My thoughts on the 31 students were kind of squished into one paragraph, but the ideas I have so far are:
(a) they were sharing that class with the Ravenclaws, and there are something like 17 Ravenclaws, so Harry is rounding up when he says there are 30 pairs of eyes on him (reasonable, since most people aren't that precise with numbers once you get over fifteen or so); or
(b) several students have left school by fifth year, either to work or because it's been overrun with monsters and murderers for four years or both, and the class contains the remaining students from all four Houses (which could be 33 or so and Harry is rounding down).
It's hard to know how to factor in passing time when we don't know how long class periods are in the first place, how many class periods they have per subject, how many are single vs. double sessions, whether it changes year to year, or any number of other factors. For example, if they have two single and one double period for a given class, of which they spend 45 minutes for the single and 90 minutes for the double session actually in class (with the remainders of the hours for passing), that adds up to 3 full hours of actual classroom time over the whole week. If it's only one single and one double class, that's only 2.25 hours total in class. But how could we know which is closer to accurate? So I picked 3 hours as a possible amount of time spent actually in class, not as the boundaries of an official class period (which would include passing time, and hopefully a lot given how long it seems to take to get around the castle). But I didn't make that clear.
They might spend more hours in class in lower years and fewer once they get to NEWT level, being presumably advanced enough to be more self-motivated with their studies by then, which would help a bit. But they might not. They don't go to each class every day, and the first-year schedules work out to give them an afternoon off once a week. But the rest is pretty hazy.
The all-Gryffindor class sounds very odd to me, unless there was some schedule weirdness that year that made it easier to cram the other three Houses together for Transfiguration and have Gryffindor by itself. I don't know what that might have been, but it's possible. Or maybe they arranged things that way specifically so McGonagall could give Gryffindors only days off homework before games. Which could allow for Umbridge teaching Slytherins separately for DADA, as you say.
Yeah, I definitely think a lot of problems go away if we assume that Remus is simply mistaken about nearly everyone going to Hogwarts. I find it a lot easier to believe one character got a factoid he's probably never particularly researched wrong than that the teachers are somehow working high-powered lawyer hours for teacher pay for decades on end. Then we can have Harry's year being 40-ish and Hogwarts total having a bit under 300 students, just as it looks, and don't have to figure out how to account for potentially dozens more invisible students in his year, or a secret second set of teachers, or all the teachers using Time-Turners constantly, or Harry's year being half the size of normal with zero notice or comment about [insert tragic war circumstances, which will surely be repeated unless Harry does exactly as Dumbledore says], or anything elaborate. (The Marauders' year could still be larger if necessary just due to normal variation--with "larger" being 60 or so.)
I do think the evidence supports the teachers being pretty tightly scheduled, mind. It makes a lot of sense of how they're never around, don't have office hours, don't notice Luna's housemates stealing her stuff, seem constantly on the verge of snapping (especially McGonagall, who is one of the most over-scheduled), and never have the energy to stop and go, "Wait, do any of these administrative decisions make sense? Is there anything we could do better?" But there's full schedules and then there's "not even magic could explain that."
The all-Gryffindor class sounds very odd to me, unless there was some schedule weirdness that year that made it easier to cram the other three Houses together for Transfiguration and have Gryffindor by itself. I don't know what that might have been, but it's possible. Or maybe they arranged things that way specifically so McGonagall could give Gryffindors only days off homework before games. Which could allow for Umbridge teaching Slytherins separately for DADA, as you say.
The thing is, I can't remember that there were ever any joint classes or students from other houses mentioned in any subjects other than Potions, Herbology and Care of Magical Creatures (at least not until after OWLS). I definitely always got the impression that those were the only shared classes until I started thinking about it and realised that there'd have to be at least thrice as many teachers to make that work anywhere in the space-time-continuum...
The whole setup is weird. Are the students from the other House(s) just really, really quiet in Charms? Do they not exist if Harry isn't looking at them? Though we can't blame Harry alone. How is it even possible for Ron not to know who Michael Corner is in fifth year? I was a pretty oblivious student in a year-cohort of 39 in high school, and I cannot fathom this. I at least knew everyone's name!
