The Plight of the Roleplaying Mathematician

[BarnabasBailey]

Right. So I was making a race in Pathfinder, and one of the abilities one can give races allows for wings that can glide. Basically, characters can elect to glide forward up to five feet for every foot of altitude lost allowing them the ability to cross large gaps or safely land from great heights.

This got me thinking. Suppose I made a character who had this particular talent and, at some point in the future, my character is presented with a large gap across which he could fly. Suppose my character wanted to know how far away a safe landing spot was on the far side and, incidentally, the chances of him making it across safely. Well, I'm no mathematician, but I know that one could estimate the distance by forming a right triangle between two points on one side of the gap at a known distance and comparing the angles to a fixed point at one's destination (Of course, I probably couldn't do it, but that's why it's so nice that my character would have a higher Intelligence score than me.).

My question is, how would that translate into game mechanics? Which of the myriad Knowledge skills would most likely translate to a worthy knowledge of mathematics? Granted, this is all academic, since one could determine distance by just looking at a map of the area and counting squares. But if a gridded map weren't provided, and my DM were the kind of DM who thinks outside the box and actually thinks of interesting ways to engage people's thought processes rather than simply providing answers to questions that don't have clear-cut rules printed about them, what sort of skills would one fall back on? This question could be extended to any use of math, assuming the world your game takes place in is one where the number zero was invented.

[geekintheground]

i dont know much about pathfinder, but a straight int check would do in my opinion, if you really wanted to add a knowledge skill, arcana seems appropriate since arcane magic involves formulas and is a "replacement" for science in many settings. or possibly a knowledge (architecture)

[JusticeZero]

Knowledge :Engineering would probably work. For tougher and more esoteric questions, you can use Knowledge : Other and define it as mathematics.

[Raven777]

It came up a couple of times with my group recently. At the time we stuffed physics and mathematics in Knowledge: Engineering and biology and chemistry in Knowledge: Nature.

Though nothing would stop a DM from whipping up a straight Knowledge: Science skill if he thinks it fits within his campaign setting.

Or shove everything in Knowledge: Arcana since arcane casters would usually be the ones to work with chemicals, astronomy, equations and the like. But to me handing science to the Wizards would be kinda disheartening.

[Kelb_Panthera]

How is this not a rather obvious know (geography) check?

This is a technique used by cartographers for centuries before gps was a thing.

[Shining Wrath]

What you are asking for is trigonometry. The ratio of the horizontal side to the vertical side is 5:1. By the Pythagorean Theorem beloved of Tin Men, the hypotenuse is sqrt(5*5 + 1*1) =~ 5.1. The angle of descent is arccos(5/5.1) = 11.3 degrees down from the horizontal.

So your PC could have a little gadget made with a level bubble in it and an arm fixed at 11.3 degrees, sight down the arm while holding the bubble level, and know approximately where the glide path would end.

[cerin616]

I would say knowledge engineering (tuned of int still) to do it mathematically with a map and stuff.

Or, since we can assume your character has done this before, make comparable DCs for a wisdom check.

obviously the math will scale better, but such is the way of life. Its always better to measure before you cut then to say "I have built houses before, i got this"

[cerin616]

What you are asking for is trigonometry. The ratio of the horizontal side to the vertical side is 5:1. By the Pythagorean Theorem beloved of Tin Men, the hypotenuse is sqrt(5*5 + 1*1) =~ 5.1. The angle of descent is arccos(5/5.1) = 11.3 degrees down from the horizontal.

So your PC could have a little gadget made with a level bubble in it and an arm fixed at 11.3 degrees, sight down the arm while holding the bubble level, and know approximately where the glide path would end.

So, how would he use this while doing a running jump to get some more altitude?
keep a ladder handy?

much more efficient to just look at a distance, and understand "if i jump here ill be at x, and use the exact same math you did to say "will i make it to y?"

[Eurus]

How is this not a rather obvious know (geography) check?

This is a technique used by cartographers for centuries before gps was a thing.

That's a very interesting point. I normally lump math stuff into Engineering, but Geography would actually work pretty sensibly in this case. I imagine either one would be fine, really.

[TheStranger]

At the risk of ruining everybody's fun, why is all of this necessary? Sure, for the player looking at the battlemat there's some math to do. But there's no math for the character, unless the DM is being intentionally mean. If I'm a member of a winged race, I expect to be able to look at a potential glide and judge where I'm going to land intuitively.

