How much do Zalanthan folks know about math?

[musashi]

Of course, I can imagine that most Zalanthans knows precious little beyond basic adding and subtracting (to count their black little shineys  ) but from one Zalanthan scholar to another, what is the level of mathematics that they've developed? Algebra? Calc? Trig?

[Tisiphone]

Of course, I can imagine that most Zalanthans knows precious little beyond basic adding and subtracting (to count their black little shineys  ) but from one Zalanthan scholar to another, what is the level of mathematics that they've developed? Algebra? Calc? Trig?

I'm going to go out on a limb here and say that, from what I've seen IG, they're probably roughly on par with the 5th century BC, meaning advanced geometry, conics (certain 2nd degree solutions to the locus problem), and maybe some rudiments of the work of Archimedes. However, they likely don't have a formalized algebra or the concept of 0, or of negatives, outside of ratiocinatal compounding and subtraction from greater.

My biggest question is how they got this far without astronomy.

[tortall]

If they haven't formed algebra, how are they building two+ story buildings?

[musashi]

Erm ... magick? 

That's a good assertion Tis, I hope that staff could perhaps chime in since the docs didn't seem too clear on math when I skimmed through them.

[Tisiphone]

If they haven't formed algebra, how are they building two+ story buildings?

Geometry. Go look at some Greek ruins.

[Bushranger]

I would say they are more advanced than this, though probably not on a widespread basis. Certainly some of the noble houses (Sath/Negean) and templarate employees could be devoting sages to mathematics, and with an understanding of magick it could have aided their studies. Formalized algebra, 0 and negatives are within reach for these people I imagine, just not something that is widely spread about.

[Tisiphone]

I would say they are more advanced than this, though probably not on a widespread basis. Certainly some of the noble houses (Sath/Negean) and templarate employees could be devoting sages to mathematics, and with an understanding of magick it could have aided their studies. Formalized algebra, 0 and negatives are within reach for these people I imagine, just not something that is widely spread about.

I would strenuously disagree, for two reasons:

1) You don't need algebra or negatives to do proper book-keeping, ESPECIALLY not in a supposed tally-system, regardless of how complicated it might be.

2) There are numerous philosophical difficulties with algebra, but most especially with nulls and negatives that I don't see Zalanthas as being in a position to accept.

[brytta.leofa]

Should addition and subtraction themselves by more laborious than we, with our swanky log notation, give them credit for?

[Bushranger]

Quite possibly, but then the way I imagined it the Sath and/or Negean sages were not studying mathematics for book keeping at all. It was precisely the philosophical reasons that I could imagine them delving deeply into mathematics and working out 0 and negatives. It might not be true, but just based on the esoteric knowledge that these two noble houses are rumoured to investigate is why I thought they could have tackled those philosphical lines of reasoning.

[The7DeadlyVenomz]

Yeh, I could see them working nulls and negatives, absolutely. It's not THAT hard to understand.

[Tisiphone]

Yeh, I could see them working nulls and negatives, absolutely. It's not THAT hard to understand.

Um....

Understanding nulls and negatives with respect to positive quantities and identities is quite different from understanding them per se (though I hesitate to use that phrase; it gives me metaphysical pause). I would, in fact, assert that you very likely think of them in the first way rather than the second, even though you probably don't think you think that way.

[Riev]

Yeh, I could see them working nulls and negatives, absolutely. It's not THAT hard to understand.

Um....

Understanding nulls and negatives with respect to positive quantities and identities is quite different from understanding them per se (though I hesitate to use that phrase; it gives me metaphysical pause). I would, in fact, assert that you very likely think of them in the first way rather than the second, even though you probably don't think you think that way.

For the love of goddamned whoever your lords are, people. This is not the philosophy thread, nor a corner to spread your slanderous lies. Math was given as a gift from the Dragon, and now he wants it back.

In all seriousness, I don't remember this being a discussion of Frege's theories of number, or a philosophy of science question. It was -basic- math.

[Clearsighted]

I reckon they know this much...

This is how to count on your hands from a book on medieval Turkish archery. Archers had to know it so they could be taught how to hold the bow.

http://www.caama.ca/kitab2/s8.html

Erm ... magick? 

That's a good assertion Tis, I hope that staff could perhaps chime in since the docs didn't seem too clear on math when I skimmed through them.

