Fixing Demographics for GURPS BANESTORM

[Polydamas]

Hal, could you please answer my question from the earlier post in the other thread? Did you assume that the populations of Megalos and Caithness had to grow at the same rate, and if so, why? I have posted the same question there.

A migration of 300,000 people over a generation seems perfectly plausible to me, provided that there were enough people in Western Megalos at the time. The question, of course, is whether there were enough.

As for compounding, rather than using a labour-intensive spreadsheet, does anyone remember the standard continuous-growth equation? Everyone derives it in first-year calculus, but I can't find it at the moment.

[Anthony]

In order to have a growth rate of 2.8%, with a generation of, say, 20 years, each mother needs to have 3.5 children, plus whatever excess is needed to negate infant mortality. A fairly small improvement in medical ability will allow this.

Historically, population tended to grow to the limits of what the land could support, fairly quickly. As such, growth rates in settled areas are nearly meaningless.

[sir_pudding]

Wasn't the Banestorm still active? Are you accounting for immigrants from Earth (and Gabbrook and whatever)? Are you taking into account that some Megalosians are not human but Goblins, or Halfings?

[Anthony]

Originally Posted by Polydamas

As for compounding, rather than using a labour-intensive spreadsheet, does anyone remember the standard continuous-growth equation? Everyone derives it in first-year calculus, but I can't find it at the moment.

Compounding: population = initial population * e^(growth rate * # of years), where e is the basis of the natural logarithm.

[hal]

Originally Posted by Polydamas

Hal, could you please answer my question from the earlier post in the other thread? Did you assume that the populations of Megalos and Caithness had to grow at the same rate, and if so, why? I have posted the same question there.

A migration of 300,000 people over a generation seems perfectly plausible to me, provided that there were enough people in Western Megalos at the time. The question, of course, is whether there were enough.

As for compounding, rather than using a labour-intensive spreadsheet, does anyone remember the standard continuous-growth equation? Everyone derives it in first-year calculus, but I can't find it at the moment.

The answer is that I didn't make an assumption with intent to prove that the assumption itself was true. The idea was to use numbers themselves to illustrate that population growth as an estimate can use a low number or a high number, and the results contained in either of the assumptions have a consequence. My "GUT" feeling is that no, the growth rates will not be the same. IF magic can make that much of a difference, then the growth rates need to be high. If they are high, then a given value for a starting population will have a reasonably decent chance of being estimated. If the growth rate is low, then again, you have a reasonable chance to estimate what the end result will be.

Note - by choosing a 2% average growth rate for either of Caithness or of Megalos indicates that population will double every (roughly) 35 years. Claiming that a man can carve out any piece of land and claim it as his own and become wealthy is hogwash. Why? Prosperity requires both the resources and the people to make it happen. Much of the history of Caithness reads like a highly settled region rather than one that is not - ie, the population density for Caithness is sooooo low, that rather than bunch together for mutual protection, they are expanded out in a major way. The ONLY way to account for this is if the land between these "holdings" are so infertile that it isn't worth settling there. Using the history of the United States as far as expansion is not in my opinion, a good model for use. Historically, America not only expanded with the population it had in its early days - but also with the influx of immigrants leaving the old world in order to get a better shot in the new world. The problem here is, that the area of Megalos is insanely HUGE for the land it claims. Lets say for the sake of argument that Megalos is 8 times the size of Caithness (just for the sake of argument - I don't have a full at a glance map drawn to scale that I can scan in and determine exactly what the area is). 8 times the landmass with only 5 times the population value, means that its population density will be worse than Caithness. Historically, France reached a density somewhere around 60 to 80 people per square mile. Oddly enough? At a time when England was listed as having about 2 Million to 3 Million in population, France had about between 6 to 14 Million. Even more oddly? Caithness is about the size of 260,000 square miles. France is listed as having about 225,000 square miles at that time (give or take). Caithness is larger than France - which historically held as much as 14 million people. 16 Million for Megalos in a region that is FAR larger than France? Just doesn't make sense to me.

So to answer your question specifically - I used the same growth rate for ease of demonstration, not to imply that Caithness should have the same growth rate as Megalos. Also - without any real means of determining just how many people show up in a bane storm, one can't really say whether or not the influx of people is significant. Personally? My gut instincts are that initially, the Banestorm's arrivals were more frequent and helped to build up a decent population in what would eventually become Megalos. Later on, after the population began to increase with native born Ytarians rather than inductees from other worlds - the number of arrivals became relatively insignificant numerically speaking. 250 here, 250 there - sure, enough to become a village, then a barony, then, over a long enough period of time, a MAJOR Barony. More people spread out - but the 250 here or there end up becoming a smaller and smaller percentage of the existing population.

