D&D General Should magic be "mystical," unknowable, etc.? [Pick 2, no takebacks!]

[Charlaquin]

(More seriously, even as a physics student I found a lot of it mystifying, but most of the strange symbols are actually straightforward if you have a little bit of calculus knowledge already.

Well that’s the rub, isn’t it

Trig was where math lost me. I did very well in trig because I could follow the formulas and get the right answers, but for the first time in my academic career, I didn’t really understand why I was doing what I was doing. Which is a shame, because my number sense is actually pretty good, and up until that point math had come very naturally to me. But for all I knew, Soh Cah Toa were magic words, which if said correctly would transmute the numbers I was given into the numbers I was supposed to give back. And since I resigned myself to simply following the instructions to get the right answer, I never retained any of it, and any math more advanced would forevermore be beyond my grasp.

Most are either "condense 3 equations into 1 equation so we don't have to write as much" or "this is just the label we use for this important number or the standard label for a measurement." Like how pi is the symbol for the number you need in order to calculate a circle's area, or x is usually the independent variable and y is usually the dependent variable. It's just Greek symbols and high-level math symbols because all the English letters had already been used up, and it's easier to know what's going on if you don't repeatedly re-use the same symbols.

Yeah, the symbols themselves don’t intimidate me. Using symbols as a shorthand to express more complex meaning is something I understand well. The problem is, again, that I reached a point in my education where I no longer really knew what the symbols actually meant or why I was supposed to use a particular one in the context I was supposed to use it in. I just knew which buttons to push to make the black box tell me what the teacher wanted me to write on the paper.

 

[EzekielRaiden]

Well that’s the rub, isn’t it

Trig was where math lost me. I did very well in trig because I could follow the formulas and get the right answers, but for the first time in my academic career, I didn’t really understand why I was doing what I was doing. Which is a shame, because my number sense is actually pretty good, and up until that point math had come very naturally to me. But for all I knew, Soh Cah Toa were magic words, which if said correctly would transmute the numbers I was given into the numbers I was supposed to give back. And since I resigned myself to simply following the instructions to get the right answer, I never retained any of it, and any math more advanced would forevermore be beyond my grasp.

Brief digression on trig then, if it's of interest.

Spoiler: Why trig is a Thing & some of what it's used for

At least with the trig functions, each of them actually does relate to some particular component of the angles and measures around a circle, with the actual "trigono" part of "trigonometry" being kind of secondary (but it's a lot easier to start with triangles than to start with the unit circle). Sine, as a trigonometric function of angles rather than as a ratio of right-angle triangle bits, takes an angle (by convention, an angle from the positive X axis going CCW) as its input and gives a distance as its output. In specific, if you were looking at a unit circle, it would tell you the vertical distance that you have to travel to go from the center of that circle to the point where a ray with that angle touches the circle. If you're not looking at a unit circle, it instead tells you the proportion of the circle's radius that you have to go up or down (up being positive, down being negative). Likewise, cosine takes in angles, and spits out horizontal distances (left being negative, right being positive). The ratios of right-angle triangle bits are, in essence, a stepping stone, getting the foot in the door until we can graduate to the more complete story, which is trigonometric functions on angles of any measure, even if they are too big to fit into a triangle (or are negative!)

Now, this might sound...kinda pointless. Who cares what the horizontal or vertical distance proportions are? But it turns out that knowing "how much of this arrow points toward the left (etc.)?" is actually very, VERY important for physics, because it turns out that forces that work perpendicular to the direction of action (motion, electromagnetic force, gravity, etc.) do zero work. So, for example, if you know that a person is pushing against a mine cart at an angle of 45 degrees to the actual left/right track direction, you can calculate that the actual work they're doing to push the cart forward is only cos(45) = 0.707... (in exact form, sqrt(2)/2) of the amount they're actually pushing. Say they're pushing with a force of 100N (easily achievable by most humans), the cart only experiences ~70.7N of forward force; the remaining ~29.3N are wasted, pushing against the normal force (structural integrity, in this case) of the track. Cosine and sine are also essential for certain ways of multiplying vectors together, which are how we can calculate things like "the amount of work done" (requires cosine) and "if you use a coil of wire to make an electromagnet, which direction does its magnet field point?" (requires sine).

Yeah, the symbols themselves don’t intimidate me. Using symbols as a shorthand to express more complex meaning is something I understand well. The problem is, again, that I reached a point in my education where I no longer really knew what the symbols actually meant or why I was supposed to use a particular one in the context I was supposed to use it in. I just knew which buttons to push to make the black box tell me what the teacher wanted me to write on the paper.

Yeah, I can understand that. The calculus stuff mostly helps to skip over explaining certain things you do to functions that are extremely important but a bit of a pain to spell out all at once (mostly what a derivative is, particularly with functions of more than one variable, and why on earth anyone would care about derivatives, especially taking a derivative more than once.)

