Scotland would be even worse, with roughly half the population of Ireland at the time and arguably even more Gifted. Of course since Magi have a willingness and tendency to move from areas with higher population to areas with lower population due to easier access to more abundant resources, you have to look at the population of the area occupied by the Order as a whole.
I do agree with you that the rate of the Gift (and possibly Magi) are too low. At 1:10k you are looking at only 6k total and 200~300 born every year with the gift in all of Mystic Europe. Those births most likely suffer a higher than normal death rate because of the negative effects of the Gift, though I only used the default 25%. To maintain their current growth rate (requiring roughly 24 per year), the Order would have to find roughly 10~16% of all children born with the gift who survive their first year of life. They would have to sort through and test nearly a quarter million children a year. If this duty was spread through the entire Order, each and every Magus would have to test nearly 200 children every year. Roughly 1 in every 5 Magi would have to spend a season each year testing children.
I personally think a ratio for the Gift of 1:1k would be much more workable. That would increase the total Gifted to 60k, reduce the required "Find" rate to 1~2%, requiring a testing of 24k children per year (20 per Magus) which while still a large amount can be performed by less Magi as a duty (assigned or self appointed). If you test 10 children per day (taking into account travel time and distractions), a season of dedicated testing could check 900 children. This would require roughly two duty seasons in each Tribunal every year (more in highly populated Tribunals, one or possibly none in the low population ones).
All those numbers lead me to conclude that the Order as a whole needs both a position/duty for mass testing for the Gift and a large number of enchanted items that can test for the Gift to reduce what would be a huge drain on Magi time. Possibly assign this position/duty to Redcaps (since they are already traveling all over) and the Order as a whole is responsible for providing them with the enchanted items. Providing enchanted items to assist the search would be a fair price for one of the Gifted children to serve as an apprentice. The Order would definitely not allow price gouging for something that is so critical for its survival.
As for the total number of Magi, most of the workups seem to go with an average lifespan of 100 years post gauntlet. However multiple simulations of the Order have placed the actual average lifespan in the 150+ years post gauntlet range. Of more direct relation to this thread, some of those simulations also generate books written. The results of one I most recently looked at produced nearly 18.5k books and 6.5k translated spell lab text written by the Order in its 450 year history that were still in circulation. It did not calculate lab text for enchanted items or casting tablets.
Plus look at it from the other side- if 1 in 100,000 people are mages and mages live 150 years post gauntlet, finishing the gauntlet at age 20-25 then living to age 175 means they are living roughly 3.5 times as long as other people, meaning the rate of recruitment would need to be at 1 person in every 350,000 to maintain that ratio. The problem is that with the above listed 6 million people in the whole of Europe (not sure that is right but we'll use it for the moment) and a land area of 3.93 million square miles that put an average population density of just over 2/square mile, which means that you would need to cover 175,000 square miles to find a single apprentice, and a covenant of 6 mages would only occur once in every 350,000 square miles, assuming that is 3.5 generations of magi as the math works out. that puts the average distance between covenants somewhere between 591 and 668 miles, and they would be overlapping each other looking for apprentices. The distance from Paris to Lyons is 241 miles for comparison. Modern day France is 248,573 sq miles, which means every generation the entirety of france (Normandy and Provincal) would produce less than one magus.
That's why the numbers make no sense.
60 million, not 6 million in the year 1200. You missed that 0 in my post and it threw off all of your math.
Adjusting your numbers gives a pop density of 15.26/square mile and you would have to cover 655 square miles (at the 1:10k RAW ratio) to find 1 person with the Gift (who might be anything from a baby to an old man).
My math for new born/young Gifted was based on the long term trend of a new generation born every 20 years and you are searching for someone age 0~5, along with the 25% fatality rate for the first year of life common for the time. That works out to ~5.33 the area/population to find someone in the age range to take as an apprentice (1 in every 3,500 square miles or 71 in France of age 0~5). The entirety of France (Normandy and Provincal) would have 379.5 total "native born" people with the Gift of all ages, ignoring transplants from the Order. These numbers are based on the population density of all of Europe. I could dig up the actual population of what is now "France" at the time and give more precise numbers but they should be close enough to get the gist across.
That is once again why I suggested 1:1k as a better ratio. It would reduce the square miles per person with the Gift by a factor of 10, while increasing total individuals with the Gift (both young and old) by a factor of 10.
