# Dealing with numbers



## AnotherGeek (Sep 5, 2011)

Working on the numbers for my world, to some people that sounds daunting however I love doing a "census" for my worlds. I love math (nerdy I know), however my latest world en devour has brought a mathematical snag that is really bugging me. Mages are of 6 types, those who have access to 1,2,3,4,5, or 6 elemental types the more types you have the more powerful of a mage you are. It is rare for a mage to be of 3,4,or 5 and very rare for a mage to be a 6 elemental type. They are referred to as single (point) mage, double (digon) mage, triple (trigon) mage, quad (tetragon) mage, a penta (pentagon) mage and a hex (hexagon) mage. The elements to choose from are Air, Water, Fire, Earth, Void(Abyss), or Spirit(Aether), within Dravok it is rare for Air or Water to be the main element and it is even rarer for Spirit to be the main element. 

The country is land locked, population 15,000,000 people, High Fantasy Magic base, all mages are of nobility and all nobility are mages. However not all nobles are of money most nobles are of the lower ranks (Knight/Dame). The country is one of the most "blessed/cursed" with mages 40% of the population is comprised of mage nobles. I want to figure out everything from school beginnings to major positions, but I am stupidly can not get past this.

Here is what is getting tricky.
15,000,000 People country wide (okay)
6,000,000 are Mages (okay)
1,200,000 are of student age (they start at 9/10 and go for 7 years) (okay)
60,000 leave by or after their 3rd year of school and join the ranks of the church (okay)

Now the issue I am having, consider that we now have 1,140,000 students that are still in school it is illegal for a student not to attend school. Study with an individual master is discouraged for point mage, digon mage and trigon mage and illegal if the student is of a tetragon mage, a pentagon mage and a hexagon mage.

I am trying to figure out how to make sense of the numbers of students per academy/school. The types of schools I have are Universities (Major schools sometimes old castles converted with the town around it other times a fancy town with the major facilities being the school), Academies (Smaller than Universities still containing large facilities within their own town), Schools (they are within a town however the town was not built for the school but may still center around it), School houses (they are within a town however the town is not centered upon them) Mage Towers, they are places for small groups to learn the mage ways. I am unable to make the numbers mesh well, every time I start working the numbers I come out with towns that seem unrealistic to me. Any other math nerds who love fantasy can help me figure this out it could help.


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## Hans (Sep 5, 2011)

So you have mages and are concerned they do not behave realistic?
I don't know much about numbers at school. What do your universities teach? Just magic, or also Artes Liberales?

An other question is, how important is theoretical training in comparison to practical skills? Are they important or are they "nice to have"? In feudalistic Europe military skills were much more important. So high education was a nice extra. But no requirement for a leading position.

Your number of 40% nobles seem very high to me. Yes, they are mages, so realism does not apply. But when we put magic aside, it seems strange.
High Fantasy does mean a more or less medieval society? Medieval would mean up to ten farmhands are needed to support on city person. And city person means peasant, there are much less nobles. Without a much more modern agriculture your society could not support itself.
Of coursy you can always throw in magic. But there are no realistic numbers about magic.


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## AnotherGeek (Sep 5, 2011)

Sorry I havent slept much lately, all the schools in questions teach magic, the larger the school the more resources. I do not like the word realistic so to speak but guess it works they attend classes to learn the basics (history, math, sciences, their element(s)). I am having trouble getting the numbers of students per school type and per school to make sense. With out going to school they wont learn much, you can read a book but you wont get as much from a book than you would being in a class room seeing it demonstrated. Many of the lower nobles still do basic jobs, farming, smithing etc, they just carry the title this nation is blessed with mages they also believe that only nobles should go to battle, and those nobles must be mages etc.