 

[Charlaquin]

At least with the trig functions, each of them actually does relate to some particular component of the angles and measures around a circle, with the actual "trigono" part of "trigonometry" being kind of secondary (but it's a lot easier to start with triangles than to start with the unit circle). Sine, as a trigonometric function of angles rather than as a ratio of right-angle triangle bits, takes an angle (by convention, an angle from the positive X axis going CCW) as its input and gives a distance as its output. In specific, if you were looking at a unit circle, it would tell you the vertical distance that you have to travel to go from the center of that circle to the point where a ray with that angle touches the circle. If you're not looking at a unit circle, it instead tells you the proportion of the circle's radius that you have to go up or down (up being positive, down being negative).

Yeah, it’s been many years at this point, but I vaguely recall understanding at the time what Sine, Cosine and Tangent were for and what their relationships to the angles and sides was. the problem was…

Likewise, cosine takes in angles, and spits out horizontal distances (left being negative, right being positive).

This. The the part where the function “takes in one thing and spits out another thing.” I never understood what it was doing to get the output from that input. I can accept that it does and use it in the right contexts to find the right answer, but if I don’t understand what’s happening “under the hood” so to speak, it’s not really going to mean anything to me.

Now, this might sound...kinda pointless. Who cares what the horizontal or vertical distance proportions are? But it turns out that knowing "how much of this arrow points toward the left (etc.)?" is actually very, VERY important for physics, because it turns out that forces that work perpendicular to the direction of action (motion, electromagnetic force, gravity, etc.) do zero work. So, for example, if you know that a person is pushing against a mine cart at an angle of 45 degrees to the actual left/right track direction, you can calculate that the actual work they're doing to push the cart forward is only cos(45) = 0.707... (in exact form, sqrt(2)/2) of the amount they're actually pushing. Say they're pushing with a force of 100N (easily achievable by most humans), the cart only experiences ~70.7N of forward force; the remaining ~29.3N are wasted, pushing against the normal force (structural integrity, in this case) of the track. Cosine and sine are also essential for certain ways of multiplying vectors together, which are how we can calculate things like "the amount of work done" (requires cosine) and "if you use a coil of wire to make an electromagnet, which direction does its magnet field point?" (requires sine).l

Funny enough, the apparent pointlessness of it was never my problem with it. I understood and was fine with the idea that it was sort of a building block of physics, plus I’ve never been one to balk at learning for its own sake. It’s enough to me that something is interesting, even if I don’t have an immediate practical use for it. But I lost interest because I never got a satisfactory answer to what was actually going on inside the magic box that transformed the inputs into the outputs. It stopped being interesting because I couldn’t understand what made it tick. And at this point it’s been too long, to build that understanding I would need to revisit the subject basically from scratch. I would also need a teacher who themselves intimately understood what the functions do and why, and had both the communication skills and the patience to walk me through that.

 

[EzekielRaiden]

Yeah, it’s been many years at this point, but I vaguely recall understanding at the time what Sine, Cosine and Tangent were for and what their relationships to the angles and sides was. the problem was…

This. The the part where the function “takes in one thing and spits out another thing.” I never understood what it was doing to get the output from that input. I can accept that it does and use it in the right contexts to find the right answer, but if I don’t understand what’s happening “under the hood” so to speak, it’s not really going to mean anything to me.

Spoiler: Further digression because man this got LONG

When you take a square root, what are you doing? Square root "takes in" one number, and "spits out" another, but...what is it doing? Most folks know that numbers have square roots, and intuitively connect perfect squares with their square roots, but it's a lot foggier when you ask for the square root of 113. We could invoke a geometric analogy--"I would build a square that I knew whas 113 square units in area, then measure one of its sides"--but that's pretty obviously cumbersome and...how would you even measure the area without knowing the side length?

What you're asking for, in a formal sense, is "What IS a function? How does it WORK? Why would I ever consider connecting these things?" Trying to avoid excessive jargon and over-explanation (which my first attempt did TONS of), a function in logical terms is a relationship between two sets of things, an input set (formally called the "domain") and an output set (formally, "codomain"). The definition of "a function" is that it assigns, to every single thing in the input set, one and only one thing in the output set. It's okay for two inputs to give the same output, but it is NOT okay for one input to give two outputs. You are, most likely, familiar with the "vertical line test": this is a graphical way of representing "does every input give only one output?" If a vertical line touches a plot more than once, then that means the value for that vertical line (some input x) is associated with more than one result (multiple y outputs).

It's easy to make functions with finite input sets. For example, I have four people in my immediate family counting myself, and each one of them has exactly one birthday. That means I could make a list, e.g. (fictitious values of course) "Father = November 1," "Mother = January 7," "Sister = July 4," "Self = August 19." This would be a function which takes "member of Ezekiel's family" as inputs, and gives "day of the year" as outputs. Since it's not physically possible for a person to have been born on more than one day of the year, we can be confident that this is an actual function. (Note that, if I had a twin, then both "Self = August 19" and "Twin = August 19" would be true--but that's perfectly fine.)