My gut "instinct" in this question about population growth ratings is thus:

Megalos has a higher growth rate than Caithness due to the advantages of certain magics. Magery 0 Mages will become relatively ineffective in a low mana region as compared with those in Megalos. How high should the growth rate be? That is a good question. A family that has 6 children in medieval times without magic could expect to lose on average, 3 of them before the age of 15. That avoids a "zero growth" issue where families have enough children to replace both the mother and the father when they die, but that is it. The Statistic "4.6 children per woman" is an interesting statistic, but then you have to apply it across the entire spectrum of information. Why? Think of it like a panoramic photo shot. You take a picture facing one direction, move your camera a little, take the next photo, and so on until you have three pictures total showing one LARGE view. 4.6 children per woman includes the grandmothers still living, the women who have borne children today - but doesn't include the girls who are too young to get married and bear children yet. Each "photo" snapshot you took, takes into account a full generation of time. So, if for example, you have 50,000 women living who are in child bearing ages, 50,000 x 4.6 = 230,000 people. Divide THAT number by the number of years in a generation, and that works out to roughly 11,500. Remember what I said about losing roughly 1 child in two earlier? 11,500 divided by 2 = 5750. That is about a 1.9 percent population increase for the generation of women in question. Now, if you can save even half the children who would have died due to disease, accidents, etc - instead of 1 in 2 surviving to adulthood, you now have 1.5 in 2 surviving to adulthood. Determining the growth rate from that would make it higher than 1.9% :)

Hopefully that answers your question. My purpose of raising the demographics issue is twofold:

If population growth is heavy enough to force a rapid expansion (ie, supporting the narrative history given in GURPS BANESTORM) - then the numbers given in GURPS BANESTORM need to be higher as far as population is concerned. If the population growth is supposed to be more medieval like (and thus slower), then the information implying a rapid expansion is a mis-match akin to trying to put a square peg in a round hole. Without a rapid expansion in population, why try to act as if there WERE a rapid expansion?

For what it is worth? I don't buy the low population growth rate for the Megalan Empire. Peasants in England (again I chose England as an example because that is all I have to work with!) paid up to 60% of their production to the Lords in the form of taxes, tithes (I include the Church as a type of Lord), tolls, fines, fees, tallage, etc. This level of "parasitic" taxation was not considered bad enough to force a tax rebellion (although one notable tax rebellion did occur later in history!) for nearly what, 300 years? Between the industrial revolution, the Black plague, and rising costs of living - this system would ultimately die out. The only other thing I can consider as giving credence to the "decadent and parasitic" lords stifling population growth is if they tax their farmers much like Rome did before it fell. When the farmers can't produce enough food to feed themselves, they aren't going to be able to feed others either. Starve them too much, and they will begin to experience something akin to what some say Western Civilization is facing today - zero population growth or even negative population growth. One statistic regarding zero growth population is that you need at least 2.1 children per family to keep the population stable. Anything less than this results in negative growth. Anything more of course results in a postive growth.

I'm tired, and it is past my bedtime unfortunately - and I didn't do much more work on the Orcs than to start working on the Orc Chief (for the knight versus 10 orcs challenge). I wish GURPS CHARACTER ASSISTANT had information (documentation would be nice!) on how to add advantages such as "Leader Talent" to the program. Ah well, I have Wednesday off - I should have all 10 done by then :)

[Turhan's Bey Company]

A few points, plucked from here and there.

Originally Posted by hal

1/3 population are children
1/3 population are child rearing
1/3 population are past child-rearing

I'd think a population of settlers is going to have a much lower proportion of people below child-rearing age, so your initial numbers may very well be off by a long shot.

Originally Posted by hal

So, you're telling me that Caithness has what amounts to TL 7 medical knowledge instead of TL 3 medical knowledge. You are also saying that their growth rate is a little over 9 times that of Great Britian's from 1200 AD until approximately 1500 AD. Interesting.

As already pointed out, Benin's level of generally available medical care could hardly be regarded as TL 7. And even ignoring the sad state of historical demographics, it's also worth pointing out that the years you have selected as your historical model for population growth include a rather tremendous plague in the middle.

Originally Posted by hal

Peasants in England (again I chose England as an example because that is all I have to work with!) paid up to 60% of their production to the Lords in the form of taxes, tithes (I include the Church as a type of Lord), tolls, fines, fees, tallage, etc.

Color me profoundly sceptical on that figure. While there may have been an exceptional case like this, I've never heard anything even remotely like that level of taxation anywhere in the Middle Ages. Indeed, from what I know of agricultural productivity in that era, the peasantry couldn't have survived that level of taxation, much less sustained it.

Oh, one other thing:

Originally Posted by DrTemp

(Why is everybody only referring to England when talking about the middle ages? I mean, it's not as if it was more important than many other parts of Europe then...)

For obvious linguistic reasons, English medieval history is infinitely more accessible to English-speakers than the history of other nations.

[Rupert]

Originally Posted by cccwebs

Any Magical healing would be better than TL7 medical knowledge. Assuming the amounts listed in Banestorm (2% population having minimal Magery, with possibly 1/10 of those capable of further training), a kingdom of 3 million will have at least 6000 people capable of learning healing spells which make TL7 healing look like "leeches and bloodletting" (possibly even more as the basic prerequisite in the chain for Minor Healing, which is Lend Energy only requires Magery 1 or Empathy).