This isn't a slam against you, but having magick explain stuff in settings like this when there are better, mundane reasons, has always been a pet peeveof mine.

[Tisiphone]

In all seriousness, I don't remember this being a discussion of Frege's theories of number, or a philosophy of science question. It was -basic- math.

Again, no. The history and development of math is rooted in philosophy. Further, math id ipsum is a philosophic ratiocination.

[musashi]

Erm ... magick? 

That's a good assertion Tis, I hope that staff could perhaps chime in since the docs didn't seem too clear on math when I skimmed through them.

This isn't a slam against you, but having magick explain stuff in settings like this when there are better, mundane reasons, has always been a pet peeveof mine.

It wasn't a serious remark, hence the emoticon.

[Rahnevyn]

I am not a math-scholar myself but I think I can say definitively that Zalanthans do understand basic arithmetic and geometry, but don't grasp things as advanced as calculus (or sciences like physics and chemistry). The most skilled mathematicians and scientists are probably among the ranks of Sath and Negean, though I'd expect Houses Valika, Kassigarh and all the merchant Houses to have some advanced number-crunchers as well.

[musashi]

So what about algerba? Do they know about whole numbers (ie 0)? Integers? Rational Numbers?

[Angela Christine]

My biggest question is how they got this far without astronomy.

There used to be the ruins of an observatory with a big ol' telescope in Tuluk, I'm not sure if it is still there.  Maybe it existed just to watch for flying monsters, but it is more likely that there was something routinely visible in the sky.  If we assume that the dust/sand storms have been getting worse over the last few centuries as a result of desertification, then it is quite possible that the skies used to be clearer than they are now.  I believe NPCs do have (or had) astronomy it was just never fleshed out for PCs.  Telescopes exist, but since PCs rarely get their hands on them, there is no compelling reason for staff to spend a lot of time developing a complex system of stars. 


Modern day Zalanthas is a degraded society, it is post-apocalyptic.  There was a society, and then there was an apocalypse, and then the survivors gradually built back up to where we are now.  It is quite likely that the pre-Dragon society was far more advanced than modern society.  Besides, lost secrets of the ancients are cool.  Before the Dragon there were no Defilers, and there is every indication that the land was far more lush than in modern times.  I like to think that pre-Dragon society was very much like your typical fantasy/Tolkien/forgotten realms type setting with friendly halflings, bearded dwarves, and noble elves prancing around the forests and all that trash.  What survived was twisted by the cataclysm.  I figure that pre-cataclysm scholars of Zalananthas were about as far along as earthling scholars in the 1700s or so.  They hadn't made the leap to the industrial revolution, but they were not savages either.  Basic algebra is certainly within grasp.   

Then along can the Dragon and his defilers, to conquer and despoil the world.  Some learning they destroyed on purpose, because it was potentially dangerous to them.  Much more was destroyed incidentally.  Some was simply abandoned, and destroyed by time and weather.  Some was preserved by accident or design, and discovered by later explorers.  That is half the fun of being an explorer, that you may uncover some ancient secret that hasn't been scene in Ages (and that may be worth a lot of money).  Documents that are hundreds or thousands of years old tend to be in rough shape, and an ignorant person who discovers them by accident might be more likely to use them as kindling than to preserve them.  The stuff that is most likely to be preserved is whatever seems useful. 

Great libraries and ancient vaults may contain traces of much more advanced things like calculus, but it is unlikely that even one person in a generation is studying them, much less understanding them.  You can give the average high school graduate an introductory textbook on calculus, and they won't make heads or tails of it.  Give them a faded, fragmented text book on calculus written entirely in Latin, and our average high school graduate won't be able to understand very much at all. 

The most learned scholars in the land probably understand complex geometry,  you'd need at least that to keep building large non-magickal structures and those amazing argosies.  Useful maths and science will be kept in circulation, and there are probably mechanically and arithmetically adept slaves who are trained in useful math and engineering, because when you have to calculate everything by hand you are going to want some helpers.  Math and science that is not obviously useful would be preserved by a few dedicated noble scholars, but is probably not well understood by anyone.

[Tisiphone]

My biggest question is how they got this far without astronomy.

I figure that pre-cataclysm scholars of Zalananthas were about as far along as earthling scholars in the 1700s or so.  They hadn't made the leap to the industrial revolution, but they were not savages either.  Basic algebra is certainly within grasp.   