In my mind, it's analogous to jumping across a gap. You don't look at it and say, "ok, that's 11 feet, and I'm jumping with an initial velocity of 10 m/s at an angle of 22 degrees, so I'll clear it easily." You just look at it and know whether you can make it easily, with difficulty, or not at all, because you've jumped before and you have some innate sense of what you can do. Even though gliding is a little more complicated, I don't see any reason to complicate things by ruling that individuals have to do math to figure out their own physical capability.

Of course, if you're a human and you want to know if your winged buddy can glide across a gap, you'll have to do some math. Carry on.

[Bakkan]

By the Pythagorean Theorem beloved of Tin Men....

Ah yes. That line makes "The Wizard of Oz" the second most painful movie for me as a mathematician to watch, after "Good Will Hunting" (Seriously, I couldn't finish that movie the math was so bad)

EDIT: On topic, my vote would be for engineering, unless it'll come up enough to make a new skill for it (and probably physics).

[cerin616]

At the risk of ruining everybody's fun, why is all of this necessary? Sure, for the player looking at the battlemat there's some math to do. But there's no math for the character, unless the DM is being intentionally mean. If I'm a member of a winged race, I expect to be able to look at a potential glide and judge where I'm going to land intuitively.

Of course, if you're a human and you want to know if your winged buddy can glide across a gap, you'll have to do some math. Carry on.

Thats like saying "As a person with legs i can always intuitively know if i can jump a gap"

Its also why i said you could make a comparative wis check. which is essentially trying to remember similar jumps and how well they went.

Or the character can understand how his flight works and do the math. There are people who do this to see if they can jump things with vehicles and such, even if they have jumped stuff before.

[nedz]

I think that there are several knowledge skills which could be applied allowing several route to the answer, but really it's a sports type question.

You can play pool without any knowledge whatsoever, and if you are a competent pool player you will get the angles right; on the other hand you could have a maths PhD who had never played any such game, and they would most likely miss.

In this case we have a character who is, presumably, born with gliding wings. From their lifetimes experience they should just be able to look at the situation and know if the glide is going to be easy, iffy or just not on. If they jump for an iffy one, then it's a roll to hit.

[TheStranger]

Thats like saying "As a person with legs i can always intuitively know if i can jump a gap"

Its also why i said you could make a comparative wis check. which is essentially trying to remember similar jumps and how well they went.

Or the character can understand how his flight works and do the math. There are people who do this to see if they can jump things with vehicles and such, even if they have jumped stuff before.

But as a person with legs, I always do know whether I can jump a gap. In all seriousness, I've spent a fair amount of time IRL jumping gaps (I like to rock-hop up and down mountain streams). As a rule, I've generally landed where I wanted to, except for times when I made a purely physical error (foot slipped, lost my balance on uneven ground, etc.), or times where I was trying to jump a gap right at the limit of my ability and knew I'd have to make a really good jump to do it.

I understand that people who jump gaps in vehicles do math. I don't see that as being the same thing as growing up with wings. I've never heard of people doing that with parkour.

You can do what you want in your game, I suppose. But if I were DM, I would not make a winged character do math in this situation.

[cerin616]

But as a person with legs, I always do know whether I can jump a gap. In all seriousness, I've spent a fair amount of time IRL jumping gaps (I like to rock-hop up and down mountain streams). As a rule, I've generally landed where I wanted to, except for times when I made a purely physical error (foot slipped, lost my balance on uneven ground, etc.), or times where I was trying to jump a gap right at the limit of my ability and knew I'd have to make a really good jump to do it.

I understand that people who jump gaps in vehicles do math. I don't see that as being the same thing as growing up with wings. I've never heard of people doing that with parkour.

You can do what you want in your game, I suppose. But if I were DM, I would not make a winged character do math in this situation.

So, did you learn how to jump all this well because you jumped pretty much only when it was necessary? or are we going to assume that this character spends time gliding around for fun?

And the problem isn't necessarily about knowing where you will land, but about knowing where exactly that limit is. As you said you screwed up some jumps when trying to jump at your limit, and unless its at your gliders limit, it really doesn't matter.

Hence my suggestion of a wisdom check to see if the character recalls how well he can jump to an exact of inches. or in this case glide. The best part? a wis check allows you to make it under tough situations, like being chased by something. a place where you don't have time to sit down and break out your pencil. A time where you wont be able to look at the gap for more than a few seconds before throwing yourself across it hoping for the best.

[zlefin]

Some things should belong in multiple knowledge categories; I think this is one of them, several knowledge categories would have this, and the options have most likely already been named.