Doing the math has at least helped me narrow down what possibilities I can believe. I mean, even a Hogwarts of 300-ish students requires some suspension of disbelief, because it seems unlikely that they would never run into an irreconcilable schedule conflict, but I can handwave that much. But I just can't believe in a larger student body without a really, really good explanation--and I can't find one. I've been going around in circles for a while, wondering whether I was unfairly dismissing the idea of a larger student body and Harry's year being unusually, extremely small... but nope. I just can't buy it.
Well, Harry just being very self-absorbed and oblivious would fit - he managed to miss someone as loud and obnoxious as Cormac McLaggen in his own common room for five years...
I don't believe in a larger student body either, and I know I couldn't tell at a glance wether a crowd was 80 people or 100 or 120. I've just thought of something else that might have thrown off Harry's impression of the number of students taking the exam in the memory, namely the seating arrangement. Let's say he knows that there are usually almost 300 students in the Great Hall for meals and fitting comfortably at the house tables. Now they're sitting at separate desks, maybe spaced a bit apart from each other to prevent easy copying off neighbours, the Great Hall might look rather rather full even with less than 80 students. And with the first war somewhat brewing at the time, I imagine not many NEWT-students would have dropped DADA either, so there could be more or less two full years there. Whatever difference remains can easily be explained with normal variation.
It is very, very hard to be so oblivious that you don't know the name of a kid in your own year when there are only 40 of them. (Heck, I probably knew the names of all 140-ish of my fellow high schoolers despite being about as social as first-year Neville. And we never ate breakfast or dinner together or shared sleeping quarters!) If it were only Harry, that would be one thing--but Ron too? That's getting downright bizarre.
And I have a hard time believing Harry never noticed Cormac despite living with the guy. I could just about see Harry vaguely recognizing him as "whatshisname, that obnoxious guy from the common room I try to avoid." Would it have hurt Rowling's story to do it that way instead of presenting Cormac as this total unknown who suddenly appeared between books?
I think the only person I know who is any good at estimating crowd sizes quickly has been working as an engineer for decades and just has that kind of mindset. Most of us have never needed to develop that skill. After a certain point, it's just "lots." So yeah, when Harry talks about "a hundred" or "hundreds," I think it's reasonable to build in a margin of error--and the bigger the number, the bigger the margin. Especially when he has a reason not to be paying serious attention to numbers because he's distracted with more important things like, "Hey, that's my dad!"
Good point about the seating, too. That probably would confuse the issue.
(a) they were sharing that class with the Ravenclaws, and there are something like 17 Ravenclaws, so Harry is rounding up when he says there are 30 pairs of eyes on him (reasonable, since most people aren't that precise with numbers once you get over fifteen or so); or
(b) several students have left school by fifth year, either to work or because it's been overrun with monsters and murderers for four years or both, and the class contains the remaining students from all four Houses (which could be 33 or so and Harry is rounding down).
It's hard to know how to factor in passing time when we don't know how long class periods are in the first place, how many class periods they have per subject, how many are single vs. double sessions, whether it changes year to year, or any number of other factors. For example, if they have two single and one double period for a given class, of which they spend 45 minutes for the single and 90 minutes for the double session actually in class (with the remainders of the hours for passing), that adds up to 3 full hours of actual classroom time over the whole week. If it's only one single and one double class, that's only 2.25 hours total in class. But how could we know which is closer to accurate? So I picked 3 hours as a possible amount of time spent actually in class, not as the boundaries of an official class period (which would include passing time, and hopefully a lot given how long it seems to take to get around the castle). But I didn't make that clear.
They might spend more hours in class in lower years and fewer once they get to NEWT level, being presumably advanced enough to be more self-motivated with their studies by then, which would help a bit. But they might not. They don't go to each class every day, and the first-year schedules work out to give them an afternoon off once a week. But the rest is pretty hazy.
The all-Gryffindor class sounds very odd to me, unless there was some schedule weirdness that year that made it easier to cram the other three Houses together for Transfiguration and have Gryffindor by itself. I don't know what that might have been, but it's possible. Or maybe they arranged things that way specifically so McGonagall could give Gryffindors only days off homework before games. Which could allow for Umbridge teaching Slytherins separately for DADA, as you say.
