Are wizards good at math? I kind of imagine magic as being like physics, but I never hear it being used that way

From Jack Vance's the Dying Earth:

>In this fashion did Turjan enter his apprenticeship with Pandelume. Day and far into the opalescent Embelyon night he worked under Pandelume's unseen tutelage. He learned the secret of of renewed youth, many spells of the ancients, and a strange abstract lore that Pandelume termed "Mathematics".

>"Within this instrument," said Pandelume, "resides the Universe. Passive in itself and not of sorcery, it elucidates every problem, each phase of existence, all the secrets of time and space. Your spells and runes are built upon its power and codified according to a great underlying mosaic of magic. The design of this mosaic we cannot surmise; our knowledge is didactic, empirical, arbitrary. Phandaal glimpsed the pattern and so was able to formulate many of the spells which bear his name. I have endeavored through the ages to break the clouded glass, but so far my research has failed. He who discovers the pattern will know all of sorcery and be a man powerful beyond comprehension."

>So Turjan applied himself to the study and learned many of the simpler routines.

>"I find herein a wonderful beauty," he told Pandelume. "This is no science, this is art, where equations fall away to elements like resolving chords, and where always prevails a symmetry either explicit or multiplex, but always of a crystalline serenity."

Problem with making wizards particularly good at math is that advanced mathematics begets technology, which conflicts with a medieval world. If the tools of mathematics were readily available, someone would apply them to solve real-world problems and the world would quickly cease to be fantasy-themed.

You need the knowledge of basic algebra to simply be able to build palaces and do extensive trade. This was possible since the antique.

Newton, Leibniz, Bernoulli, et. al. introduced the modern concepts of derivation, integration, differential calculus, and so on. After that, sky's the limit. We have the tools to understand electricity, heat transfer, momentum, to see the whole clockwork of heavens - there's no stopping the advance of science.

tl;dr: Wizards can be good at math, but if you want a medieval-themed world, make it simple, classical math.

>Magic is physics
>Ever
>In any setting

The minute your spells describe atoms and molecules, you've removed all the mysticism and mystery from your setting's magic and made wizards into literal übermenschen.
Also, this:

Why would I do math myself when I can cast a spell to tell me the answer?

iirc the guy that made that rune magic system did a take on a complete game system that used it for magic. Don't remember the name and what has become of it though.

Okay just searched a bit, that seems to be the system he's done then: drivethrurpg.com/product/165870/The-Runed-Age-Corebook

...Why should I be able to do this?

The last time I even looked at advanced maths was in school. I have had absolutely no use for it since then and even then, I never studied this.

Unless your job actively requires use of higher maths, all you need is addition, subtraction, multiplication and division and some derivatives of them, such as percentages.

So tell me again why the average person 'should be able to do this.'

Magic is usually considered things beyond our understanding that science seemingly cannot explain. Wizards are just very good at knowing what these forces do and how to trigger them, but not necessarily why they happen. That'd just be science in a world with magic then.
Of course you could just say magic is that exactly, but then your wizarding colleges may as well merge with your mundane colleges.
Basically it depends on what you want from your game.

Wizards by the D&D standard where they differ from sorcs that just use instinct and force of will mostly strike me as programmers.

a). so you aren't a stupid uneducated moron and can adapt to learn various scientific fields when necessary over the course of your careers.
and, leading directly from this:
b). because Logarithms and their related properties are heavily used in Differential Equations (the most useful part of Calculus), which in turn is used for growth and decay models that are universally useful in almost every modern field.

I think magic is less like mathematics and more like programming. You're not neccessarily trying to understand narture methodically from scratch like with physics and mathematics, but you're starting from some universal "source code", so to speak. You learn to rewrite entire parts, some small (I guess something like a "light" spell would be akin to switching a certain argument from "TRUE" to "FALSE" or vice versa), some large (something like stopping time would require advanced knowledge and (re)writing an entire method to stop time and then reactivate it after you're done as if nothing had happened, erasing all evidence of that spell's existence along with it).

So it's not so much about understanding as much as it is about knowing how to manipulate (kind of like how you can program a code without knowing how the program you're using to write the code itself operates, or without knowing how the computer you're using works).

magicians seem more like magic engineers rather than mathematicians. they know the formulas are there and what they can be used for, and when they need it they draw on it. Otherwise they aren't normally associated with it.

Nanoha has math wizards and Intelligent Devices that can cast spells on command using your magic.

Wizards are probably good at math, but I prefer to imagine that the practice of magic is as much an art, a spiritual journey, and/or a philosophical exercise as it is a science, if not more.

Well that depends on the type of wizard, which isn't a distinction made usually in games like D&D.

your scholarly tower-residing wizard would be more like a mathematician or physicist, depending how much they lean toward theory/application.
The engineer analogy works best for the adventuring wizard, who knows the methods and applications of what they work with even if they don't know the barest bones of every sliver arcane energy/mathematical root formula.

Is that one of those things that start a PEMDAS argument because Americans are, for some inexplicable reason, more adamant about following it than the constitution of their own country?

>depends on the Wizard
>even within a setting there are multiple ways to approach... magic
Whether or not that's true depends on the setting

Of course not! Everyone who has ever studied Wizards and their magic knows that they can't know complex maths or it upsets the careful mental environment in their head and makes it inimical to spells residing there.

Same goes for most branches of actual science, as in order to understand them the wizard must break down the mental patterns that are set up in his own brain to catch and hold spells

Wizards are relatively good at math for their time/world because they are full of book learning. However, magic is not math. In fact, one might say magic and math are opposites. An experienced professional who need to be trained in math for their field, such as an engineer or accountant, is going to be more skilled at math than a wizard.