It's harder to make such clean connections when the input set is infinitely large, like "positive whole numbers" or "all real numbers" etc. We can't make a complete list of every number and its square, because that list would be infinitely long. Instead, we either make a table that is good enough for what we need, or we figure out a procedure to calculate it. Trig functions are in this category. You can "look up" the associated value for any input angle, and you'll get some output that is between -1 and 1.

As for the physical thing you're doing, well, looping back to the "what are you doing when you take a square root?" example, you're relating the length of horizontal or vertical distances to going a certain amount of angle around a unit circle. I have made an image to assist:

For each and every value θ (a traditional variable for angle) you choose, there is one and only one value for how far up (or down) you have to go in order to hit the unit circle along a line with that angle. That is what sin(θ) tells you. Likewise, there is one and only one value for how far left or right you'll go. In formal terms, cosine is the "projection" of that blue line onto the horizontal, while sine is the projection onto the vertical. Unlike with the triangle-bits version, though, you can have an angle that goes beyond 90 degrees, indeed, you can use any angle you want, it just means going around the circle that many times before you stop and measure how far up/down and right/left you are.

But most people, just like with the "how do you find a square root," don't think overmuch about physically plotting a unit circle and measuring distances. They instead treat it as though "sin(θ)" and "cos(θ)" were machines, where you can feed them the input number (in this case, the angle), and the machine (usually an actual machine, a calculator) will report the associated vertical distance or horizontal distance without you having to do a whole bunch of drawing and careful measurement to find out. These pairs of numbers--θ and sin(θ), for example--are associated with one another (in some sense) "because of" the properties of the unit circle, just as numbers are associated with one another (in some sense) "because of" the properties of square geometry.

I am not a teacher, of course, and this is quite a long digression, so I won't push on it any further than the above. But I do hope that this at least provides some small utility to you, should you consider immersing yourself in the subject anew.

 

[Minigiant]

I prefer magic as science. But science only the gods and higher beings understand. The ground level magic users understand bits and pieces but it is seems nonsensical and arbitrary even to them. It's mystical because it runs on "insane troll logic".

 

[MGibster]

I'm going to petition WotC to combine science and magic into the Mathemagician class.

 

[Fanaelialae]

I'm going to petition WotC to combine science and magic into the Mathemagician class.

Will they get a spell to square round pies?

 

[Charlaquin]

When you take a square root, what are you doing? Square root "takes in" one number, and "spits out" another, but...what is it doing?

Well, when you square a number, you multiply it by itself. Taking the square root of a number is finding out what number you can multiply by itself to get the number you’re finding the root of. And, yeah, you can use the geometry analogy to work that out, which is where the term “square” comes from. The area of a square with sides of length X is X^2, or “X squared.” Taking the square root is simply doing the reverse. You know the area of the square and you need to find the length of its sides. That’s something I can grasp, it’s basically algebra.

As for the physical thing you're doing, well, looping back to the "what are you doing when you take a square root?"

Like I say above, what you’re doing (or what I’m doing, at least) when taking a square root is algebra. I have a known variable and an unknown variable and I understand the relationship between the two: the known variable is the product of the unknown variable multiplied by itself, solve for the unknown variable.

But most people, just like with the "how do you find a square root," don't think overmuch about physically plotting a unit circle and measuring distances. They instead treat it as though "sin(θ)" and "cos(θ)" were machines, where you can feed them the input number (in this case, the angle), and the machine (usually an actual machine, a calculator) will report the associated vertical distance or horizontal distance without you having to do a whole bunch of drawing and careful measurement to find out.

Yeah, but in the case of the “find the square root machine,” I understand what it’s finding and how. The relationship between the input and the output is clear to me, so I’m comfortable letting the machine do that work for me, and the output it gives me is meaningful to me. I understand what happened to the input to turn it into the output. In the case of the Sine, Cosine, and Tangent machines, the relationships between the input and the output were never clear to me, so the output was just a contextless, meaningless number. The calculator did some magic to the numbers I fed it and transmuted them into the numbers that made me pass the class. I could do it, but the lack of meaning made my ADHD brain decide it wasn’t worth caring about.

 

[Gammadoodler]

Arthur C. Clarke was a science fiction writer, not a fantasy writer. I think if you asked J.R.R. Tolkien for his opinion on the subject, you'd get a very different answer.

I'm not entirely sure that's true. There is a fair bit of technologized magic in Middle Earth. The Rings are constructed items after all. As are many other bits and bobs along the way.

It's just that all the folks who understood that construction are inaccessible to the reader.

 

[jmartkdr2]

I know we get a lot of "it depends" answers in this kind of thread, but should we? If we're talking about gaming in general, sure, it depends, but we're talking about D&D. And for the most part, the universe pretty much works the same across all D&D settings so far as magic is concerned.

In that case we have to take into account the fact that players can play wizards, and wizards can do research to invent a new spell. A wizard pc, therefore, needs to have an understanding of how magic works - a deep enough understanding to do engineering with it.

This doesn't work if magic is unknowable. DnD magic is knowable, RAW.