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I would imagine a PC's degree of math skill would go up according to INT, but few PC's routinely delve into math beyond dividing up treasure. Is a 19 INT wizard automatically a math wiz?
How much math do they need to know? - is it applied mathmatics, or abstract?
I would say no, a 19 Int doesn't automatically make you a math wiz, any more than a 18 Cha means every woman you pass instantly makes a pass at you due to your manly man-ness.
I would imagine a PC's degree of math skill would go up according to INT, but few PC's routinely delve into math beyond dividing up treasure. Is a 19 INT wizard automatically a math wiz?
This is really an RP question that is up to the player. Some really smart people don't do math well.
I would think your Int has only the affect of how much math you can learn not what you know.
Look at your appropriate knowledge skills and the ranks you have in them then judge from there. 0 knowledge skills probly not alot of math. 15 ranks in Engineering and Skill Focus and there is probly alot of math.
I would think your Int has only the affect of how much math you can learn not what you know.
Look at your appropriate knowledge skills and the ranks you have in them then judge from there. 0 knowledge skills probly not alot of math. 15 ranks in Engineering and Skill Focus and there is probly alot of math.
I'm leaning toward this interpretation.
If you know how to use a kind of math, you're very good at it. (and faster)
With basic math, for example: If someone with 19 Int threw 10d6 die, they could calculate the sum by glancing at it for 2 seconds. If someone had 9 Int and was trained in basic math, they could eventually total it by counting with their fingers.
Math is more likely to fall into a profession or knowledge skill and not a raw ability score total.
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Well, any skill that could possibly have anything to do with math ought to influence your knowledge of it.
Appraise - a little
Craft (carpentry) - you should be reasonably good at basic calculus and some exponential calculation
Knowledge (engineering) - a lot of math
Profession (siege operator) - Should be reasonably good with angles and actualy more of a physics type.
Spellcraft ought to also have some math in it imo...
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Well, any skill that could possibly have anything to do with math ought to influence your knowledge of it.
Appraise - a little
Craft (carpentry) - you should be reasonably good at basic calculus and some exponential calculation
Knowledge (engineering) - a lot of math
Profession (siege operator) - Should be reasonably good with angles and actualy more of a physics type.
Spellcraft ought to also have some math in it imo...
Add Profession (Astronomer) and (Astrologer), both require some serious math.
Then you can add Profession (cartographer), (Accountant), (Merchant), (Sailor [at the higher levels]) and so on, .Almost all profession require some mathematical knowledge.
Question: Does having 19 Int AND Breadth of Experience automatically make you a math wiz?
Although still young for your kind, you have a lifetime of knowledge and training.
Prerequisites: Dwarf, elf, or gnome; 100+ years old.
Benefit: You get a +2 bonus on all Knowledge and Profession skill checks, and can make checks with those skills untrained.
...I guess so.
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I would imagine a PC's degree of math skill would go up according to INT, but few PC's routinely delve into math beyond dividing up treasure. Is a 19 INT wizard automatically a math wiz?
What kind of math are we talking about?
I'd say solving mathematical problems is pretty much a matter of pure intelligence. Similar to high strength allows you to lift heavy things.
Question: Does having 19 Int AND Breadth of Experience automatically make you a math wiz?
** spoiler omitted **
...I guess so.
Depends on your accepted definition of 'wiz'. Breadth of Experience plus Int 19 only means that you get a +6 on untrained knowledge.
Given that DC 15 is for 'basic questions' that's all you can answer with a take 10. Even if you knuckle down and study all night you can only boost that to 26, which only answers half of the 'really tough questions' that have DCs ranging from 20 to 30.
I'd suggest that for a competent mathematician you would need at least a +10, so you could hit a DC of 30 by taking 20.
A math 'wiz' to me would need a +20 on Knowledge (pure math) so that he can answer 'really tough questions' just by taking 10.
I'd say solving mathematical problems is pretty much a matter of pure intelligence. Similar to high strength allows you to lift heavy things.
Most high schoolers (I hope) could answer basic algebra questions pretty easily. The super-genius you pulled out of the closet wouldn't understand what 'x' is without someone explaining it to him at least once.
I'd say solving mathematical problems is pretty much a matter of pure intelligence. Similar to high strength allows you to lift heavy things.Most high schoolers (I hope) could answer basic algebra questions pretty easily. The super-genius you pulled out of the closet wouldn't understand what 'x' is without someone explaining it to him at least once.
