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amandac777I finally dealt with a longstanding problem I've had with the Wizarding world population size. DH spoiler if that's still a problem, but mostly
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fernwithy commented that with "about fifty" casualties in the final Hogwarts battle, the effect on the Wizarding world's population, which JKR once stated was "about 3000", would be extreme. Others pointed out that total casualties of the war were much higher, and that it's no doubt how JKR intended it, but that the numbers, especially for population size, do run into JKR's near-complete innumeracy. For instance, Hogwarts has about ten kids per house per year, for 280 total, but there are scattered comments about "200 Slytherins" and such. Moreover, the infrastructure suggests a much larger population.
Because I'm a geek, though, and a biologist, I've always had an additional problem with her population size -- basic ecology. She once commented that the students at Hogwarts were about a quarter purebloods, half halfbloods, and a quarter Muggleborns. That posits a very high rate of Muggleborn wizards, which is supported by the many we meet. The books also state that squibs are very, very rare, which is also supported -- we meet two, and hear vaguely about a third (the Weasley accountant). In other words, the input into this population from outside sources (the Muggle world) is much, much higher than the output to outside sources, yet despite being an ancient population, it's supposed to be incredibly tiny.
So I finally worked out a few numbers. This is a quick calculation, and as such includes several bad but necessary (for this level of analysis) assumptions. They're also the part you should skim over if you're too bored to read this all.
-- Bad assumption number one -- stable population size. Every person gets married once and has two children, or at least the average is close enough to cover this; in other words, every person replaces him or herself in the population of the next generation. Historical events play no significant role in birth or death rates or their role is balanced out. This is least logically true, but I think it could logically be replaced with the assumption that growth rates are equal among different segments of the population; the math would be harder.
-- Bad assumption number two -- no social implications to childbearing. Muggle families, wizard families, and mixed Muggle-wizard families all obey this equally.
-- Bad assumption number three -- rates of genetic 'anomalies' are constant. With stable population size, we'll go with 10 new Muggleborn students per year, every year, or one-quarter of Harry's class. For squibs, we'll go with constant 0.5% squib offspring.
-- Bad assumption number four -- except for the constant squib rate mentioned above, all children of Wizard-Muggle matches are wizards. If this weren't true, wizard-Muggle marriages would be very rare and heavily discouraged by wizards of *all* political leanings. Both squibs and Muggleborns are equally likely to occur without regard to the ancestry of the parents.
-- Bad assumption number five -- the proportion of wizards marrying Muggles is constant. For Harry's year, we've said half the kids are halfbloods. I'll be generous and assume that most of those are "halfbloods" the way Harry is, with both parents actually wizards already, but with one a Muggleborn or within a couple generations of one. The remaining handful are halfbloods like Voldemort, with one Muggle parent. For relative simplicity, I went with one-fifth of "halfbloods", or 10% of the total population, having one Muggle parent. In reverse, 10% of wizards marry Muggles. That seems high to me for such an isolated population, but it does seem to happen often in the books.
So the actual math. To pick real numbers to work with, I started again with the numbers from Harry's year, but using a cohort of a decade (this is less a bad assumption and more inexact math, because despite the way I'm typing this, I really didn't put *that* much effort into it), and a starting cohort population size of 400. However, I moved them backwards in history for perspective. Specifically, I moved our 400 wizards to 1689. Why? That's when the International Statute for Secrecy was signed, which seems to give a starting point for "modern" wizarding history. So that was 309 years before the end of the series (1998), or 12 generations of 25.75 years each. (I calculated 25 yr generations, then rounded.)
We start with 400 wizards, including 100 Muggleborns. Forty of them will marry Muggles, 360 will marry each other, for 220 total marriages. They'll have 440 kids, two of whom will be squibs. The rest will be joined in their generation by 100 more Muggleborns, for a first-generation cohort of 538 kids. Follow this for twelve generations.
Result, or 'the important part': Our 1689 population of 400 wizards born in a decade has become 3251 wizards in 1998. Roughly an eight-fold increase in population. Figure the old ages and young deaths balance out to an average life span of eighty years, and our British wizarding population went from 3200 people to just over 26,000. That's still pretty small actually. Except. Assumption number one -- constant population size. In 1700, the population of Britain was 5 million people. Our 3200 wizards were 0.064% of the population, or 1 out of every 1560 people. In 1998, our 26,000 wizards are 0.52% of the population, or 1 out of fewer than 200 people. If more wizards marry Muggles or fewer squibs are born, these numbers grow considerably.
That's a population more in line with the infrastructure we see in the books, but way too big to account for the 'everyone knows/is related to everyone' nature of the books, not to mention for one seven-year school of 1000 students, much less of 280. Moreover, given the dramatic nature of this population, that strikes me as getting unfeasible to hide, and maybe even so in the actual British population of about 60 million.
And the time frame problem. The wizarding world hardly began in 1689, which was my fairly arbitrary starting point. Hogwarts was founded "more than 1000 years ago", and Ollivander's goes back to 386 BC or so. Using the same rates and assumptions (certain of which get *very* unfeasible at this point), I ran this to 40 generations, or 1000 years. I didn't start with our 400 wizard cohort, but a 100 wizard cohort, which would also be the start point for *all* Muggleborns at the rate I'm using. In that case, by 1998, the total wizarding population would be 334,700, with each year at Hogwarts having over 4100 students. Out of our theoretically constant population of 5,000,000.
As I said, a lot of these numbers are arbitrary, and I admit they discount a whole lot of factors, but I hope the basic point comes through that a tiny population doesn't work if it's existed for a long span of time and has lots of people entering it as Muggleborns or halfbloods and comparatively few leaving it via squibdom. Oh, and huzzah for Excel and copy/paste. And oh my God did that get vastly out of hand.