"Only requires" - that's your 1/10th right there. And it's noted (Banestorm, p.24) that many move to lager centres for the opportunities there. This is good - it puts potential healers where they can stop epidemics, but it is also bad - it takes them away from the majority of the population.

Of that 1/500th that can learn healing spells, how many specialise to the point on learning Cure Disease? That's a year's full-time training. How many are bright enough to make use of the training? Remember that Cure Disese is a one-try only spell. Also, a Diagnosis roll is required to avoid a -5 penalty to the casting, and Diagnosis takes penalties for odd diseases, is limited by TL and available knowledge, and is IQ/Hard, so a decent level in it is another 6 months or more of full-time training. We're looking at the sort of training an MD has today here, and that means someone has to pay for it all - and that means treatment is likely to be limited to those with money. Everyone else gets to use the sevices of the local wise woman or miracle worker, who might have Minor Healing and Relieve Sickness, but who probably mostly relies on herbal remidies - just as they did in medieval Europe.

As for TL7 (actually TL8 if you mean modern medicine) healing - for it to be like "leeches and bloodletting" you need Cure Disease, Remove Contagion, Great Healing, and to a lesser extent the "Restore" and "Relieve" spells.

[hal]

Originally Posted by Turhan's Bey Company

I'd think a population of settlers is going to have a much lower proportion of people below child-rearing age, so your initial numbers may very well be off by a long shot.

You may be correct in that assumption. Problem is? What do you think would happen if instead of taking 1 in 6 population from across the board, you took the bulk of it from the most productive segment of society?

Originally Posted by Turhan's Bey Company

As already pointed out, Benin's level of generally available medical care could hardly be regarded as TL 7. And even ignoring the sad state of historical demographics, it's also worth pointing out that the years you have selected as your historical model for population growth include a rather tremendous plague in the middle.

Part of the problem with today's "poor" countries being compared with medieval populations stems from what I fondly refer to as "The Germ Theory". Something as simple as washing yourself before delivering a baby has profound effects on the survival rates of not only the baby, but the mother as well. Knowing that contaminated water is responsible for cholera and a host of other problems saves lives there as well. While these third world nations are not up to OUR standards of living - just the knowledge alone helps.

Originally Posted by Turhan's Bey Company

Color me profoundly sceptical on that figure. While there may have been an exceptional case like this, I've never heard anything even remotely like that level of taxation anywhere in the Middle Ages. Indeed, from what I know of agricultural productivity in that era, the peasantry couldn't have survived that level of taxation, much less sustained it.

What the peasants are left with after they toil on their 15 acres of land, does leave them enough to handle their own personal requirements. The rest get consumed by the Lord or a portion shipped off to the nearby cities/towns. I can try and dig up my notes on consumption rates required by an individual to survive for a year (or you may have it yourself). The assumptions given in the book for a 15 acre holding - two field rotation system assumed I think 1 acre of peas, maybe 2 acres of wheat, and 4 of barley. Harvest yields of 10 bushels for peas, 16 bushels for wheat, and 64 bushels of barley was meant to feed a family of 5. Remove 3 bushels of peas, 4 of wheat, and 16 of barley for seedstock and that was what was left. Some of the additional income stems from the use of cattle on what lay fallow.

All things considered? My understanding of taxation of modern day America is no where near what the medieval levels were - but that we pay more of our income in taxes than we realize.

Consumption taxes on things such as Gasoline, Cigarettes, liquor etc (governments raise their prices by adding taxes and fees against the products)

Sales taxes on items purchased (again, a consumption tax)

Property taxes
Withheld taxes for insurance, social security etc
Income taxes

When all is said and done, we're paying something in the high 30 or low 40 percentiles if I recall correctly.

[hal]

Originally Posted by Bruno

Got a question: When you ran the math backwards to get the population of Megalos, did you realize that you'd get the population *sans* the settlers?

The modern population of Megalos is by definition decended from the nonsettlers, so just running the numbers backquards, and THEN subtracting the settlers, means that if you then run the numbers forwards you get less people in Megalos than there are now - you're double dipping.

The method of backtracking a population from current numbers assumes that you are talking only about those population descendants from actual forebears.

I worried about the prospect of trying to account for immigration from one population to another (such as Europe to America for example). So what I did was add 310,000 plus the figure I got for Megalos (1.86 million or so?) and multiply the sum by the growth rate for 205 years. Then I should have realized that whether your equation is 3X + 3Y or 3*(X+Y), the answer is the same. The point where a difference is made is when the growth rate from one population grouping is different than the growth rate of the other pop grouping.

[hal]

Originally Posted by Anthony

Historically, population tended to grow to the limits of what the land could support, fairly quickly. As such, growth rates in settled areas are nearly meaningless.

Actually, what I get from the statement above is that growth rates in settled regions does give useful information. It tells you at what rate population expands onto marginal areas just to get the lower growth rates. Put another way? Water fills a bottle at a set rate. Once that bottle is full, it begins to overflow. What is the rate we need to find more bottles to handle the overflow?

It was pointed out to me that as a population grew, it settled upon more and more Marginal land. Your comment reminded me of that.