I met someone taking pre-algebra in college. I was like... I never even took pre-algebra! I started with algebra in 7th grade! (I'm sure 90%+ of the people in this forum are in the same boat)
Anywho, agreed, you need some amount of education or experience if you hope to make something out of the non-numeric symbols.
This is tough, since "math" covers a very wide range of things. As for how many ranks you'd need to be a wiz at it, here's my take, and only my take, on what it would mean. First, I make the assumption that anyone over 5th level is beyond human possibility, and also that the math skill would fall under a knowledge and be int based. In Pathfinder, the human maximum for a 5th level expert would be +16, +5 for a 20 or 21 int, +5 for ranks, +3 for a knowledge class skill and +3 for skill focus. That would literally be the very highest possible mathematical skill attainable by someone on our planet if you agree with my assumption(stolen from the Alexandrian blog since it's an excellent idea) of 5th level being the true human maximum.
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Most high schoolers (I hope) could answer basic algebra questions pretty easily. The super-genius you pulled out of the closet wouldn't understand what 'x' is without someone explaining it to him at least once.
A super-genius should be able to understand something without additional explanation. Intelligence is more than just applying learned algorithms. Any computer could do that. It's about inventing new problems and ways to solve them.
A super-genius should be able to understand something without additional explanation. Intelligence is more than just applying learned algorithms. Any computer could do that. It's about inventing new problems and ways to solve them.
True, Intelligence is not just about applying learned algorithms. However it's hard to solve a math problem when you can't read, or have a concept of numbers, etc. You need a few tools in the toolbox before you can go away and solve problems.
The real question is how much math is actually developed in the world.
In our historical development, calculus didn't exist until Descartes. Engineers and other practical technical professions, even in pre-classical times, could do an amazing amount of things that our society sadly underestimates a lot, and this without our kind of math. They did not have calculus for it. The ancient Greeks used something similar to what we now call geometry. No math for numbers though.
In your world, has there been a brilliant mind already that invented calculus? What kind of mathematics does the character want to do? Does it actually need that kind of math?
Seeing how you mentioned it, a good example: dividing treasure (let's stick to GP for the example) should be a simple thing anyway and does not really require any math. If it's about small amounts you can hand-count or use an abacus (it's in the equipment list!). If it's about larger amounts you should do what merchants did: use scales and calibrated weights.
Just a minor correction: Calculus was invented by Newton and Leibnitz (more or less concurrently), which was a little after Descartes.
Interestingly, probability theory wasn't invented until the 17th century either. And god knows every gamer is extremely familiar with that :)
Also, the concept of zero is only a few hundred years old. And negative numbers are a pretty recent phenomenon (in the grand scheme of things).
My point is that it's almost impossible for us to imagine doing math without these fundamental concepts, and I'm not sure it's that interesting an exercise to try. I guess I'd call modern math an abstraction that we just accept in the game (accepting that people can make use it, I mean) and move on.
I use Appraise skill to determine calculation abilities and Knowledge (Engineering) for more physics related things. But that is just me...
Just thought I'd throw this trait into the mix:
Mathematics has always come easily for you, and you have always been able to “see the math” in the physical and magical world.Benefit: You gain a +1 bonus on Knowledge (arcana) and Knowledge (engineering) checks, and one of these skills (your choice) is always a class skill for you.
Just thought I'd throw this trait into the mix:
Mathematics has always come easily for you, and you have always been able to “see the math” in the physical and magical world.Benefit: You gain a +1 bonus on Knowledge (arcana) and Knowledge (engineering) checks, and one of these skills (your choice) is always a class skill for you.
Basic math like splitting loot is an everyman skill. For accounting more advanced then balancing a checkbook I'd require PS: Merchant or something related
For "higher" math engineering and arcana seem like the right one to me. KS: Engineering for more "practical" math, and KS: Arcana for more "theoretical" stuff. But if someone wants to bring forth another skill for math related to a specific activity, that's good as well. Even a scholarly backstory will grant you the ability to be good at basic math IMHO. Dumb barbarians don't get it for free though unless they blow some skill ranks.
Personal anecdote: At one point I was going for a Math major in college. It got to the point where the math was making my brain hurt and had NO application in reality. At one point I could do n-dimention vector matrix calculus. The only thing I could think of when I was learning that was "this is what hyperspace navigation looks like" Definitely KS: arcana stuff. When The Wife was in school for architecture she had to learn all sorts of math for force distribution, bearing loads, and the like. Some of that stuff was hard for me to figure out, and I've had more math then is healthy. KS: Engineering.