Great libraries and ancient vaults may contain traces of much more advanced things like calculus

I'll agree with the first point, but basic algebra doesn't comprehend nulls and negatives; 'tis more of a geometric subsitution system. Take a look at Diogenes. As far as calculus, I must strenuously disagree, unless the Dragon was a lot more destructive even than believed thus far. The leap to calculus boggles the mind.

[Lizzie]

Does your PC know how to cut and sew a dress, in a way that will actually fit someone? Then you're using geometry. Using math doesn't require knowing the right terminology, or even knowing that this -is- what you're doing. We use math, complex and basic, in our lives all the time. Even recognizing our own depth perception is using math. Being able to "look west" and see "very far" there's something that might be a mantis, is using math. You don't -need- to know exactly how far away it is, you don't -need- to know the exact trajectory or angle between you and that mantis, compared with the wind velocity and slope of the terrain. What you -do- need to know, is that it's "very far," that you have a "really uber war bow" and "a kick-ass arrow," and that the wind is blowing -toward- the mantis from your direction, so the arrow is most likely to actually get that far.

Your character won't know about 70-degree lifts or catching wind currents at precisely 22.6 degrees latitude and 197.94 degrees longitude. Your character won't NEED to know that. But that is exactly what your character is doing, even if he isn't aware of the terminology. He is applying math in his daily life, whether he knows it or not.

I would also say that any Nenyuk family member would have been born, raised, and bred to learn about complex math - they're the ones who make the locks, make the keys, make the sids, hold the sids, arrange the deposits and balances and withdrawals, negotiate construction on apartments, keep track of who is renting where and how much rent is owed and the odds that this person will die soon so they can/cannot promise Lord Bumfuck Borsail that his favorite big-dicked catamite will be able to move in to the building in the next month and yes, there is room in the apartment to accommodate his catamite's pet chalton, though it might be a tight fit. All this kind of thing involves not only simple addition and subtraction, but complex geometry (locks and keys), algebraic expression (average volume of a chalton + movement + velocity of its digestive waste, to determine whether or not his craps will actually land out the window if they keep him tied facing the living room, because no Nenyuk in their right mind would impose the job of cleanup on even their least valued slave).

[The7DeadlyVenomz]

Yeh, I could see them working nulls and negatives, absolutely. It's not THAT hard to understand.

Um....

Understanding nulls and negatives with respect to positive quantities and identities is quite different from understanding them per se (though I hesitate to use that phrase; it gives me metaphysical pause). I would, in fact, assert that you very likely think of them in the first way rather than the second, even though you probably don't think you think that way.

You're prolly right. But I only know of one way to think of negatives and nulls. I didn't even know there were other ways.

[Iota]

Yeh, I could see them working nulls and negatives, absolutely. It's not THAT hard to understand.

Um....

Understanding nulls and negatives with respect to positive quantities and identities is quite different from understanding them per se (though I hesitate to use that phrase; it gives me metaphysical pause). I would, in fact, assert that you very likely think of them in the first way rather than the second, even though you probably don't think you think that way.

You're prolly right. But I only know of one way to think of negatives and nulls. I didn't even know there were other ways.

Scrab ambush

[musashi]

Lizzie ... while I do appreciate where the first half of your post was going, it's sort of off the topic of what I had asked. I want to know how much math scholars in Zalanthas know ... which would imply that they would in fact need to have thought about it, come up with terms, and be able to understand it on that level.

While I do agree with everything you said in reguards to people using math without realizing it, that wasn't what I was asking about.

Per the 2nd half of your post though, I am of the mind that the banking house should probably have some advanced math-users in its ranks, given all the seemingly impossible things they do with currency and with housing in the game world.

[Lizzie]

Actually I was thinking on the order of the GMHs in general. I imagine the spice refinement process requires some serious precision and (guessing) Maybe even a little bit of chemistry understanding to ensure that the Kurac-stamped brick of Tho doesn't contain any significant amount of something -other- than Tho in it. I imagine that the -reason- that only Kadius can make "a plain red silk vest with green beaded buttons down the front" is because -only- they have enough understanding of math to get the pattern right without fucking it up. I imagine that the reason only Salarr can make *that* bone dagger, as opposed to *that other* bone dagger that every knife-making crafter can make, is because only Salarr has enough understanding of the math to get the blade honed, set, and balanced in exactly that way, consistently.

