The point I was trying to make is that, yes, the 1220 population does not really "anchor" the 1020 population by itself. But the combination of the 1220 population and of the 8th century population does provide a stronger anchor, or forces one to justify a truly explosive growth in the early centuries and a very sluggish one in the late ones.
See, but explosive early growth is exactly the model that I get out of the early "Join or Die" wars, and this quote:
On a personal level, I have a hard time seeing 50 magi 'dominating' a continent's magical community.
There are two different possible models (actually many more, but two to look at now):
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(Yours) An Order that grows with a pretty steady rate of expansion from the beginning to the modern day, excluding only a drop during the Schism.
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(The one I'm adopting) An Order that experiences an explosive growth in the first century or so, from various sources: the excitement of regional wizards wanting to join a new magical society (and get access to that sweet, sweet Parma), the Join or Die mandate, legendary wizards with long lines of apprentices (Elaine, Bonisagus and Trianoma, etc), the Ordo Ex Miscellanea joining... and then slows drastically in its rate of expansion.
I don't THINK there's anything in the books that suggests that one or the other is 'canonical'. So it comes down to preference, and things can be justified however you please.
Not really - at least, not after two centuries or so! Try to do the math assuming a magus is lost to death or twilight 120 years after gauntlet, with the lineage of Unus taking a single apprentice exactly 10 years post-Gauntlet, and the lineage of Gemina taking a first apprentice exactly 80 years post-gauntlet and a second one 100 years post-Gauntlet. Assume we start in 800, and record the number of magi in each lineage:
800: Unus 1 - Gemina 1 (the founders of the two lineages are gauntleted)
825: Unus 2 - Gemina 1
850: Unus 3 - Gemina 1
875: Unus 4 - Gemina 1
895: Unus 4 - Gemina 2
900: Unus 5 - Gemina 2
915: Unus 5 - Gemina 3
920: Unus 4 - Gemina 2 (the founder of the two lineages die or are otherwise lost)
925: Unus 5 - Gemina 2
945: Unus 4 - Gemina 2
950: Unus 5 - Gemina 2
970: Unus 4 - Gemina 2
975: Unus 5 - Gemina 2
990: Unus 5 - Gemina 3
995: Unus 4 - Gemina 3
1000: Unus 5 - Gemina 3
1010: Unus 5 - Gemina 5
1015: Unus 5 - Gemina 4
1020: Unus 4 - Gemina 4
1025: Unus 5 - Gemina 4
1030: Unus 5 - Gemina 5
1035: Unus 5 - Gemina 4
1045: Unus 4 - Gemina 4
1050: Unus 5 - Gemina 4
1070: Unus 4 - Gemina 4
1075: Unus 5 - Gemina 4
1085: Unus 5 - Gemina 5
1095: Unus 4 - Gemina 5
1100: Unus 5 - Gemina 5
1105: Unus 5 - Gemina 8
1110: Unus 5 - Gemina 7
1120: Unus 4 - Gemina 7
1125: Unus 5 - Gemina 10
1130: Unus 5 - Gemina 8
1145: Unus 4 - Gemina 9
1150: Unus 5 - Gemina 8
1170: Unus 4 - Gemina 8
1175: Unus 5 - Gemina 8
1180: Unus 5 - Gemina 9
1195: Unus 4 - Gemina 9
1200: Unus 5 - Gemina 13
1205: Unus 5 - Gemina 12
1220: Unus 4 - Gemina 18
Fair enough, you're taking me much more literally with the 'only one' and 'tend to 2' than I intended. I'm an antiquarian, not a statistician. 
I'll be less exact, and simply say that the 'age' at which magi take their first apprentice is another factor correlating to growth, and the right combination of numbers can yield numbers that would justify my expansion model, or another combination could justify yours.
I don't, but I guess this is were we differ 
Hmm, this would require a much longer discussion. But I think there are essentially two sources of growth: endogenous (apprentices trained by current members) and exogenous (hedge wizards joining). You seem to be positing that the endogenous growth is very slow - and that there was a big burst of exogenous growth early on. This seems unlikely to me, for two reasons.
Endogenous growth follows an exponential curve - and it's likely that the longer lifespans and safer times post Schism war should make the growth, if anything, even faster. Exponential growths usually explode or implode into nothingness - it's extremely unlikely that they remain almost constant (I'm being extremely sloppy in my phrasing here, please bear with me). Also, if endogenous growth was not a bit stronger than you posit, True Lineages would almost disappear due to bleeding into other houses (unless, again, you somehow posit that they keep their "reproduction rate" just that right differential higher)
As for exogenous growth, remember that a hedge wizard joining does need a) to be found and b) to be trained. That a dozen magi and their apprentices might induct several hundreds other wizards into the Order over the span of 40 years strains credibility, at least to me.