[TheStranger]

So, did you learn how to jump all this well because you jumped pretty much only when it was necessary? or are we going to assume that this character spends time gliding around for fun?

And the problem isn't necessarily about knowing where you will land, but about knowing where exactly that limit is. As you said you screwed up some jumps when trying to jump at your limit, and unless its at your gliders limit, it really doesn't matter.

Hence my suggestion of a wisdom check to see if the character recalls how well he can jump to an exact of inches. or in this case glide. The best part? a wis check allows you to make it under tough situations, like being chased by something. a place where you don't have time to sit down and break out your pencil. A time where you wont be able to look at the gap for more than a few seconds before throwing yourself across it hoping for the best.

If you had wings, wouldn't you glide around for fun? Even if it's not just for fun, it's a mode of movement that your character has had their whole life; I'd assume they've used it extensively.

I can see your point with being right at the limit, though. I'm not 100% sure I agree, but I can see where you're coming from. I guess I consider it to have been a failure of execution rather than perception; a botched Jump check, if you will. Since there's no skill check for squeezing a few extra feet out of a glide, I'm not sure how to represent that.

[PlusSixPelican]

Easy Math (http://dndtools.eu/spells/song-and-silence-a-guidebook-to-bards-and-rogues--48/easy-math--3324/). It's a Bard cantrip from 3e, but it's easy enough to convert to 3.5 or PF. If it was added to other class lists, one might change the Perform check to some other skill, like Knowledge: Arcana.

Not that it's required for math, but Math in a Can is always really cool.

[elonin]

If the character is trying to eyeball the "flight" he is making then I'd make it a perception check. The Math comes in from the dm to determine the dc of the check. The skill for the attempt itself is fly.

[cerin616]

If you had wings, wouldn't you glide around for fun? Even if it's not just for fun, it's a mode of movement that your character has had their whole life; I'd assume they've used it extensively.


Well, If i spontaneously grew wings damn straight i would glide around and stuff, but if i had them when i was born and grew up with them I would probably find it somewhat mundane. I enjoy pushing myself to jumping and balancing on occasion, what boy doesn't, and I probably would do the same with gliding on occasion, but I don't imagine that would be enough for me to look at a gap, no matter the distance or vertical difference and immediately know if i could glide it. I can't even do that with a jump. Half the fun of the jump is saying "im not sure if i can make that, lets just go for it."

[BowStreetRunner]

This is a clear use of Knowledge (religion). I can't believe you are all forgetting that mathematics was often seen as a way to gain greater understanding of the divine. The Pythagoreans were a mystical sect, de Cusa attempted to approach God through a geometric infinite, Spinoza's philosophy was geometrically inspired. There are numerous other examples throughout history. Many of the earliest mathematical theories were developed by religious scholars attempting to study the divine. It would be likely that the majority of mathematical understanding in an early to middle-age society would reside solely in the hands of the church.

[Hand_of_Vecna]

Thats like saying "As a person with legs i can always intuitively know if i can jump a gap"

I always intuitively know within a few inches. Having made a jump or two I shouldn't have in my day I can say I've always missed a vertical by a hair and skinned my knee or leaping horizontally I've had just my toes catch the lip and fallen backwards or had my toes hit the wall of the opposite side and either gone forward and fallen where I meant to jump to or tipped backwards.

For a natural gliding race like the one described, I'd this should translate to being able to guess to within five or ten feet whether a glide will be successful and some kind of check would be called for the corner cases. This check would probably be pretty difficult without pen and paper, since we'll be dealing with big numbers (for head math by most peoples standards) and second guessing something that is usually instinct.



I don't think I'm a distance guessing prodigy, but if several people say I am I'll accept it.

[cerin616]

Wis check, high DC for "I know exactly if i can do it" medium DC for "I am pretty sure I can do it" low dc for "I might be able to/might miss it"

add modifiers for distance so that the closer the distance is from you the easier it is to ascertain.

[Bakkan]

This is a clear use of Knowledge (religion). I can't believe you are all forgetting that mathematics was often seen as a way to gain greater understanding of the divine. The Pythagoreans were a mystical sect, de Cusa attempted to approach God through a geometric infinite, Spinoza's philosophy was geometrically inspired. There are numerous other examples throughout history. Many of the earliest mathematical theories were developed by religious scholars attempting to study the divine. It would be likely that the majority of mathematical understanding in an early to middle-age society would reside solely in the hands of the church.

I would like to change my vote to this.:smallcool: