Another Note on Wands... · 5:16am Mar 26th, 2020
CAUTION: Extreme Math Ahead!
Now, about a week ago, I did a bunch of calculations pertaining to Ollivander's shop and the wands in it- and posted them on a blog post that you may have seen. However, On the Implications of Parallel Worlds hasn't gotten anywhere since then in the writing department, and so is on track to miss another scheduled chapter. One of the problems is that 2.4 million wands, enough to last him about 190 years of full-blown Equestrian attendance if he stopped making wands at all, is just too many.
Plus, the production rate I assigned him and his ancestors last week- at avg. 3 per day- was a bit... generous.
- Salesfloor capacity: 36,864
- Upstairs capacity (like salesfloor): 61,440
- Upstairs capacity (compact storage): 675,840
- Upstairs capacity (compact storage, expanded room): 3,041,280
- Years worth of potential backstock: 2402
That's actually all the calculated numbers that we should need from last week.
This week, I'm going to assume the same average annual demand of a hundred wands per year. And I'm going to assume he's got backstock from umpteen bazillion years ago, as well, because magic can- when used correctly- be an amazing preservative.
The big change I'll make is production rate. Assume he and his ancestors only made wands on weekdays- so, 260 days out of each year. Assume that a wand was completed only every other day, for an average production of 0.5 wands/day, we get 130 wands produced per year. Subtract the hundred wand per year demand, it's only 30 wands backstock increase per year. This is slow enough to be unnoticeable... And you'll notice something: 30 is a lot less than the 1,000 backstock increase I came up with last month. Besides, two days of work per wand means a lot more care goes into them, making them much better wands, worthy of his reputation.
30 wands per year, multiplied by 2402 years of backstock, makes hardly 72,060 wands of total stock... he'd run out after hardly five years.
Unfortunately, that's a little too few. Say... a wand was finished two out of every three workdays- 0.666 repeating wands/day, 173.333 wands/year. Minus a hundred, times 2402, 176,147 wands of stock... make it 14 years.
Perhaps that's a few too many... Three wands a week, so three out of every five days. 52 weeks in a year, so 3*52=156; 56*2402=134,512... 10 years. Sure, I can give him that- I don't want him to run too low, as he may start running out of wands to suit any given customer.
Looking at the numbers from last week, there's a small problem: Either salesfloor and upstairs are overflowed with full-size boxes, or they're not, thanks to compressed storage, and there's a ton of space. The latter case is also true if the upstairs is expanded without compressed storage.
So the question comes... If Ollivander were to put a wand in a paper or fabric sleeve and stack it on top of other wands, would it stack neatly? Chances are, the answer is no. So, if he stores them in a 2' by 3" square box on the sales floor, but a 2' by 2" square box in his backstock upstairs...
Salesfloor capacity remains the same, at 36,864 wands.
Upstairs capacity, however, is different. It contains the same shelves, making it 20 units deep by 4 aisles, each aisle being two shelving units wide- make it 160 shelving units, or 1280 shelves. Assume these smaller wand boxes are stacked 5 high... and placed 24 across on each shelf. 1280*24*5 is a lot more than 60k, at 153,600 for upstairs. Combine that with the sales floor, and he has space for 190,464 wands- which will be, overall, 70% full.
I like this.
Final numbers:
Salesfloor: 36,864 wands.
Upstairs (space): 153,600 wands.
Upstairs (wands): 97,648 wands
Total wands: 134,512 wands
Years of pony-attendant drift (if he stops making wands): 10.2
Years of pony-attendant service (if he continues making wands): 10.4
Thus, he's going to run out sometime... but it's far enough ahead I won't need to worry about that, and he'll have plenty of time to train up (multiple) successors to his wand production line, reclaim a positive backstock rate, and expand his business.
Well, that was fun. I might actually get somewhere with OtIoPW this week...
To be fair, I'd give him the 14 years of backstock due to population growth over time. If there are only 100 british wizards/year in 1991 (2021), then there were likely substantially fewer during the 1000-1100 period (the first full century of Hogwarts, which was established in 990 AD) and as such a much larger backstock from this era.
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Though, just because Hogwarts didn't exist doesn't mean they wouldn't still need wands...
And you have a good point, population growth. Then again, there's also population shrinkage, from things like the Salem Witch Trials, which no doubt happened on and off through the ages, resulting in a potentially "stable" wizarding population approximately equal to that which could stay convincingly hidden. Soo....
In the end, it really doesn't matter... it's rather pointless worldbuilding anyways, searching for a plausible number so I can decide exactly what he's going to think...
You know, until you started this discussion, I've just realized I never question this before.
If wand choose wizard, it should be true that not all wands Ollivander made would find its suitable wizards. And since he has continue to make new wands, that must mean there should be a number of wands left in store throughout the years (and possibly from his predecessors as well).
But that would mean... does the wand has expiration date or anything? I don't think it can work indefinitely. At least it should rot or the core expire or something.
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Completely mundane hair can last decades without any deliberate attempts at preservation (source: the exhumation of Salvador Dali for a paternity suit) so unicorn hair can probably last longer when it's sealed in airtight wood.
I don't know if you're following book or movie canon here, but I think you may be overestimating the number of wands Ollivander has. This article is particularly relevant: essentially, the three "supreme" cores in canon are an invention/discovery of Garrick Ollivander himself (Ollivander essentially revolutionised how wands were made and sold, with some initial resistance to his methods); his father and prior ancestors "wrestl[ed] with substandard wand core materials such as kelpie hair".
It's possible that Ollivander retains wands from earlier times, but probably not in bulk, and he would not be at all willing to sell them (he's a stickler for quality). So no wands prior to the early period of his career.
Ollivander was born prior to 1908, according to the wiki, and likely at least a few years before that. If we assume he was about 100 to 130 years old when he met Harry, that gives you up to about 100 years of backlog, give or take; time must be allowed for his schooling and his research to develop his then novel methodology. Note that this methodology requires him to make a lot of wands, to best enable a match, so that is in your favor.
That might give you enough wands for the initial wave, but no more than that really. A possible solution might be Ollivander himself training a group of suitable Equestrians in the art wand making, possibly using Equestrian materials (access to these materials would be good motivation for Ollivander). That itself might lead to a nice side plot where a good, productive exchange of resources and ideas happens.
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Yes. In my headcanon, the materials already have a very long lifespan- and the magic of the wand, coupled with proper storage, is enough to give it an indefinite lifespan. This is, of course, coupled with my headcanon for how they work, with absorbing ambient magic for utilization. They wouldn't be burned out just by self-protecting like that, so a properly stored wand could last as long as the planet, in theory.
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This is where we get into another small problem... Specifically, Ollivander is a stickler for quality. In order to make just 13,000 wands of backlog in a hundred years, he'd have to make 230 wands per year- or, about one every single workday, without fail. And, I don't see him making wands at such rate that he gets any more than an apparently 'stable' stock count once he has enough- materials are likely expensive, and it gives him more time to cultivate each wand. As such, and especially considering I don't want him to run out for a minimum of 7 years... 91,000 Equestrian wands in 106 years forces 960 wands per year, which is mighty close to the number (1100) I had for 3 wands per day, EVERY day... and would suggest a production line, rather than the care he would put into it.
So unfortunately, I'm basically forced to go Alternate Universe on him, to satisfy demand without forcing him to go OOC. Either Garrick Ollivander is the latest in a long line of wandmakers that used quality materials, or he has lived for millennia. I rather suspect I won't need to specify which in the story, so I haven't bothered deciding.
... Either that or I go The Gate's route, forget this calculation, and make him nearly run out every year, but somehow have fully restocked with full quality wands each year. Nobody seemed to question that, however illogical it might have been... But I really don't want to do that, soo...
The real question has yet to be asked.
These are wands that "want" / are looking for / "want to choose a wizard" that is more or less britain, right?
What's the chance of a wand wanting to choose a talking
horsepony?Even if you assume that a suitable substitute can be found, why not run with the plot idea that they can't get perfect matches for the Equestrians in the first year.
It helps you limit Equestrian wand magic, so it isn't overpowered. It gives a really good incentive for Olivander to train several equestrians in how to make wands, so that they can start making wands that want to choose ponies. It adds in who-knows-what sort of plot complications and twists.
And it gives a chance to compare wanded magic when you are not using a good match, something Rowling barely touched on.
Other limiting factors in wand manufacture:
(1) Acquisition of materials (Where does he get the unicorn hairs / dragon heartstrings / etc.? Where does he source the presentation boxes? How much time does this consume?).