Rennick probably isn't taking a wild guess on watering and fertilization techniques when it creates its gorgeous gardens. It probably is using very precise measuring methods with equally precise proportions of various substances, and has calculated when to water, when not to water, when to send the slaves out to check, how far to cut back after a harvest of seeds, etc. etc. etc.

All of these things involve not only math, but an *understanding* of the math involved. Anyone can guess, or approximate. But people who specialize in various things that require the use of math, probably have been educated on that math. Otherwise, they'd just be some guy who tosses seeds in the ground, dumps a skin of water on it, and hopes some day it will grow into a plant. Or just some guy who makes generic green silk djellabahs, and not the ones Kadius makes, with the fine, almost invisibly thin silken thread on the hems, with a lace pattern no one has ever been able to duplicate during the entire existence of the current incarnation of the known world, post-dragon.

[Rahnevyn]

So what about algerba? Do they know about whole numbers (ie 0)? Integers? Rational Numbers?

I specifically avoided answering that one because really, I Don't Know. I'm not a math major (computer science comes close, but doesn't quite get there), and I don't want to answer definitively.

Part of the problem is that technology/culture in Zalanthas varies and can't be tied to one specific period in the ancient or classical world. They use bone and stone tools, have only primitive gunpowders, and little advanced seige technology to speak of. On the other hand, they are capable of creating giant, multi-room wagons, and advanced architecture. They have roads and sewers, and processes to refine natural resources into more usable forms, like Kuraci spice.

Let's assume they know all the math that is required to produce all the things you can find commonly used ICly in the world. If someone wants to write up an argument that proves Zalanthans would need knowledge of algebra, 0, complex numbers, etc. in order to produce what they have, I'd be interested in reading it. Answering any more definitively is probably above my pay grade.

[touringCompl3t3]

I'll agree with the first point, but basic algebra doesn't comprehend nulls and negatives; 'tis more of a geometric subsitution system. Take a look at Diogenes. As far as calculus, I must strenuously disagree, unless the Dragon was a lot more destructive even than believed thus far. The leap to calculus boggles the mind.

I don't want to argue with you about zero or negatives, given that you appear to have strong feelings on the subject and seem to have researched the matter more thoroughly than I.

Historically, calculus was invented to solve problems in astronomy.  Given an absence of necessity for Zalanthans to study astronomy or conduct complex (sea) navigations, I don't see why they would currently maintain calculus especially without the ability to write that sort of stuff down.

I think that some of the posters here who favor conservative estimates tend to underestimate the amount of calculation necessary to successfully construct an industrial-grade structure like a city-wall, or a road that withstands erosion or a gladiatorial stadium.  Even the maintenance on those sorts of structures tends to get pretty engineering-intensive.

Changing the subject, I've often been surprised at the amount of arithmetic blue collar people use in the course of their jobs, even when they haven't finished high school. 

Most children and adults will need to understand multiplication and division in order to conduct commerce (i.e. shop for groceries) as well as keep score at sporting events.

[KIA]

House Tenneshi would probably have a good deal of knowledge about any mathematics needed for architecture, as they've spent a good King's Age rebuilding Tuluk. Some of the architecture in Tuluk is quite impressive, especially the estates. But the math would perhaps be implicitly linked to physical and material substances. Theoretical math would hardly be seen as useful or tenable.

[touringCompl3t3]

House Tenneshi would probably have a good deal of knowledge about any mathematics needed for architecture, as they've spent a good King's Age rebuilding Tuluk. Some of the architecture in Tuluk is quite impressive, especially the estates. But the math would perhaps be implicitly linked to physical and material substances. Theoretical math would hardly be seen as useful or tenable.

Yeah, I definitely feel you.

I remember trying to play my House Tenneshi PC as something of an engineer.  People really didn't get the character, but that's probably because he wasn't a hunter, a frou-frou noble or a dickens-whelp.


=-)

[Bilanthri]

This thread has made me think a lot about the reasons that primitive people learned math. Often it was a by-product of more spiritual studies.

I offer two examples:

1) The Greek philosopher, Pythagoras, and his close contemporaries (ie Groupies), known as Pythagoreans, were on a quest for knowledge. They founded a religion based around the mathematical truths they discovered. The important thing to note is that it was their desire for spiritual growth that led them to the discovery of some of the foundations of modern mathematics.