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## JCFarnham (Sep 5, 2011)

Making the numbers work is fine, but my main concern is how that then translates into fiction. Do your characters quote numbers a lot? I guess its worth working out if those census numbers are integral to the plot, I can get behind it if its to get things straight in your head, but what I'm saying is does a slight inconsistency really matter? Is it going to effect the telling of the story of a rare element student mage [I'm making an asumption here, forgive me  ]?

Solely as a reader of your book however I doubt I would really notice something was up with this, so in reality you could let this slide, if we're being completely honest with each other.


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## TWErvin2 (Sep 5, 2011)

Just as I read the numbers, 40% are nobles--that is a very high percentage, unless the nobles are also going to be engaged in performing the mundane and average jobs that have to be done to support a nation of 15,000,000 individuals. I know you addressed this, but that makes the title of 'noble' mean other than what it does. A stablehand with a pitchfork being a noble may be a stretch for a reader. A knight plowing fields and a dame out beating dust from tapestries (since that is the majority of the nobles as you define them), again might be a stretch for the average fantasy reader. Not that you cannot pull it off, just a hurdle to consider. Maybe a title of 'lesser noble' or something such as that would be appropriate. 

For example, in the military, a large percentage of the 'enlisted' men would be nobles, and thus, knights? Then really, knight doesn't mean what 'knight' in the traditional sense. So why not use a different title?  And if the titles don't really mean anything since 40% of the population has them, then why have them? 

Again, I only am reading from a slice of the world you're creating and just posing questions. These are the same questions that an agent or editor might have in mind as they consider representing/publishing your novel (they will only likely initially read a synopsis and/first three chapters, and often look for reasons to say 'no' to a project than to say 'yes'). Even if you self-publish, a reader reading the description with this or another anomaly might question and move on.

Just my two cents.


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## Johnny Cosmo (Sep 5, 2011)

I agree with TWEvrin2 in using different titles. I even think 'lesser noble' is a bad title, because just the word 'noble' has these connotations that I doubt you'll be able to shake, and people will likely imagine them as they've been taught to by history, and existing fantasy works. 

Perhaps only the rarer mages should be nobles?


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## AnotherGeek (Sep 5, 2011)

The main reason for making them work has to do with the atmosphere of an institution. The numbers are for me and a character, the main story I am working on there is a character similar to me when I was younger but even more obsessed with the numbers. For me it is about understanding how many students is at each institution for the various sports teams, various events. Every time I start to part it out and make it work out I get outrageous numbers for the larger institutions. For example Universities have 134117 students, Academies have 67058 students, Schools have 16764 students, School Houses have 3352 students, Mage Towers have 1676 students, all of these numbers are per institution with 59 students being independent study.

Yes the number is high, and yes the many nobles do not seem like nobles however this is not the whole world just this nation. To be a mage means you are of noble blood. Only nobles can fight in wars or protect the people (hence the lowest rank being of a knight) however no noble is allowed to be idle even if they have money, they must have something that keeps them busy. Many of them become teachers or take on another task. Mages have to learn to be apart of the land/world/society as apart of an ancient tradition. Knights often serve as smiths or farmers something physically demanding while also serving as apart of an order that stems like a more traditional sense of knighthood. The 40% is very high, other countries maybe have 2%-10% mages for the country.


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## sashamerideth (Sep 5, 2011)

Maybe you are coming at this from the wrong direction. Start with one class size, of say thirty people including one teacher and two assistants. For every twenty classes you have a school, and for every five staff you have one administrator.  Build the school district like this. 

Now, how many people can a farmer feed? How many beasts of burden does he need, what is your average family size? Builders, servants, poop cleaners, chimneysweeps... it's like statistics porn with furries!


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## Johnny Cosmo (Sep 5, 2011)

If so many people had noble blood then the history of these mages obviously goes a long way back. In which case, your nation would be fundamentally different than the typical medieval society that you seem to be trying to accommodate. I imagine that the amount of mages would work to decrease the value of 'noble blood' in time, to a point where they couldn't be equated to historical nobles, or nobles of existing fantasy works. So calling them nobles would then be confusing, because as TWevrin mentioned, the titles would be meaningless. 