(2) Wizards and witches will occasionally break wands or have them destroyed. Hogwarts students will not be Ollivander's only customers This will eat into backstock and also into time (for those cases where Ollivander repairs an existing wand rather than offering a replacement).
(3) Personal time (any given rate of manufacture must represent a best-case scenario and not account for vacations, personal emergencies, etc.).
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... I actually already have a pony-wand-magic-nerf plan in place, and I'm sorry to say, that's not it. It's more intrinsic... so, harder to get around.
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(1) Yes, one of the reasons three wands per day seemed ridiculous. It's plausible he'd be able to acquire enough materials for a couple hundred wands per year, but not thousands.
(2) The exact reason why the 'wizard demand' is estimated at 100/yr, 250% of Hogwarts new students. This allows for each wizard to go through 2 1/2 wands (average) through their lifetime. I still don't know why Ron had Charlie's old wand... I mean, Wand chooses the Wizard, and if Ron got Charlie's old wand, that must mean Charlie got a new wand. And there's always wizards like Harry, who only ever go through one wand in their lifetime.
(3) One of the things that a 3/wk rate offers: Assuming it takes one uninterrupted day to make each wand, he's got 104 "work" days per year to slack off or sell wands... Notice how that rather closely coincides with the estimated British annual demand (No, that was not intentional). If nothing else, we can expect his annual production rate to fall at least a little with how many ponies are shopping, and the time it will take to serve them... And of course, the vacation he will undoubtedly take afterwards, to celebrate/recuperate.
On the topic of wand materials, yes, Equestrian materials- such as pony tail hairs/feathers, postmortem-donated unicorn horn cores, Equestrian phoenix feathers, Equestrian dragon heartstrings (also a postmortem donation), and so on, will be perfectly viable and potentially "superior" core materials as well, albeit new to Ollivander. Equestrian woods, the same. Once ponies know about that, you can bet they'll start making donations... and selling him wand boxes & woods from Equestria en masse, because they can- and once he gets a good supply chain beyond that which he can exhaust himself, you can bet he'll be hiring and training assistants, who may (or may not) be Equestrian. As for his store... with the influx of Equestrian customers, he'll be making *many* thousands of galleons (est. 88,000 galleons per year), based on the very canon price of 7g/wand... Considering a galleon is worth approximately $100USD (in my story at least; canon value varies quite a bit), that makes out to $8.8 million annually... not far from a lottery jackpot. He would no doubt buy/build a bigger building that's better suited to having assistants.
... That would be how, in the long term (including after this story ends), new British and Equestrian children going to Hogwarts would all be able to get wands. And yes, going to Hogwarts- which itself, after seven years (at least) of ridiculously massive attendance, will have gone through some extensive upgrades, acquired a larger staff, and so on.
Something else you'd better take into account.
The ministry of magic is incredible conservative. They are clearly the "just us" justice types.
Can you imagine how they will react to ponies? Even if they are reasonably "ok, sort-of ... maybe" with unicorns and their native magic, earth ponies especially will be considered less-than-muggles (at least until they understand the natural herbology magic that they have. Even then, they might just be thought of as magical beasts, less than humans, on par with parrots or such).
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Yeah...
When they realize that those differences exist, at least. That's an Equestrian national secret, right now...
I love using math to work out interesting things like this. (You've seen my comments on The Gate estimating the mass of magical blasts!)
But I have to object to this:
Your post contained a large amount of arithmetic. I would have solved the problem with algebra. But i wouldn't call either of those "Extreme Math".
Maybe "CAUTION: Lots of Math Ahead!"?
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You'd be amazed by how many people call large amounts of simple arithmetic extreme math.
... Yes. I've gone through college, I've studied calculus. I'm a programmer, math is, like, my thing.
I put that warning up as a courtesy to those who get headaches from trying to think about too many simple math problems in too short a time (I've met multiple like that).
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I understand that. That's why I didn't object to the warning existing -- as much as I don't like that people are scared of math, I understand that they are.
I just feel like there are things far more deserving of the title "Extreme Math".
For instance, science fiction author Greg Egan rederived the laws of physics for his Orthogonal series!
But maybe it's just been too long since I've been around non-mathy people.