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In our historical development, calculus didn't exist until Descartes. Engineers and other practical technical professions, even in pre-classical times, could do an amazing amount of things that our society sadly underestimates a lot, and this without our kind of math. They did not have calculus for it. The ancient Greeks used something similar to what we now call geometry. No math for numbers though.
On your general principle, that the mathematics possible in a world with mnemonic enhancement spells and outsider tutors is different from historical development, I agree.
But the history of mathematics is one of my hobbies, and I find myself disagreeing with virtually all of your assertions.
See this easy-to-find example of the work Euclid wrote down in 300 BC, and this page for the mathematics that was being developed about 6 centuries later.
Theodosius addressed the area under curves and Zeno of Sidon was examining infinitessimal movement, the central problems of both integral and differential calculus.
You are the first writer I've read, who has suggested that the Greeks didn't have arithmetic. And "what we now call geometry", they also called geometry.
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I think they had a substantially different arithmetic. For one thing they did not have the concept of Zero.
Sure they did. They didn't consider it a quantity, but they understood it as a concept. (How could they not? "How many bulls in that field?" "None.") Indeed, Democritus introduced the idea of "infinitessimals" and Archimedes was using them in his "method of exhaustion", and you can't have a discussion of those works without the concept of zero.
For that matter, when Leonardo of Pisa wrote his Liber Abaci in 1202, he introduced the Hindu-Arabic numeral system to Christian Europe, he explained that the system used nine numbers 1 - 9, and a symbol 0, to indicate place-value.
I agree with your last paragraph. Being able to sight distances exactly ("If I center my fireball just so, its radius hits the were-gator, but not my halfling friends flanking him.") is probably not even mathematics.
There is a certain amount of role playing involved here, including determination of character concepts.
However, unless a character has some knowledge ranks in an area that includes specific mathematical knowledge (or just "math" for the rare role player who wants to play a medieval geek) I would not expect a typical PC to have knowledge of anything beyond basic arithmetic.
Concepts (much less skills in) things like algebra, exponentials, trigonometry, or even anything beyond very basic geometry, would be completely unknown to most PCs, including educated ones.
Wizards would be the only exception. I would expect wizards to have learned algebra and geometry as part of their magical training.
Concepts like "calculus" or other "advanced math" subjects should probably be restricted to the rare super-genius who has maxed out math skills.
According to Wikipedia, zero is older than Jesus (used as a placeholder in both Babylon and Mesoamerica).
Certain members of the expert class might choose to specialize in math skills. there might even be a math tutor at a wizard school that is an expert that knows math with a few wizard levels and now mostly teaches math to the students.
An abacus are in the advanced players guide so arthemtic exists. so there is some math and I do not think they have actually any skill requirment to use by Raw so there is some calculation.
I just thought of a scholar looking for a lost scroll with a proof of a mathematical therom on it as a plot hook.
.... You are the first writer I've read, who has suggested that the Greeks didn't have arithmetic. And "what we now call geometry", they also called geometry.
You sayin' that the greeks had differential equations, integrals and coordinate systems?
.... You are the first writer I've read, who has suggested that the Greeks didn't have arithmetic. And "what we now call geometry", they also called geometry.You sayin' that the greeks had differential equations, integrals and coordinate systems?
The Greeks had multiple coordinate systems, in fact there was a great debate about coordinate systems in ancient Greece. They did not have "integrals" or "differential equations" because both of those are specific mathematical artifacts of the Calculus system developed by Newton and Leibnitz (is that right? Been a long time since I took advanced Math classes in college) but the concept of infinite series was not unknown to them. In fact to this day "Zero's paradox" of Achilles racing a turtle is still used as an introduction to infinite series which have finite solutions. Much of what we now call "trigonomotry" was developed by the Greeks.
Greek math was pretty advanced.
A lot of math was Greek in orgin. In fact, it's all Greek to me.
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You sayin' that the greeks had differential equations, integrals and coordinate systems?
The Greeks had multiple coordinate systems, in fact there was a great debate about coordinate systems in ancient Greece. They did not have "integrals" or "differential equations" because both of those are specific mathematical artifacts of the Calculus system developed by Newton and Leibnitz (is that right? Been a long time since I took advanced Math classes in college) but the concept of infinite series was not unknown to them. In fact to this day "Zero's paradox" of Achilles racing a turtle is still used as an introduction to infinite series which have finite solutions. Much of what we now call "trigonomotry" was developed by the Greeks.
The Greeks didn't have algebraic geometry; that was indeed the contribution of Descartes.