So why not create your own term that describes the genetic gift that makes someone a mage, rather than letting us imagine something entirely different when you use 'noble'?


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## mythique890 (Sep 6, 2011)

With respect, AnotherGeek is asking for ideas about the numbers, not for comments on the setup world/country, which seems set.  It is his(?) story, and I'm sure he can work it out.

As for that, how large do you want the largest institutions to be?  I went to a university with 30,000 students, but I know there are some that have around 90,000 students.

Keep in mind, also, at larger universities, the number of people in a class depends on the subject.  The two classes I took that EVERYONE in the school was required to have consisted of lecture sessions twice a week in an auditorium with 900-1,000 other students and lab sessions three times a week  of 20-25 students with a TA.  More specialized classes ranged anywhere from 30-200 students, depending on the subject. 

As well as following sashamerideth's advice (and keeping in mind that I am NOT a math person) could you increase your number of institutions?  If you quadrupled the number, for example, you'd have universities with an average of 33,529 students.

If that seems like a lot of schools, keep in mind that in some areas, you find large schools close together.  Here we have two schools with an average of 30,000 students that are less than five miles apart (UVU and BYU), and the towns they're in (which are so close together they run into each other) have populations of 85,000 people and 105,000 people, respectively.  The reason is that UVU draws its student population mostly from the local area, while only 31% of BYU's student population comes from its home state.

Anyway, like I said, I'm not a math person, so I don't know if this helped at all, but I think your idea sounds interesting!


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## AnotherGeek (Sep 6, 2011)

Thank you so much what you have said has helped a lot.


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## Johnny Cosmo (Sep 6, 2011)

Ah, I guess you are right. Though, the way the 'nobles' work would relate to the numbers. I suppose it doesn't really have to be that realistic for a fantasy, which is fair enough.


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## JCFarnham (Sep 6, 2011)

I just want second the idea of working your way up from the bottom in terms of the numbers. If you assume a skeleton representation of an institution, how many people do you definitely need for it to run smoothly [or roughly for that matter haha]? After that you can add on surplus students. I can't say how your demographics work exactly [in the sense of what feeling you're going for as opposed to the data] but ,aybe some of the trouble here is not taking into account the amount of people who would be expected to attend such an institution but don't, or the number of your mages who don't institutionally teach and wont take on a pupil, or drop outs? I mean I know you listed drop outs in your initial work through, but may that number needs to be re-thought, perhaps it would make class sizes more realisitic. 

I'll also agree with the idea of increasing the number of academies, etc to cope with the amount of people you need going through eduction. Have you put thought into how society supports this large number of mage students? I'm assuming since you gave a figure of 40% nobles, that the other 60% of society can support that? I'm sorry if this has already been said, I may have missed a previous mention.

I'm not 100% certain on the set up of your society so I might be talking rubbish, but I do think something can be said for building up from the bottom so to speak. maybe if you're basing this on a medieval feudal system then thought needs to be put in regarding the amount of people at each level of the hierarchy. It could help you solidify your ideas on education demographics if you know the facts about the world their going into? again sorry if you've already thought of this and you're having issues any way heh...

What I'm trying to say is you could jusitfy your 40% by saying thats how this _fantasy_ society works, and that would be enough for a reader reading through the eyes of a non-mathematically brained protagonist, but since you say your main is like you in that sense, he[?] would draw a lot of attention to any minor inconsistancies. So do be careful yeah.  Oh but don't forget that even though everything can be broken down into numbers there will always be a percentage of statistical anomalies (I took a few economics/statistics lectures in Uni, and thats what _I_ gathere at least. May not hold up in every case but its worth thinking about I reckon).


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## AnotherGeek (Sep 6, 2011)

Thank you, all.