Assuming a population of about 25 million for Europe at around the time of Charlemagne (the only figure I could find quickly with Googlemancy, I have no solid backing for that one but it comports reasonably with what I know of other eras, that's 2,500 Gifted people in Europe, not counting non-Gifted members of Hedge traditions (of course, those people would not be eligible to join the Order.
50 could dominate that body under certain models, but not (to my mind) under the model that is the Order.
What does your vision assume was the outcome of "Join or Die"? A lot of 'Die'? And how many magi does your model posit were at the meeting in 773 which had to subdivide the order into regional Tribunals? Surely under your system it couldn't have been more than about 20?
Granted that mine carriers the implicit assumption that prior to about 800, magi were able to "Join" without a full-on 15 year apprenticeship. We each have to make assumptions but I don't think either one contradicts canon or is entirely impossible logically. That's all I'm saying.
Also, longevity charms may have increased over the length of the Order's life. This is hinted at in several supplements, and is categorical in some of earlier edition supplements. SoI in particular.
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Early on, there would be "plenty" of magi not yet in the order. Later on the probability of finding such nonaligned magi goes down dramatically as most such have already been recruited, peacefully or not, or are dead.
Explosive growth early and sluggish later is what i would consider what can be expected really.
Only if the supply of apprentices are unlimited.
A hedge wizard doesnt need to be trained, they´re already more or less capable magi.
And what do you think is harder, finding a gifted apprentice to be or someone who is already practising magic?
Which i would say is extremely likely to be the norm. And there isnt any requirement what so ever that anyone joining MUST go through apprenticeship. I even have to say that it would be exceedingly odd for middleaged or older hedgemagi to do so. The 15 year apprenticeship is mainly for NEW magi, gifted people that so far has little or NO training at all.
Good thread, on a subject dear to me. Please see the old discussion of related stuff here:
https://forum.atlas-games.com/t/attrition-rates-for-magi/1311/1
FYI, my spreadsheet tells me that in the hermetic generation after the schism war, there are about 400 magi in the Order of Hermes.
-DC
I do too. In general I have a hard time seeing an order of Carolingian magicians spreading out and dominating the rest of Europe at a time when political unity and communications are rudimentary. But if you confine the story to the Frankish heartland plus Britain (where there Order of Hermes backstory is very well detailed and holds together) then I can easily see how a few magi with obviously superior traditions of learning could dominate. We make a mistake in projecting the continent-wide order of the cosmopolitan 13th century back before the turn of the millenium. Europe in 1220 was very different from 1020 and the Order of Hermes should also be very different in the two periods.
I do play on emphasizing the difference between the Order in 1032 and 1220 rather a lot, and in fact am taking ideas for how to do that in another thread. (I'll probably share some of my ideas collected from a read-through of the canon this weekend)
I will make one further point which I uncovered during a re-read on Fenicil's rituals last night, for everyone's consideration.
Canonically, in 1014ish, Primus Antonius of Guernicus summoned 30 senior magi of Guernicus (and the Inner Council of Magvillus) to perform the Curse of Thoth. That much is certain. From this wording, we can extrapolate with reasonable certainty that there were also "junior" magi of House Guernicus. My own thought is that the senior magi of the house can represent at MOST half of the total house, and probably a little less - but even a conservative estimate to my mind indicates that there would be at least 50 in that House.
Assuming that their proportion of the Order as a whole hasn't deviated WILDLY since then (in 1220 they represent about 9% of the Order as a whole) this supports a figure of 550 Gifted Wizards as a rough minimum in 1032, minus war casualties. You can make an argument for a lower figure too (if "senior magi" in 1014 means all non-apprentice Guernicus, for instance, then that same proportion works out to about 300 or so, the number that ezzelino supports). Once again, I'm not trying to convince anyone with the 'small Schism-era Order' conviction that they are wrong. Simply that a large-ish 1020 Order, with the large exogenous growth and slower endogenous growth that this implies, is possible without doing violence to canon.
That would seem highly unlikely, as then there would be no need to differentiate between "senior" and non-senior, as there would only be apprentices and magi.
Probably more. I doubt that the seniors of a house make up more than a third or even less.
More likely than not at least.