They'd probably be able to do classical mathematics and basic mathematics; quadratures, axiomatic geometry, arithmetic, algebra, possibly mathematics that lead to defining early transcendental functions.

But I wouldn't expect a wizard to worry too much about proving Fermat's last theorem or be working on the Birch and Swinnerton-Dyer conjecture.

If you can work with exponents then you should be able to work with logarithms. It's basic math.

this

I'd wizards to be able to learn complex mathematics, at least, them having the capacity to.
I always pictured arcane magic as a study being more like as it is shown in harry potter but with more bookkeeping. A bit of chemistry here, a lot of proper technique there.

>OP skill
lol. name a typical game situation in which math would come in handy.

Orcs are raiding the town. What math do you use to save the townspeople

Proofs are always a pain in the ass for me because I can't come up with a way to convince myself that yes, I am doing the proof the right way, and I don't bother to remember some of the major properties of sums and even integrals because I don't use them regularly.
I'd get a whole lot better at doing math if I needed it for anything other than one equation a week.

Map triangulation.

What fucking map are you using?
Look, I know a lot of wargames use direct-line measurement, but I don't remember a single strict RPG that isn't played theater-of-the-mind or on a grid of some sort.

Allocation of arms and soldiers. Ammunition. Estimates of losses and planning attrition. What lengths of what timbers are required for fortifications.

Cmon.

Magic needs more creativity than math can provide

...

I read a book once with an interesting setting.
To nutshell the relevant bits, it's a high magic world where everyone's a mage, science and technology are outlawed, and each mage fits into a certain class and caste.
The most powerful caste are the rate ones that don't cast spells, but channel magical energy to other mages, thereby functioning as magical bankers doling out power.
One of the main characters is a young, low level such mage who excels at casting because his vastly superior math skills allow him to channel the power much more precisely and efficiently.
He gets a suicide mission to the forbidden zone, or whatever, due to being nearly heretical by asking questions.
Math is too close to science and technology to be actively discussed.

The superior math part was well established but not expanded on in the first book. I never read the others but I plan to eventually.

>I kind of imagine magic as being like physics
I do as well, but if anything, the most common math used in magic seems to be geometry.

Ok, but the mathematician doesn't know he's in a grid or someone's imagination. The character themself would need to use map triangulation.

>math is not imaginative/creative
lel what is non-Euclidean geometries and Topology

>I'd get a whole lot better at doing math if I needed it for anything other than one equation a week.
You can do math just to do math.

Mathematics requires a lot of creativity and insight, especially in proof construction and developing/exploring new mathematics.

FUCK MATH

Isn't Laundry 'lol everything sucks idealism is for nerds' the RPG?, except with less war than 40k?

No, but Magical Girls are.

Basic mathematics and physics as it relates to geometrics can be useful, the classic wizard ala Solomon is someone who knows the correct symbols and words to evoke the spirits that allow magic to work. Read the area goetica

Read Agrippa's 2nd book in the 3 books of occult philosophy. It has long descriptions of maths connection to magic and the principles through which they interact. There's also neat little anecdotes about how you can count to a million using just one hand and how Agrippa thought he was watching people summon demons when in reality he realized they were just counting and multiplying really big numbers.

It'd also interesting how magic circles are really just number puzzles like sudoku.

It depends on the setting. IRL, absolutely yes. In addition to , Isaac Newton was also into alchemy. The muslim mystics were great believers in sacred geometry, jewish mystics often played games with the interactions between language and numerology.

In my opinion, though, if you're going to have a typical fantasy setting, I'd recommend against it. Many gamers are also have strong STEM backgrounds, or at least enough that they want to harness modern understandings of science and technology to use magical effects in novel ways, or even replicate technology. Firearms is the obvious example, but there are others. Also, if you admit that physics works in a fantasy setting as it does IRL, you then have to figure out where magic fits into the cosmology and face all kinds of logical inconsistencies.

So what I prefer is that magic is how science would work if it was run by English literature majors. Symbolism, theme, mood, context, metaphor, and intent are all critical to understanding an using magic. Magic isn't alive or conscious, but in a weird way it does think and feel. You don't use magic so much as you persuade it into existence. The theatrics are and ritual are meant to create a scene where the effect is thematically appropriate.

In a way, it's what would happen if you realized that you were living in a somewhat hackish fantasy novel and decided to start behaving in a way that would kind of force the author to take the path of dramatic least resistance and give you the effect you're asking for.

This is a good post.

Wizards, generally with high INT, would be good at math - if they weren't too busy memorising spells and joining bands of adventurers.

I get the impression from a lot of fantasy and roleplaying material that magic is a type of physics, just that it operates according to laws which bear little or no link to the mundane laws of physics. However, physics (and therefore maths) still largely controls the result of spells: the stone wall falls down if not secured properly, the fireball tossed in the air explodes in a sphere rather than a cube because of uniformity of pressure in all directions etc.

I imagine maths would be exceedingly useful in the research of new spells, but I think it's more likely to be used by the old wizards and liches whose adventuring days are done, who have the time to establish proofs that the Koch Snowflake is superior to contain demons instead of a circle or pentagram, or craft a variant of Wall of Fire that is a mobius strip instead of a ring, so that both sides of the wall are affected by the fire damage (or both sides of the wall are non-damaging sides, but still damage creatures passing through it), or hypercube Mage's Magnificent Mansions that are massively larger than the normal versions.

Link?

>but I think it's more likely to be used by the old wizards and liches whose adventuring days are done, who have the time to establish proofs that the Koch Snowflake is superior to contain demons instead of a circle or pentagram, or craft a variant of Wall of Fire that is a mobius strip instead of a ring, so that both sides of the wall are affected by the fire damage
Love it.