Yeah, I definitely think a lot of problems go away if we assume that Remus is simply mistaken about nearly everyone going to Hogwarts. I find it a lot easier to believe one character got a factoid he's probably never particularly researched wrong than that the teachers are somehow working high-powered lawyer hours for teacher pay for decades on end. Then we can have Harry's year being 40-ish and Hogwarts total having a bit under 300 students, just as it looks, and don't have to figure out how to account for potentially dozens more invisible students in his year, or a secret second set of teachers, or all the teachers using Time-Turners constantly, or Harry's year being half the size of normal with zero notice or comment about [insert tragic war circumstances, which will surely be repeated unless Harry does exactly as Dumbledore says], or anything elaborate. (The Marauders' year could still be larger if necessary just due to normal variation--with "larger" being 60 or so.)
I do think the evidence supports the teachers being pretty tightly scheduled, mind. It makes a lot of sense of how they're never around, don't have office hours, don't notice Luna's housemates stealing her stuff, seem constantly on the verge of snapping (especially McGonagall, who is one of the most over-scheduled), and never have the energy to stop and go, "Wait, do any of these administrative decisions make sense? Is there anything we could do better?" But there's full schedules and then there's "not even magic could explain that."
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The all-Gryffindor class sounds very odd to me, unless there was some schedule weirdness that year that made it easier to cram the other three Houses together for Transfiguration and have Gryffindor by itself. I don't know what that might have been, but it's possible. Or maybe they arranged things that way specifically so McGonagall could give Gryffindors only days off homework before games. Which could allow for Umbridge teaching Slytherins separately for DADA, as you say.
The thing is, I can't remember that there were ever any joint classes or students from other houses mentioned in any subjects other than Potions, Herbology and Care of Magical Creatures (at least not until after OWLS). I definitely always got the impression that those were the only shared classes until I started thinking about it and realised that there'd have to be at least thrice as many teachers to make that work anywhere in the space-time-continuum...
Thanks for working out the maths :-)
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Doing the math has at least helped me narrow down what possibilities I can believe. I mean, even a Hogwarts of 300-ish students requires some suspension of disbelief, because it seems unlikely that they would never run into an irreconcilable schedule conflict, but I can handwave that much. But I just can't believe in a larger student body without a really, really good explanation--and I can't find one. I've been going around in circles for a while, wondering whether I was unfairly dismissing the idea of a larger student body and Harry's year being unusually, extremely small... but nope. I just can't buy it.
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Well, Harry just being very self-absorbed and oblivious would fit - he managed to miss someone as loud and obnoxious as Cormac McLaggen in his own common room for five years...
I don't believe in a larger student body either, and I know I couldn't tell at a glance wether a crowd was 80 people or 100 or 120.
I've just thought of something else that might have thrown off Harry's impression of the number of students taking the exam in the memory, namely the seating arrangement. Let's say he knows that there are usually almost 300 students in the Great Hall for meals and fitting comfortably at the house tables. Now they're sitting at separate desks, maybe spaced a bit apart from each other to prevent easy copying off neighbours, the Great Hall might look rather rather full even with less than 80 students. And with the first war somewhat brewing at the time, I imagine not many NEWT-students would have dropped DADA either, so there could be more or less two full years there. Whatever difference remains can easily be explained with normal variation.
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And I have a hard time believing Harry never noticed Cormac despite living with the guy. I could just about see Harry vaguely recognizing him as "whatshisname, that obnoxious guy from the common room I try to avoid." Would it have hurt Rowling's story to do it that way instead of presenting Cormac as this total unknown who suddenly appeared between books?
I think the only person I know who is any good at estimating crowd sizes quickly has been working as an engineer for decades and just has that kind of mindset. Most of us have never needed to develop that skill. After a certain point, it's just "lots." So yeah, when Harry talks about "a hundred" or "hundreds," I think it's reasonable to build in a margin of error--and the bigger the number, the bigger the margin. Especially when he has a reason not to be paying serious attention to numbers because he's distracted with more important things like, "Hey, that's my dad!"
Good point about the seating, too. That probably would confuse the issue.
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