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## Lord Darkstorm (Sep 6, 2011)

Maybe I missed it, but if you have that many mages, and the bulk of them only have one potential area of skill, then the system you are proposing doesn't make sense.  Now if a mage isn't trained they die...that would make some sense, but if not, then the schools would be more likely for those with two or more magics, and the top being for those most talented.

A local tutor would be a more productive system for most fantasy worlds, since there is so many magic users, the chances of a single use magic usere being taught in the town they are in by a local mage would be simplistic.  The local mages would do it as part of their duty, and they would instill this into those they teach.  Those more gifted get sent to the higher schools as they find them.  

Your system seems like it is trying to imitate a modern system, which it can, but for a fantasy setting it is less likely, and will require more work to make it seem plausible.  I don't think you would have a problem doing it that way, but as you have already discovered, you have some flaws in your numbers, and maybe a change or two in the system might fix the problem.  

I just think a complex form of schools that only teach magic would be more localized than centralized in a non industrial environment.  Just my thoughts.


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## Ravana (Sep 8, 2011)

40% of a society involved in _anything_ other than food production--actually, involved in everything other than food production _combined_--in a pre-industrial setting would be vanishingly rare... I'd go so far as to say flat-out impossible without some fundamental changes in the structure of the setting: the normal proportion in Medieval Western Europe was closer to 90% in food production. But, of course, that's what fantasy is _for_, so....

Assumption 1A: either the majority of your mages have other occupations and just happen to be able to use magic (and note that historically "noble" and "occupation" tended to be contradictory, though you make it clear here that "noble" doesn't mean anything more than "magic-capable"), or else magic itself can be and often is used to aid food production, or both. Alternate assumption 1B: crop yields for plants in your world are at least twice what they are in ours. Alternate assumption 1C: this land imports a _lot_ of food... which in turn requires something they can profitably export. (Say, trained mages?) Any of those, or a combination thereof, can take care of that objection. Before moving on, though, there are other issues....

Your "landlocked country" has about the same population as Charlemagne's empire at its greatest expansion--which, geographically, included nearly all of present-day France, a portion of Spain, the northern half of Italy, most of Austria, pieces of the Balkans, the entirety of the Netherlands, Belgium, Luxembourg, and Switzerland (and Andorra, Liechtenstein, and Monaco, if anyone's counting), and the majority of Germany (essentially, nearly all of what was West Germany). In other words, your population is bloody _huge_. Not saying you can't have it that way, just that you might want to take that into consideration.

Also, your percentage of student-age population may be somewhat high. 20% of your population is between the ages of 9/10 and 16/17... and assuming the total population remains constant, roughly another 26% is younger than this (0.2 / 7 = .028, x 9 years before becoming a student = .257). That leaves just 54% of your population as adults; divide that by the same 2.8% that represents one year's worth of the younger population, and the average age of death for your mages comes out to be just over 36 years old. (In reality, each year of age would represent a slightly smaller percentage of the population, as accident, disease and violence took their toll... but the average itself doesn't change.)

Now to the question you did ask. First, I'll need to ask you a few, though--I don't need the answers, but you probably do, for your own purposes. (1) I don't see you mention anywhere is whether or not a student needs to learn from a teacher who knows the correct element--I'd assume yes, but maybe not. Which leads to (2): do students pick their elements, however many they can learn, or are these something innate? (You do mention them "picking" at one point.) If the elements are innate, then no, you'll probably never get a good "system" worked out, as every institution will require as many as six teachers to handle their student body. (A slightly gentler alternative would be to have students shipped off to boarding schools where the correct teacher is available... which could be a logistic nightmare, though not necessarily an insuperable one.) (3) Do they learn one element at a time, or progress simultaneously in all of the ones they can manage? If it's one at a time, that will make things a bit easier: "primary" schools could teach only one or two elements (again perhaps reshuffling students to get the right ones to the right teachers); as students progressed, they'd go to institutions with broader curricula and more talented teachers. (4) Do the teachers need to be as adept as the students? That is, does it take a trine to teach a trine, or can a trine learn from three point mages? (5) How many students can one teacher handle at a time? (5A: How intensive is the instruction? Can multiple faculty members pass students around from class to class in a day... and if so, is this normal? At what levels?)