EDIT: My math for new generations is actually fairly simplified, since there are depending on life spans roughly 3 generations alive at a given time in that time period, with only the middle one having children but they have roughly 3.33 children per pair before infant/child mortality to maintain the population and they should be growing at a rate to reach 80 million total population in roughly 100~150 years. That works out to 111 Gifted children born every year across Mystic Europe who will make it to adulthood before you work in the required increases to take into account population growth, unforseen events, and the portion of the population that does not produce children (due to Vows, sterile, etc). Why I came up with the 150~225 which does not include the death rate for the population that makes it past infancy but dies before they turn 20 and includes the required population growth.
EDIT 2: Oh, and I did dig up the population of what is now "France". It was 12.6 million which increases the population density within it to 50+/square mile, 240 Gifted children ages 0~5 (16~24% of all people born with the Gift each year in Mystic Europe), and 1282.4 "native born" with the Gift. Normandy and Provencal are both fairly population dense for their size.
And if you are wondering where I got how many apprentices are needed to sustain the current growth rate of the Order, it is based on ~30% of the actual members as settled on both by Mark Shirley in his write up for Sub Rosa #14 and the varies simulations I have looked at if you knock the population down for the key events in the Orders history by rough percentage of the order killed at that time.
EDIT: That would require Magi to train on average one apprentice every 50 years. That might sound high, but it is an average that covers the range from prolific (1 every 20 to 25 years) to minimal (1 every 100+ years or none at all). Counting in their longer lifespan and longer "fertile" period the Order is growing at a rate 20~40% faster than the mundane population.
The first generation of the Order was also training at a rate 2~4 times higher, though many of their "apprentices" required a much shorter time because they were already skilled adult magic users. 5 years to open them to the Hermetic Arts, teach them Hermetic Magic Theory, basics of the Arts, some Hermetic Spells, Parma Magica, and enough Latin/AL to function. There was not really much of any Organization Lore: Order of Hermes or Code of Hermes at the time since it was actively being constructed and those first apprentices lived it.
The once in a generation might be the one cranking out Q14, but even that is only a combination of 6 Attribute points and 3 Minor Virtues at character creation. Q10 on the other hand is a single Attribute point in Communication and 1 Minor Virtue, which is fairly common depending on which House the Magus is part of (Bonisagus).
Then of course you have magically improved Attributes. While some like to argue they are a Cult of Heroes thing, they are in the Core book. How extensively they are used is very Saga dependent (none to all over) but they are an effect that has been in AM5 since the beginning.
I agree with everything else you said, just wanted to point out that 10+ is not all that rare in the Order. 13+ is where things start getting rare.
I donât know if my players are spoiled but they wonât âwasteâ a season in a tractatus with a quality of less than 9-10. They are still reading the best ones. No need to waste time with the lower quality ones... yet. So most apprentices (or magus) canât produce competitive tractatus. The ones that can get their work copied fast.
Consider that a 9 can be produced by anyone with a com of 3 or a com 0 and the good teacher virtue, even if most magi can't produce one they consider worth their time there will still be a very large number who can. With resonant materials and glossing this becomes even easier. A quality 7 tractatus copied onto a parchment made from basic (+1) resonant materials and then glossed by someone with a higher communication will be at quality 7 after these treatments. As I read it a tractatus can be glossed while it is being read, which means having a magus with a high com can lead to an improvement of a lot of tractatus.
The options given in Covenants will result in both a higher max and average quality (Resonant materials, Clarification, Glossing, Commentaries, Florilegia). They raise the maximum quality of a Tractatus to 17 without Clarification (which is wasteful of time and vis for its additional +1).
Glossing of text by writers with average Communications and Good Teacher will be fairly common. Those writers are good at covering a subject but just need a little editing that a large portion of Magi are capable of providing.
Commentaries on Arts would actually be very common, though not in the way found in most games (written by PCs, based on only Summa on a subject they contain). Those are often of very limited circulation value. How they would commonly be written is based on the Roots and Branches, which are text both widely spread and commonly read across the Order.
You find the same thing in Ability Tractatus, where for example any written on Theology (Christianity) have a high chance of being a Commentary on the Bible. The Bible is the Authority (oh, we don't have those in 5th? so sad) on Theology (Christianity) and everyone who is interested will have studied it. The same goes for things like Physics by Aristotle on Philosophiae and Elementa by Euclid & Ars grammatica by Donatus on Artes Liberales.