2) The highly intelligent, stone-age Mayans developed a number system based on the length of the solar year, developing two distinct, interwoven calendars used to make surprisingly valid predictions about the ebb and flow of humanity as a whole. It was their need to understand the heavens, and the ties of people to the world, that spawned their powerful mathematical skills.


So if there is some strong spiritual reason for people to develop these kinds of sciences, they are likely to succeed. A great example is House Tenneshi, who would be encouraged to study architecture as a dedication to their own spiritual validity.
If there are astronomers looking to the sky, they are quite likely, if not destined, to discover a great deal about geometry and, perhaps, trigonometry.

But then, sciences are found and lost. Who knows what knowledge is lost to the sands.

[KIA]

However, knowledge of writing is illegal, (except perhaps in cavilish by the bankers and merchant family seniors). No commoner would be allowed to use mathematical notation farther than a merchant's rod or an abakus like device (should one exist). Without notation, things might get very difficult. Zalanthas is much more akin to ancient Egypt, where heiroglyphics and demotic script were still in the hands of the priests and scribes.

[Bilanthri]

However, knowledge of writing is illegal, (except perhaps in cavilish by the bankers and merchant family seniors). No commoner would be allowed to use mathematical notation farther than a merchant's rod or an abakus like device (should one exist). Without notation, things might get very difficult. Zalanthas is much more akin to ancient Egypt, where heiroglyphics and demotic script were still in the hands of the priests and scribes.

This is all very true. I would suspect that only the ruling castes would have any access to math aside from tally tablets and the like. But you gotta remember, these Egyptian priests and scribes had enough mathematical knowledge under their sashes to realize they needed to make an on-the-fly adjustment to an architecture project of massive proportions, and it still stands today.

[Jingo]

Keep in mind that there is a difference between what me might call "pure" math and "applied" math.

The egyptians for example had some interesting systems of mathematics for methods of astronomy, monument building and irrigation. But they didn't have a universal system of mathematics. Basically this was applied math.

A few thousand years later, we got the Greeks. They borrowed what the egyptians (and others) knew and turned it into an abstract system of logic that doesn't necessarily apply to irrigation of pyramid building. This is pure math.

My guess is that Zalanthas is on the same level of the egyptians where as they don't have a universal system of math. But they do have a math that applies to engineering.

[Krath]

Hehehe, The answer to this is simple ASSUMING this is a POST_Apocalypse game. They would know as much as us, assuming Post-Apocalypse was referring to an Apocalypse on earth.

[Bilanthri]

Hehehe, The answer to this is simple ASSUMING this is a POST_Apocalypse game. They would know as much as us, assuming Post-Apocalypse was referring to an Apocalypse on earth.

But, given socially cataclysmic events, people are forced to reassess what is important to their survival...Maslow's Hierarchy.
So, given enough of a backwards push, all the smart people are gonna be too busy making arrowheads to keep track of higher science.

[FantasyWriter]

Hehehe, The answer to this is simple ASSUMING this is a POST_Apocalypse game. They would know as much as us, assuming Post-Apocalypse was referring to an Apocalypse on earth.

But, given socially cataclysmic events, people are forced to reassess what is important to their survival...Maslow's Hierarchy.
So, given enough of a backwards push, all the smart people are gonna be too busy making arrowheads to keep track of higher science.

Ten points each to Krath and Bilanthri.

[AJM]

Hehehe, The answer to this is simple ASSUMING this is a POST_Apocalypse game. They would know as much as us, assuming Post-Apocalypse was referring to an Apocalypse on earth.

If this was earth, then where did the giants, and elves come from? I may be off here but isn't this world similar to that of the Dune series? I didn't read it, and my G.F. doesn't remember, but was there any sign of math-ability in the books?

[Bilanthri]

There are touches of Dune in the setting...political intrigue, Great Houses, isolationist desert tribes, lotta sand. But that's about where the similarities end. Despite the gritty, mortal feel of Zalanthas, it is still (high) fantasy with monsters, sorcerers, and the like. I'd recommend reading some of the DarkSun novels...not just as references, but because a lot of them are damned good.

Code Select Expand


>forage artifact

You find a dusty wierding module and pick it up.

