I imagine magical theory working.

 

Agrippa is canonically recognised so let me quote him:
"The Doctrines of Mathematicks are so necessary to, and have such an affinity with Magick, that they that do profess it without them, are quite out of the way, and labour in vain, and shall in no wise obtain their desired effect."
Of course, the following text would reveal that it's all about symbolism in the end and not physics-like equations. And we see an example of magical meaning assigned to a number in canon with Voldemort's splitting soul into seven pieces plan.

Is there more? Possibly. For example in HBP we see the "magic power" being tied to being an adult wizard. Maybe there is a meaning to the number 17 then.

 

I mean, it's definitely canon that numbers can have an influence on magic. Tom didn't have 7 horcruxes just for a laugh after all.

I suppose my view is that day to day mathematics beyond the absolute basics isn't that useful for Wizards, just the same as it isn't that useful for most muggles. You can get by quite happily in the magical world with just enough maths to sort out your grocery bills and do some unit conversions, so that's all most people bother to learn.

That said, just as in the muggle world, there are magical professions and fields where understanding some maths and how it relates to magic is useful and has practical benefits. Warding perhaps, or divination or spell development or complex enchanting. Most wizards can't do these things anyway, so knowing why it might be a good idea to anchor your wards to a certain number of points at certain angles, how to mathematically derive a wand movement or how to divine with numerology is a little irrelevant to them. Hence it's an elective for those with an interest, just the same as Divination.

I'd describe it as the difference between the basic maths everyone is obliged to do at school, versus specialist mathematics theory you might learn as a statistician or an engineer. Molly Weasley has knowledge of the former, Bill has knowledge of the latter from his work as a cursebreaker.

 

I misread your comment, but thanks for elaborating. Do you think Arithmancy is statistics then, or some other type of math? Also, in a story where mathematics can add understanding that isn't necessary for successfully casting the spell, how much do you think Hogwarts would delve into the mathematics of it? Would it be done as part of the courses, or would there be electives specifically for mathematics?

I've actually read that chapter and even commented on how much I liked it in WBA. This post is actually somewhat a result of having read that chapter. When concepts such as secrets can be interacted with as if they are existing things and spells can succeed in various ways or fail for various reasons, I have trouble understanding what it means for mathematics not to be unreasonably effective in describing magical ideas.

This is why I also made the distinction between mathematics being useful in magic and mathematics applying to magic. You seem to be against both the former and the latter if I am understanding correctly.

So then I wonder, as you start studying magical theory, what happens with the abstractions? Do they not fit within a system or systems that could be considered mathematical? What kind of magical concepts would prevent turning the theory into mathematical models (I recall you mentioning in the past something along the vein that a wizard could disprove mathematical concepts using magic)? How would there be consistency in spell casting with a theoretical body that has no mathematical structure?

So do you think that mathematics applies, but that the fields would be different from the ones common to muggle sciences? Or do you just meam that there is abstract theory using symbols and sometimes mathematical objects, without the systems themselves being mathematical?

Why would mathematics be useful for niche areas like warding and spell crafting, but not basic spell casting? Or do you think mathematical could improve casting as well? If so, why wouldn't that deeper math be taught to all students, even if most don't completely understand it? What else would they be learning in their classes?

 

My logic is that an understanding of the understanding logic behind the spells might be useful to all practicioners, but isn't necessary just to perform magic.

It's like us muggles with computers for example. I can use a computer, I even vaguely understand why it does what it does, but I don't need a computer science degree to type out this message. Practical application doesn't require in depth theoretical knowledge, but everyone needs to be able to work a computer, read a book, write a letter, do their tax return, so schools focus on those skills, the basic fudamentals of being a functioing human being. Schools don't, by and large, focus on the intricacies of coding any more than they do a deep dive into developmental biology, particle physics or plate tectonics. You get enough of a background to have a vague idea of what is going on and the tools to find out more if you care to, that's it.

I consider it the same for magic. You can cast a levitation charm by simply swishing and flicking and saying some words. You can make a potion by simply reading out of a book. That's the base minimum to magic. Sufficient underlying understanding to make it work day to day. This is probably a fair bit more info than we, as readers, see of course. Harry spends a lot of time writing out essays on spells and potions, which we as the reader see nothing of. Presumably he gets a fair amount of theoretical info that is useful to a Wizard but isn't plot relevant or interesting enough for us to peek round the curtain at. I'd say that knowing more about the why of magic would make you better at it, sure, but you've only so much time and resource to spend, so you gotta keep the syllabus manageable, give people the basics and let folks who care expand their skills further in their own time.

