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While reading Seekers of Secrets, I became suddenly inspired by all the references to cartography, and I have done a little research on ancient map-making. With a little help from the technology in Golarion thread, I've come to the conclusion that many areas of Southern Golarion would certainly use the tools that the Greeks, Romans, Babylonians, etc. had, and maybe even some surveying/navigation equipment of the 16/1700s. So how would they do the math? Trigonometry has been around since around 120 B.C., so it seems they ought to be able to do sine, cosine, tangent and some of the rest. My question is, would they use a slide rule or tables? The slide rule was invented in the 1600s, but if they have a printing press, would they also have invented some form of a slide rule?
Lest you fear I am the most boring GM to walk the planet, this is not for a campaign. It is a) for my own curiosity and b) because I am trying to write a short story and c) maybe I would want to play a mapmaking Pathfinder someday. If I picture my Pathfinder exploring the deserts of Osirion, would he/she draw his maps (because I am sure the Pathfinders want their maps to be as accurate as possible) with the aid of a slide rule or trigonometric tables?
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I think that with a given magical setting, mathematics should be fairly advanced (certainly beyond what the medieval people of our world had) but also less emphasized. Many people would probably prefer to use magic to solve issues that otherwise are solved with science and mathematics in the real world.
Your character might even be seen as eccentric for insisting on using methods more difficult than the magic ones available. He could be the guy who insists on using an ancient AM radio in a world of podcasts, because he either doesn't trust the newfangled contraptions, or because he romanticizes the older devices for their elegance and brilliance.
Also, as has probably been discussed with every fantasy system or world setting ever created, what among all the stuff we invented in our mundane world would never have even been tried in a world where you have magic to do things for you?
Many inventions/developments we think of as modern are actually very ancient. Often they are lost and rediscovered. Considering the ancient cultures of Golorian, this is likely true as well.
That said, Osirion has fairly advanced astronomy and the engineering feats of ancient Thassilon (even with the aid of giants and magic) support the existance of advanced engineering practices.
I would tend to disagree with the idea that Golarion has any sort of advanced math. Why bother when you can simply divine and answer magically.
I would hazard that even though the cantrips or orisons accurate count and know distance aren't in the Core Rules, they do exist. Along with a plethora of non-combat related spells and magics.
CJ
There's totally advanced math in Golarion. Yes, you can use magic to get the same answers, but:
1) Most of the wizards I know aren't going to waste a valuable spell calculating how many bricks the workers need to build their tower.
2) Most gods are going to look askance at the priest who communes with them every time they need to know whether it's more economical to plant yams or russet potatoes.
3) The vast majority of the population doesn't have access to magic, and I dare say 99% of mundane masons, architects, shipwrights, military leaders, etc. aren't going to hire expensive magic users just to practice their trade.
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There's totally advanced math in Golarion. Yes, you can use magic to get the same answers, but:
1) Most of the wizards I know aren't going to waste a valuable spell calculating how many bricks the workers need to build their tower.
2) Most gods are going to look askance at the priest who communes with them every time they need to know whether it's more economical to plant yams or russet potatoes.
3) The vast majority of the population doesn't have access to magic, and I dare say 99% of mundane masons, architects, shipwrights, military leaders, etc. aren't going to hire expensive magic users just to practice their trade.
I envision it more to be that cultures use magic to gain mathematical knowledge initially, but once something has been explained (usually by magic) they keep the formulas and do it the good old fashioned way whenever they can.
So those professionals who need to use math have access to advanced math knowledge which was originally gained by a curious wizard or the like.
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3) The vast majority of the population doesn't have access to magic, and I dare say 99% of mundane masons, architects, shipwrights, military leaders, etc. aren't going to hire expensive magic users just to practice their trade.
That's kind of what brought me around to the question--if I'm making an explorer/ranger who draws maps, how can he do it accurately without access to a barrage of spells.
Thanks for the feedback, everyone, particularly the official response. Also the Gods and Magic reference--it didn't occur to me to look there.
I like to think of magic as a means of making mathematical computation easier/possible. If mathematical formulas had to be "revealed" by magic, it doesn't seem to me that people would understand them well enough to use them--or explain them to others without divination spells at their disposal. And I can't see how people--especially centuries-old elves--would be content not learning something or not discovering something available to the humanoid mind. I tend toward the idea behind the magic item for Abadar mentioned above--magic, like my calculator, can crunch the numbers, but I have to know how to use it. In my specific case, I think there might be a magical device that calculates trigonometric functions, but I'm not sure how widespread it would really be. On the other hand, it is sure a lot more interesting than a book of tables.
Considering the scale of the architecture in ancient Thassilon, even with the use of magic, they would have to have some good mathematical knowledge.