[Taven]

The question seems to be where the line between intuitive math (such as what Lizzie's post covered) and "actual" math is. Due to the set up of Zalanthas, and strict limitations on knowledge and writing, the people who could have such knowledge is very limited to a handful, all of which would be connected to some major House. Nearly every House would have SOME form of math involved, but how "actual" it is defidently varies.

Another consideration is mathmatical notation. Nenyuk's notation is probably VERY different from, say, Tenneshi or Sath's. I'd imagine that even mathmatical notation would be a closely guarded secret; if you had to write math out in words it would be a gigantic handicap, and a shared notation doesn't seem like something the nobles or House Merchants would tolerate. Those in power want to guard and keep it.

Why is that important? Well, it means that whatever current math there is, I doubt there's much discussion of it outside of the select group in one's House that knows it, leading to specializations. For example, unless Nenyuk slaves are actually building the apartments they have, Nenyuk probably doesn't need Geometery the way, say, House Tenneshi does. Specializations mean that the math known overall is limited, and it's likely that if a House doesn't have a use for it, they won't both with it.

I don't think there are negitives on Zalanthas. Zero, yes, but no negitive numbers. None of the Merchant Houses have anything set up in such a way where they can loose coin. If you don't buy it, then you're not getting it. There are no negitive balances, or "money owed" unless, maybe, an individual of that House is doing that, and even then it would be the individual who might loose money, or be owed something, not the House. Odds are that individual isn't going to need negitive numbers to keep track of that.

However, short of magick, there has to be some more advanced mathmatics. How exactly did they make Tektolnes' tower, which is sky-scraper in height? Either it's some advanced math, or some advanced magicks-- Or even a combination of the two. The thing is, is that incredible structures like that haven't been built for eons, so whatever knowledge was used to build it is either forgotten or such a closely guarded secret you'd better not think about getting anywhere near it unless you're a black robe, or a slave who never sees the light of day.

Potentally, the Houses who have the most advanced knowledge of mathmatics would not be those who use it directly, but rather seek to understand everything. Negean, Sath, and possibly (to a MUCH lesser extent) Voryek. As collectors and keepers of history, those fit the bill and have access to older and more advanced texts. The math that may not have an immediate pratical use might be studied by them, along with the associated philosophic concepts. However, I think many of the other Houses, if aware of such knowledge, would probably dismiss it as eccentric and not useful, and short of conceptually, I doubt even those history-collecting Houses would have use for it.

[My 2 sids]

I'd say math and accounting practices could be fairly far advanced, even with an illiterate society.  Because it's not the skill per say that is dangerous -- its accumulated knowledge.

Amos brick layer and Lord Muck-muck may both be using the same math skills to construct and "decorate" their new home.  But, Amos' scale of "price of sand stone * 20' space"  and "10% of spending 200 sids at the shop"  is quite different than Lord Muck-muck's 200' castle and how to acquire the best and rarest decorations and servants. 

Also, Amos candle maker's scale of the world (in sales) v. Mr. Kadian's is also vastly different.   Amos might take notice that after a year the color plum sells slightly better than red (and he has a few odd-ball scrolls which may or may not point to this).  Mr. Kadian, however, has sales records going back hundreds of years all extremely detailed and covering the majority of transactions on all customer bases -- that kind of accumulation of records can be dangerous.


It's not that individuals are dumb, or even encouraged to be,   it's that individuals can't make ripples.  They can't upset the order.   Any knowledge that would  make someone stand out -- that's where the nobles and rulers may take notice.

[jstorrie]

I think it's safe to assume that Zalanthans know about the number 0 just because we already use it in-game a lot, and because it would be difficult for us all to break out of using it. We may as well just assume that the Empire of Man was advanced enough to know about 0, and because it's a pretty resilient concept no one has forgotten about it.

We can see where math isn't. Neither maps nor siege weapons are very common, so geometry and especially trigonometry are probably rare among un-Housed commoners. Nenyuk doesn't apply interest to many things, so the common man probably doesn't understand percentages and likely isn't very good at multiplication or division. There's definitely no evidence of calculus in-game.

There are also some interesting situations where math might crop up. Allanaki Council mages might have a good grasp of negative integers, for example, because some amount of positive/negative dualism is implied by the docs on the magick system. Merchant houses and military planners both might have some ideas about probabilities, though I doubt they're as advanced as Bayesian stuff.

[BlackMagic0]

Most my PCs can count to ten.  1... 2... 3... 10! 