As for more complex magic like spell creation, I'd suggest that maybe, to design, to develop, to innovate, that superficial info isn't enough. To continue the computer analogy, it takes a lot more knowledge to write a program than it does to use one.

Magic is the same. Any idiot can read out of a book and see, right, dice the lacewings, three stirs counterclockwise, blah blah. But to make a new potion, you need to understand why it's 7 stirs clockwise and 3 anticlockwise. To develop a spell you need to be able to derive the arithmancy to work out what the wand movement is. You can rely on trial and error, sure, but I think there is a bit more knowledge to that kind of deeper magical activity. This is I think where stuff like 'magical maths' would start to come into it.

 

The number resulting from mathematic transformations wouldn't represent scale but some meaning in itself.

 

I swear my brain keeps misinterpreting your posts for some reason. I didn't even notice the whole numerology part. I hope I haven't been completely misreading everything I read today. Anyway, that's why I asked what type of maths you thought would be in arithmancy.

When you said you like maths in arithmancy for divination, I was expecting something more mathematical than numerology, which just seems to use some mathematical objects and operators, though I don't know much about it yet.

What I want to get out of this thread is an understanding of what a diminished presence of mathematics in magic would mean for the system. I'm also not sure the system as presented could actually be unmathematical, which is why I'm so interested in that idea.

I don't particularly want maths to be a major part of my magic system, but I also need to understand why it's okay to exclude it. I wanted to explore other people's thoughts on the subject to see what I was missing.

Regarding your headcanon, is the maths you like to see in magic restricted to the type of maths seen in science and engineering or do you like to include areas of pure math that currently seem very far from being applicable for our muggle purposes?

 

The meaning to that is probably imposed by magical society. It is by deciding to acknowledge a young magic user as an adult at the age of 17 that confers a tangible difference in their ability.

Consider the first time that Snape saw the Marauder's Map. He commands it to reveal its secrets under the authority vested in him as a teacher at the school the map was in. He said that fully expecting it to work, because to be a teacher at a school carries a conceptual mantle of authority recognized by everyone within and without the institution. Society saying "You are an adult, with all the rights, privileges, and responsibilities therein" would likely carry a similar weight.

It is not that 17 is special and thus you are an adult, it is you becoming an adult that makes 17 special.

 

Yes there is a distinction between representation and convenience of use. That math could represent magical understanding shouldn’t be controversial. Even if magical theories were purely linguistic and a-reductive, we can just convert words/letters into numerical characters and get some kind of translation, as well as mathematical relations that represent linguistic ones.

Many philosophers of mathematics think that even if the universe were fundamentally random and lawless; that nevertheless math could be used to represent it. The difference for us is that the universe happens to be highly reductive; so that fundamental characteristics can be easily represented via mathematics. That is the crucial criterion (reduction) that makes math unreasonably effective.

That is an important distinction, because even though math may technically apply to HP magic; if magical law is not easily reductive then such application is pointless. Better to stick to language as it’s easier to explain. Further, magic may be so complicated that even if it were mathematically reducible; wizards and witches may not have found out how to do this.

So the point is that you are right to draw the distinction between applicable vs useful, but just because math is applicable to magic doesn’t mean we should expect wizards and witches to use it.

 

The concept of magical computation is interesting especially in divination. One reason why modern methods of forecasting complex systems is near impossible is because one we have no methods of measuring the exact initial conditions and two, even if we did know the exact initial conditions our computers are limited in how accurately you can simulate things, leading to ever greater divergence from the reality the further you compute.

With magical data gathering and magical computation you could get around those limitations: just cast the "what's current weather" charm and plug the result into your magical number crunching algorithm, and you have a weather forecast way more accurate than any current supercomputer can hope to simulate. Things like solving n body problems could be staple for second year astronomy, taught to students the same way long division is taught in muggle world.

Or you could have a modern day wizard making millions by using magic to mine bitcoin...

 

Arithmancy seems more like Physics as it tries to predict the future through numbers