Because the Pythagoreans (who worshipped numbers) beleived that every number was rational, and because the diagonal of a square exists as a length that is incommeasurable with the side of the square, arithmetic and geometry diverged. The Eudoxian Theory (Euclid's Elements, Chapter 10) is an attempt to show that, for example, the ratio 2*sqrt(3) : 3*squrt(3) is equivalent to 2 : 3. (If you get the chance, actually sit down and read Book 10. It's a joy to read, and the clarity of the arguments stand out, even in translation.)
Now, Zeno's Paradoxes were written 150 years before Euclid, and were actually attempts by Zeno to show that adding a bunch of very tiny things was ridiculous. But take a look at Euclid, Chapter 9, and that's where you'll find the sum of infinite geometric series (proposition 36).
And math didn't stop at Euclid. Archimedes proved that the area enclosed by a parabola and a straight line is 4/3 times the area of a corresponding inscribed triangle. He expressed the solution to the problem as an infinite geometric series with the common ratio 1/4. Ptolmey wrote on astronomy (working out the size and distance of the Sun), optics, music, and geography. In addition to his work on polygonal numbers and other facets of number theory, Diophantus applied Euclid's habit of careful study of systems to arithmetic, inventing algebra in about the year 250 CE.
So, yeah, no coordinate systems, but serious heavy lifting of mathematics.
Now, Zeno's Paradoxes were written 150 years before Euclid, and were actually attempts by Zeno to show that adding a bunch of very tiny things was ridiculous. But take a look at Euclid, Chapter 9, and that's where you'll find the sum of infinite geometric series (proposition 36).
And math didn't stop at Euclid. Archimedes proved that the area enclosed by a parabola and a straight line is 4/3 times the area of a corresponding inscribed triangle. He expressed the solution to the problem as an infinite geometric series with the common ratio 1/4. Ptolmey wrote on astronomy (working out the size and distance of the Sun), optics, music, and geography. In addition to his work on polygonal numbers and other facets of number theory, Diophantus applied Euclid's habit of careful study of systems to arithmetic, inventing algebra in about the year 250 CE.
So, yeah, no coordinate systems, but serious heavy lifting of mathematics.
And yet the default coordinate system in use today is quite paradoxically called "Euclidian space".
I suppose my professor may have had a different take than yours, but Zeno's paradox was deliberately devised to describe how you could take the distance between two moving objects and that if you described that as a series of steps of 1/2 the distance that Achilles would never pass the turtle, and yet pass the turtle Achilles did.
No, the Greeks did not solve the problem (thus it was called "Zeno's Paradox") but unless you believe that Zeno actually thought the turtle would never get passed, clearly the fact that he described the problem shows that they were aware of the need for a way to solve problems with infinite series, which is what I was trying to demonstrate.
I miss WFRP. That's when PCs were illiterate, having the ability to read made you a god, and counting over 10 was really difficult unless your shoes were off.
And yet the default coordinate system in use today is quite paradoxically called "Euclidian space".
Euclidian space is called that because it fulfills Euclid's fifth postulate, the so-called parallel postulate (there are a number of different ant equivalent formulations), but it is that postulate that causes space to be flat - and therefore one which Euclid's geometry describes.
So it's not a coordinate system, but rather a description of the expected behavior of space and movement through that space.
Cheers,
MI
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I use this reasoning with my characters:
INT is only part of what can help determine what a character knows and does not know. Class, INT, skills, and upbringing all have a hand in what knowledge my character has.
Math in it's basic form should be known by almost anyone. A barbarian would still be able to count, though his counting could sound like, " 1, 2, 3, 4, many. 1many, 2many, 3many, 4many, many many. 1manymany, 2manymany, 3manymany, 4manymany, lots."
Druids wouldn't go much beyond multiplication and division.
An intelligent fighter (yeah, they exist.) could possibly do higher multiplication and division. If this same fighter was trained in a formal military school, his skills with math would be higher then if he was trained by a mentor in the woods.
A paladin, ranger, or cleric might be on the same level as that smart fighter. I would expect them to be slightly more advanced though.
The rogue with the right skills would be expected to know any math associated with engineering and architecture.
Bards also have a possibility of having knowledge of complex math. Art and music, for example, do often make good use of complex maths.
A wizard should know the most complex maths, and with magic studies they might even know a type of math not known in our real world. Naturally, a higher INT would mean they would be able to work out more complex maths.
Skills would be important, like knowledge: Arcana, or knowledge: engineering. Any number of craft or profession skills would also need to know and use complex math o. A regular basis.
This is a little off the topic, but it brings up an issue that has been bugging me about how casters know (with precision) where to target AE spells.