And they are happy with that. Who needs to count all their newb boots, just knowing you got a shit-load is good enough.

To add to the topic, to be at least less crazy in his lack of sleep:
I believe that most commoners have absolutely no real knowledge of math, other then what they need to know for selling/buying.
Other commoners may know a bit more basic math, though I doubt they would know anything more (definitely not geometry) for most jobs done by them have no real need for it, and why would you keep something you no need for. You are already living on the edge of the blade, so to speak.
I could see nobles, Templars, merchants, and anyone work for these stations to have reasons to know quite a bit more about math/geometry. Maybe just because the snobs can know more, pfft.

In simple terms, I just don't see anyone on Zalanthas doing anything over simple math / geometry.

[Gunnerblaster]

Let's say:
Merchant buddy says to bring down forty branches so that they can make three arrows from each.
Me says that, from each branch comes three arrows, so that would be 120 arrows.

Having knowledge of lumberjacking, said character also knows that logs can be split into three planks. Then from those planks can be made three objects capable of being crafted into five arrows each. That would mean fifteen arrows from each plank. Would the character have the knowledge to then deduce that each log would be a yield's worth of forty-five arrows?

Then going a step further, would he be able to assume that three logs, giving off more arrows, would be more valuable then forty branches?

Or should I just assume that my character should go with the logic of "My two quarters are worth more than your dollar because I have one more of it than you do!"

[Doppelganger]

Having knowledge of lumberjacking, said character also knows that logs can be split into three planks. Then from those planks can be made three objects capable of being crafted into five arrows each. That would mean fifteen arrows from each plank. Would the character have the knowledge to then deduce that each log would be a yield's worth of forty-five arrows?

If he deals in arrows, yet does not know how to count, he would know that each log produces about four dozens or two quivers or three planks worth of arrows.

Then going a step further, would he be able to assume that three logs, giving off more arrows, would be more valuable then forty branches?

Yes, if arrows is a local currency.

Or should I just assume that my character should go with the logic of "My two quarters are worth more than your dollar because I have one more of it than you do!"

No, unless your character has negative wisdom. Even monkey would chose one banana over two kicks in the butt any day.

Opinion above is my own, not that of Armageddon staff.

[Angela Christine]

Let's say:
Merchant buddy says to bring down forty branches so that they can make three arrows from each.
Me says that, from each branch comes three arrows, so that would be 120 arrows.

Having knowledge of lumberjacking, said character also knows that logs can be split into three planks. Then from those planks can be made three objects capable of being crafted into five arrows each. That would mean fifteen arrows from each plank. Would the character have the knowledge to then deduce that each log would be a yield's worth of forty-five arrows?

Then going a step further, would he be able to assume that three logs, giving off more arrows, would be more valuable then forty branches?

Or should I just assume that my character should go with the logic of "My two quarters are worth more than your dollar because I have one more of it than you do!"

As a rule of thumb, I figure that math I can do in my head or with my fingers is within reach of most PCs that have bothered to spend time learning figuring.  Illiterate people often have very good memories, so if I can remember it, they can probably remember it too.  This may not apply if you are a math prodigy.

Just remembering the formula is not enough, either.  I can remember  a²+b²=c², and I can usually even do squaring in my head to get c², but there is very little chance that I will be able to figure the square route of c² in my head, so I reckon simple, ancient geometry is going to be beyond the vast majority of my PCs.  I can also remember the quadratic formula, but there is no way in hell I could solve it without writing things down, so I feel confident that it will be well beyond the capability of all but the most educated and specialized NPCs.

Most my PCs can count to ten.  1... 2... 3... 10! 

Are your PCs trolls half-giants?  One, two, some, many, lots!

Counting, adding and subtracting should be within the metal capabilities of most people.

In simple terms, I just don't see anyone on Zalanthas doing anything over simple math / geometry.

Someone on Zalanthas knows enough engineering to build huge, multi-level wooden argosies that don't shake to pieces the first time they hit a rough patch in the road.  Admittedly, that person is probably not a PC.  But there are feats of construction that would be challenging even to a modern, university educated structural engineer and architect to pull off using only Zalanthan materials.  It is possible that Zalanthan engineers are savants who build by dead reckoning and implicit understanding of their materials rather than using planning and blueprints, but it seems unlikely. 

[Archbaron]

My biggest question is how they got this far without astronomy.

This is true, something to ponder on.