It also has the potential to generate a fair amount of lower quality Tractatus through Correspondences. However I would think that only collections made from the writing of two Magi with fairly high Communication would be worth the trouble of bounding unless you are using the Research Rules.
I don't think you could get them at all for the Arts, which require one on one instruction. I just read that again while researching for a new thread I was considering.
You might, in theory, if you had a bombastic instructor prone to pontification and a scribe sitting quietly recording the one on one instruction. Theoretically, maybe...
it certainly would not be a significant contribution to the available reference material.
Lecture notes on magic theory on the other hand is definitely possible. lecture notes on parma magica work mechanically but should result in a whole bunch of people getting marched before the notes are burned...
Parma Magica is one of those weird topics for books. Magi want them to study, but they are a very big security risk. Handle them the same as all other dangerous/secret books. Not in the general library but a secure storage location. Only copied by and access given to by Magi.
Though I often wonder at many of the publicly posted libraries that have books on it in their collections. Are they just part of the general library where even the mundanes can see them? Is there several Librarians scattered across the Order who have read those books? They would already have at least a minimal skill in Magic Theory. Is the Gift required to use Parma Magica and what happens if they actually do try using it?
The Gift is required to use Parma Magica, one thing that is often suggested but rules have not been officially created is the idea of books in code, so you need, presumable, a minimum ability of some sort to read anything meaningful from the book. Often the discussion is that such books are hidden as vulgar poetry.
A section in writing in code is just above the Bonisagi House Acclaim we are discussing in another thread. "The Cipher of Trianoma" has two versions, one decoded like a normal Magus lab shorthand and the other is an actual cipher. You could require the use of a similar cipher for for books on Parma Magica.
My group has used variations of it for things like concealing our shipping logs and a few Scripts.
However that seems to be for a code which is clearly a code, and secondly it is based on language ability alone- I'm thinking of something a bit more complicated- a bit of vulgar literature for example which also works as a tractatus or summae (a summae might have to be a collection of vulgar literature) which requires a certain ability score of a certain level in order to catch the references which make it useful as a summae or tractatus. For example if Gullivers travels were code requiring magic theory to read which was a tractatus or summae on area lore:magic realm. (yes, I know the wrong century, but it is a useful example) Of course in reality it was a political tract, as was the wizard of Oz (supporting the free silver movement) but each book also stands on its own for those who do not catch the references, because they perhaps grew up in the wrong century and know next to nothing of old political debates. A lot of allegorical works existed- mostly religiously based at the time, so I think it could be an interesting branch to expand upon...
You don't have to use Latin. Change it from Int + Latin + die roll to Int + Magic Theory + die roll. The difficulty would still be 6 + author's Com + author's Intrigue.
The younger generation today is even less likely to catch references in works, since they are used to "Instant Information" and "Think This Way" overt programing. They are less taught how to look for the meaning behind the words and tend to suffer from nearly constant information overload. I am very glad I did not grow up having to deal with things now.
Edit: I am not trying to say that kids today are stupid or blind, just that the world is very different for them then every generation before them which makes it hard for them to deal with things like catching to subtle references to a political track buried in a book. The political track in things now'a'days tends to hit you over the head with a sledge hammer, repeatedly.
Thinking on it, things that require a specific Hermetic Virtue to use make no sense to people without that Virtue when they read books about them. So you could coach a book on say Parma Magica in the mysteries access is provided by such a Virtue and those without the Virtue would not be able to make heads or tails of it. It would in effect just be a book of vulgar literature.
For example, trying to learn a Faerie Magic spell without Faerie Magic.
Perhaps there are many gifted children out there that the order never notices. There could be dozens of gently gifted people in every city just waiting to be found. Without widespread testing (or some story event) they will never be discovered. Doomed to live out their lives as mundanes.
Characters who have The Gift may start play with a single Supernatural Virtue without having to take any other virtue...
Which probably should mean that any Gentle Gifted characters, be they raised in cities or elsewhere, will not be entirely "mundane". Stories about peasant X who talks to dogs, or Lady Y who can see what the weather will be, will get out. It won't be just the Gifted who have a supernatural talent, there will likely be other NPCs who have a supernatural virtue or two, for whatever reason. So winnowing out the Gentle Gifted from the chaff of all the other supernatural occurrances (actual or imagined) will still require a little work.