To be able to target spells with precision, wizards and sorcerers (and other characters with ranged AE spells) have to be geniuses in spacial geometery. I mean, they would have to be mathmatical savants to be able to precisely place a 20' fireball between closely spaced enemy and friendly forces at 400-500+ ft away (and doing from a non-elevated position, no less).
This, of course, comes with using battlemats and such which allow spell casters to pick exactly where they want their spells to land. I just kind of handwave that lack of realism in favor of the ease of using battlemats and miniatures.
I have been toying with the idea of introducing a level of uncertainty to AE spells to reduce targeting AEs near friends. Would you really throw a grenade near a buddy even if you "thought" he was just outside its effective area? Maybe I could make the caster target a specific grid point and have then roll to hit like with splash weapons.
Also, the concept of zero is only a few hundred years old. And negative numbers are a pretty recent phenomenon (in the grand scheme of things).My point is that it's almost impossible for us to imagine doing math without these fundamental concepts, and I'm not sure it's that interesting an exercise to try. I guess I'd call modern math an abstraction that we just accept in the game (accepting that people can make use it, I mean) and move on.
Actually, the first known person to define zero (though he had no symbol for it) was Brahmagupta in 628 AD. He also had negative numbers and a form of algebra, though modern algebra isn't directly related to his works.
Bhāskara I, was the first person to write zero as 0 only a year later in 629. He also worked out a rational approximation for the sine function. He also worked out that if p is a prime number, then 1 + (p–1)! is divisible by p. This is one of the earliest known formulas for attempting to calculate prime numbers, though in practice, the theorem based on it ,Wilson's theorem: (n-1)! = -1(mod n), requires too many calculations to be useful.
What really pushed European scholars forward, in my mind, is the printing press. It suddenly became easier to replicate and disseminate knowledge, letting more people learn what others had discovered, which freed up more time/brain power learning new things.
My point is these concepts existed for 1400 years, but it's the opportunity to learn from the lifetime of knowledge of others that makes advances possible. In a non-print society, that knowledge can only be gained from the person who made the advance, or one of a handful of books. Without that serendipity, people just make the same discoveries over and over.
According to Wikipedia, zero is older than Jesus (used as a placeholder in both Babylon and Mesoamerica).
It was a placeholder, but it's value was contextual. On it's own, the placeholder had no value. The Babylonian version would essentially look like this:
The current year is 2[blank]11.
The [blank] is essentially spelled out. The problem was they didn't have a differentiation for different digits either, so the equivalent of 10 and 100 would look exactly the same without context.
10 = 1[blank]
100 = 1[blank]
The only way the reader can know the difference is if he understands the context. If you and I only read ancient Babylonian, and I wrote to you: "the new verizon iphone costs 1[blank] dollars with a contract" you'd probably understand that I meant 100.
This is an example more relational to our numeric system, they used base 60, so it was more confusing telling the difference between 2, 2x60, 2x60x60 and 2/60.
The Greeks had multiple coordinate systems, in fact there was a great debate about coordinate systems in ancient Greece. They did not have "integrals" or "differential equations" because both of those are specific mathematical artifacts of the Calculus system developed by Newton and Leibnitz (is that right? Been a long time since I took advanced Math classes in college).I think integrals are from Riemann. Why else speak about the Riemann sum?
Derivation-integration relation came from Leibniz&Newton. However saying that integrtion is derivation backwards doesn't actually say what is clever way to calculate integrals. Riemann came up with most commonly used method, so the normal integral is called Riemann Integral (there are other ways, witch are more useful in some cases).
P.S. And isn't the discussion about the coordinate system still present today? Don't quantum mechanics calculate in a Riemann space (with multiple parallel lines through a point) instead of the standard Euclidean normal people use?
Quantum mechanics are calculated in function spaces.
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What really pushed European scholars forward, in my mind, is the printing press. It suddenly became easier to replicate and disseminate knowledge, letting more people learn what others had discovered, which freed up more time/brain power learning new things.
More to the point, the printing press / movable type created a demand for printed books, which created a demand for cheap paper. Once we had a cheaper writing surface than vellum, it became practical to develop arithmetic algorithms that used up a small sheet of paper for a calculation.
For a variety of reasons, scholarly mathematics works like Almajest and Elements were almost always hand-copied, well after the printing press came about. The first printed math text was the Treviso Arithmetic, a practical book intended for the students at the reckoning school there.
P.P.S. And why do you want to know what math your character knows Kilmore? Do you plan to born monsters to dead? Or just drive you dm crazy?Just something I thought of while cruising Wikipedia.