Now for the good news: your numbers per institution are, as far as I can determine, way off. I mean _way_ off. First of all, you name five different types of institution, but only have seven years of education: do universities really teach all seven years? If not, then consider:

You have 163,000 students enrolled in each year's class (a bit more at the lower end, a bit less at the higher: I just divided the total by 7 years of instruction, rather than figure out separate classes for pre- and post-clergy departure). According to what you give, that means that you have nearly an entire year's worth of students attending a single "university." (One that is three times the size of the entire city of Paris in the Middle Ages, by the way. And that's just the student body: it doesn't include all the people involved in their education. The support staff alone must be staggering.) In one way, it doesn't actually matter: the size of any given educational institution is whatever you want it to be... you just end up with a lot _more_ institutions. Though a proliferation of institutions can come with its own problems. 

Assuming an average of 1 teacher per 20 students, that means you'll need 57,050 teachers total... a bit less than 1.2% of your total population. That's not high, in modern terms at least: the U.S. has roughly 5.8% of its total population involved in education (though that's all levels and types, including training personnel, library employees, and administration). In all likelihood, I'd expect magic to be no easier to learn than any other subject, so that's probably too low: even if only half the U.S.'s "education" workforce is teachers, that would still give more than twice as many--2.9%. That is, of course, for an industrialized nation with a vast infrastructure; conditions in your setting may make even this number unrealistically low, unless there are good ways to concentrate students at the point of education. Which in turn can lead to other problems--the two most obvious being who pays for all this, and how do they get fed? Housing, by comparison, is a distant third: if you can't deliver the food to the people who need it, they aren't going to stick around long enough to worry about crowded conditions. Though you aren't out of the woods even then, as there is cleaning, laundry, medical care, administration, and a whole host of other items to work through before you ever reach items like the number of sports coaches. Oh, and it might be nice if the students learn things other than magic, too... though all that might mean is that a given teacher doesn't teach magic all day long, but is also responsible for some other subjects as well.

Anyway: I'm not sure how much of that's an "answer," and how much is things to take into consideration. But the simplest solution would be to re-evaluate your population and percentages in a more "realistic" light, and then see what you come up with. As others have mentioned, if you aren't worrying about reality in other areas, you're probably applying real-world concepts to a situation they don't--possibly can't--actually be applied to.


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## sashamerideth (Sep 8, 2011)

Ravana, maybe they exist on a diet of potatoes. Potatoes changed the world. If medieval society had embraced the potato, well, imagine the military campaign they could mount using potatoes as their foodstuff.  

They could abolish hunger as long as the Blight doesn't get the crops. Hell, even electricity


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## Lord Darkstorm (Sep 8, 2011)

And potatoes with a bit of hard liquor and a decent tube becomes a weapon.


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## AnotherGeek (Sep 8, 2011)

Thank you all for all of your help and advice I have made the numbers work out perfectly for me now.


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## Ravana (Sep 9, 2011)

Quite welcome. 

The problem with using potatos and hard liquor for a weapon is that you need to know when to stop making the liquor from the potatos so that you have enough ammo left... or alternately, when to stop drinking your propellant. 

I seem to have missed the Incas taking over the planet. When did potatos "change the world"? I can think of a couple instances where they _didn't_....


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## Lord Darkstorm (Sep 9, 2011)

> The problem with using potatos and hard liquor for a weapon is that you need to know when to stop making the liquor from the potatos so that you have enough ammo left... or alternately, when to stop drinking your propellant.



Good points, but if you make enough liquor from potatoes, and spend more time drinking than fighting, then you might not even notice you ran out of ammo for the weapons?  Still, the thought does produce some comical images in my mind.


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