Fair point, I was extrapolating that minimum from the fact that in any Tribunal, about half are usually considered 'senior' enough to stand for Presiding Quaesitor. It's the only rubric I could find.
Hmm, i had not seen(or at least not recalled :mrgreen: ) that quote...
That makes even more of a mess of it, as "senior enough" might be the same as "senior" but in my guess probably isnt. Oh well...
I know that the number of magi given by the 5th edition is around 1000... (that's is one gifted by 60.000 people as there were 58 millions inhabitant in Europa in the XIIIth century)...
I would say in fact that's there should be in 1220 around 5000 to 8000 magi in the Order, so
2 century before there were around 30 million people in Europa, so there should be around 2000 to 4000 magi in the Order at that time...
So I would count twice the number of magi given for 1220...
But Merlina, aren't you conflating (to my mind incorrectly) the terms "Gifted individual" and "Hermetic Wizard"? Plenty of Gifted individuals (by my calculations based on approximations given in Canon, four out of every five, in fact) are not Hermetic wizards - be they Hedge Wizards, members of Rival Orders, possessors of untrained, self-developed Arcane abilities, or what have you.
An Order with 5,000 wizards? YMMV but that just seems far too large to me (speaking now not in terms of canon interpretation but in terms of aesthetics).
I am not confusing, when you look the number of secret societies, lieneages, etc. 1000 is very to few...
With 60 millions people in Mythic Europe.
If there are around 6000 to 10000 people who are gifted, as far as I know, at least 80% are in the Order of Hermes as they are often compulsed to enter as ex misceleana if they are talented hedge wizards.
I am not speaking about non European mages
nor I speak about the many hedge wizards which are not gifted...
So there must be between 5000 to 8000 hermetic mages
1000 to 2000 gifted european hedge wizards
around 5000 non-gifted hedge wizards
(which would give around 6000-7000 hedge wizards)
We have decided home, by facility, to considered each house being 10 times more numerous, so around 10.000 hermetic wizards... which is quite a lot, but more logical than 1000... what would give around 5 to 10 people in each group or society...
For exemple around 50 (or less) flambeau is the legion of Mithras is ridiculously low... but if you imagine 400-500 people, it starts to be a real and efficient legion...
sorry if my expressions are sometimes bad, I am frenchspeaking
Do not worry about the expressions, it was all intelligible, et votre anglais est meilleur que mon francais!
That is all a reasonable thing to say, especially as regards the matter of taste, which is subjective - but by the books it's not canonical. The books say that there are A) about 1100 Gifted wizards in the Order [totalled from the Houses of Hermes books] and B) about 10,000 unGifted to every Gifted [Ars Magica core book, pg 75]. Combining them with population estimates for the European world in 1220 (which is the fuzziest part of the whole thing) yields somewhere between 5000 and 6000 Gifted individuals at that time. There's room for some wiggling, of course - maybe the ratio of Gifted to unGifted isn't QUITE that precise, maybe the population of Mythic Europe isn't quite as big as its 'mundane' counterpart, etc. But I don't think it takes the most generous tinkering to bring you to a figure where the Order represents even half of the Gifted in Europe. (Aside: If we assume that the 1 in 10,000 figure meant 1 in 15,000, and we assume that mythic Europe has half the population of real Europe, then we arrive at such a figure. But that seems an enormous stretch to me, and it still doesn't approach your 80% figure. )
Now of course, tinkering with canonical ideas to make a setting that fits your vision is AWESOME. I do it myself with Criamon, for instance, bringing the numbers of that House way down. But by the books, the Order does represent only about 20% of the continent's Gifted population; the rest are Hedgies or 'solo magicians' or more likely just never develop their magical potential and remain 'outcasts'. By the books, too, most of these leagues and minor societies must be fairly small. (A more interesting option, it seems to me with mystery cults in particular, is that maybe they have a fair number of non-Hermetic, or maybe even some non-Gifted, members.)
ok, but what to do with the fact that the books make a mistake when saying that Europa was 30.000.000 population, when it was around 60.000.000?... it would mean that the Order of Hermes is at least the double, that is around 2000... 
But anyway, I guess that each DM is making as he feels, the most important being to enjoy playing
Where are you getting that 30,000,000 figure? I only mentioned it in my post because I was making a thought experiment. I've never seen any population estimates for Mythic Europe in any of the line, though it's possible that I've just not been reading carefully enough.
And ultimately, of course, you are absolutely right about every Storyguide just doing what he and his troupe enjoy. Nothing wrong with intense discussion of the setting as well, though.