On her journal,
fernwithy commented that with "about fifty" casualties in the final Hogwarts battle, the effect on the Wizarding world's population, which JKR once stated was "about 3000", would be extreme. Others pointed out that total casualties of the war were much higher, and that it's no doubt how JKR intended it, but that the numbers, especially for population size, do run into JKR's near-complete innumeracy. For instance, Hogwarts has about ten kids per house per year, for 280 total, but there are scattered comments about "200 Slytherins" and such. Moreover, the infrastructure suggests a much larger population.Because I'm a geek, though, and a biologist, I've always had an additional problem with her population size -- basic ecology. She once commented that the students at Hogwarts were about a quarter purebloods, half halfbloods, and a quarter Muggleborns. That posits a very high rate of Muggleborn wizards, which is supported by the many we meet. The books also state that squibs are very, very rare, which is also supported -- we meet two, and hear vaguely about a third (the Weasley accountant). In other words, the input into this population from outside sources (the Muggle world) is much, much higher than the output to outside sources, yet despite being an ancient population, it's supposed to be incredibly tiny.
So I finally worked out a few numbers. This is a quick calculation, and as such includes several bad but necessary (for this level of analysis) assumptions. They're also the part you should skim over if you're too bored to read this all.
-- Bad assumption number one -- stable population size. Every person gets married once and has two children, or at least the average is close enough to cover this; in other words, every person replaces him or herself in the population of the next generation. Historical events play no significant role in birth or death rates or their role is balanced out. This is least logically true, but I think it could logically be replaced with the assumption that growth rates are equal among different segments of the population; the math would be harder.
-- Bad assumption number two -- no social implications to childbearing. Muggle families, wizard families, and mixed Muggle-wizard families all obey this equally.
-- Bad assumption number three -- rates of genetic 'anomalies' are constant. With stable population size, we'll go with 10 new Muggleborn students per year, every year, or one-quarter of Harry's class. For squibs, we'll go with constant 0.5% squib offspring.
-- Bad assumption number four -- except for the constant squib rate mentioned above, all children of Wizard-Muggle matches are wizards. If this weren't true, wizard-Muggle marriages would be very rare and heavily discouraged by wizards of *all* political leanings. Both squibs and Muggleborns are equally likely to occur without regard to the ancestry of the parents.
-- Bad assumption number five -- the proportion of wizards marrying Muggles is constant. For Harry's year, we've said half the kids are halfbloods. I'll be generous and assume that most of those are "halfbloods" the way Harry is, with both parents actually wizards already, but with one a Muggleborn or within a couple generations of one. The remaining handful are halfbloods like Voldemort, with one Muggle parent. For relative simplicity, I went with one-fifth of "halfbloods", or 10% of the total population, having one Muggle parent. In reverse, 10% of wizards marry Muggles. That seems high to me for such an isolated population, but it does seem to happen often in the books.
So the actual math. To pick real numbers to work with, I started again with the numbers from Harry's year, but using a cohort of a decade (this is less a bad assumption and more inexact math, because despite the way I'm typing this, I really didn't put *that* much effort into it), and a starting cohort population size of 400. However, I moved them backwards in history for perspective. Specifically, I moved our 400 wizards to 1689. Why? That's when the International Statute for Secrecy was signed, which seems to give a starting point for "modern" wizarding history. So that was 309 years before the end of the series (1998), or 12 generations of 25.75 years each. (I calculated 25 yr generations, then rounded.)
We start with 400 wizards, including 100 Muggleborns. Forty of them will marry Muggles, 360 will marry each other, for 220 total marriages. They'll have 440 kids, two of whom will be squibs. The rest will be joined in their generation by 100 more Muggleborns, for a first-generation cohort of 538 kids. Follow this for twelve generations.
Result, or 'the important part': Our 1689 population of 400 wizards born in a decade has become 3251 wizards in 1998. Roughly an eight-fold increase in population. Figure the old ages and young deaths balance out to an average life span of eighty years, and our British wizarding population went from 3200 people to just over 26,000. That's still pretty small actually. Except. Assumption number one -- constant population size. In 1700, the population of Britain was 5 million people. Our 3200 wizards were 0.064% of the population, or 1 out of every 1560 people. In 1998, our 26,000 wizards are 0.52% of the population, or 1 out of fewer than 200 people. If more wizards marry Muggles or fewer squibs are born, these numbers grow considerably.
That's a population more in line with the infrastructure we see in the books, but way too big to account for the 'everyone knows/is related to everyone' nature of the books, not to mention for one seven-year school of 1000 students, much less of 280. Moreover, given the dramatic nature of this population, that strikes me as getting unfeasible to hide, and maybe even so in the actual British population of about 60 million.
And the time frame problem. The wizarding world hardly began in 1689, which was my fairly arbitrary starting point. Hogwarts was founded "more than 1000 years ago", and Ollivander's goes back to 386 BC or so. Using the same rates and assumptions (certain of which get *very* unfeasible at this point), I ran this to 40 generations, or 1000 years. I didn't start with our 400 wizard cohort, but a 100 wizard cohort, which would also be the start point for *all* Muggleborns at the rate I'm using. In that case, by 1998, the total wizarding population would be 334,700, with each year at Hogwarts having over 4100 students. Out of our theoretically constant population of 5,000,000.
As I said, a lot of these numbers are arbitrary, and I admit they discount a whole lot of factors, but I hope the basic point comes through that a tiny population doesn't work if it's existed for a long span of time and has lots of people entering it as Muggleborns or halfbloods and comparatively few leaving it via squibdom. Oh, and huzzah for Excel and copy/paste. And oh my God did that get vastly out of hand.
