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March 23 2007

Buffy universe harbors no more than 512 vampires. This is a fun little math problem.

It's a few days old, but I just found it on my RSS feed and didn't see it posted here. Vampires are proved to be a myth, according to math, and the columnist uses the math model on the Buffy universe.

But what about the thousands of slayers? Maybe that's why there are no vampires in season 8! ;)

An article about the paper was linked to last Autumn but this one has some stuff about points of equilibrium that's maybe interesting.

(and the comments at the linked blog have already mentioned our biggest objection last October i.e. not every vampire attack results in another vampire being produced so the maths is based on a faulty assumption from the start. I especially liked the one that countered the oft-trotted out anthropic principle with the rarer - but funnier - 'vampiric principle' ;)
I like the idea that the existence of vampires and the existence of a slayer are mathematically intertwined.

But what I don't like about the original vampire calculation thing is that they assume the vampires feed once a month and turn each of their victims into vampires.

Most of the mythology I'm familiar with has the vampires feeding more often, but very rarely turning anyone else into a vampire by letting them drink vampire blood and then feeding (or some varation).

So, maybe it'd be more like the average vampire turns someone every 100 years or so. If you worked it with those numbers, I bet vampires would be a mathematical possiblity. Maybe I'll run the calculations sometime if really bored and attempt to make my first Whedonesque main page post.
I'm always reminded of:
Buffy: To make you a vampire they have to suck your blood. And then you have to suck their blood. It's like a whole big sucking thing.

Celluloid Novelist, if you happen to do the calculations, just remember to ask someone else to post it for you, as we don't post our own stuff in the front page.
So, maybe it'd be more like the average vampire turns someone every 100 years or so. If you worked it with those numbers, I bet vampires would be a mathematical possiblity.

Err, yeah. Given that the original paper assumes a starting point of 1 vampire in 1600 AD we'd only have 2^4 = 16 vampires in total. Not exactly a global epidemic ;).

If you assume vampires have been around since the dawn of recorded history (say 4000 BC) then it's a different story. It'd take about 33 centuries for their number then to exceed our numbers now ! So we'd all have been wiped out by 700 BC at the latest (in reality much earlier, estimates of the world's population put it at something like 50 million in 1000 BC which the vampires would've exceeded after only 26 centuries - or by about 1400 BC).

The linked article itself seems to assume most vampires are local to the Slayer (if they were more spread out she couldn't maintain a kill rate of 2-8 per night) and if that's the case i'd argue you actually couldn't maintain a vampire population since she'd just kill 'em all inside the first week ;).
Turn two, the rest is food. - Disharmony

Now that's a whole different set of mathematics. Mmmm, Pyramid scheme. Tasty. ;-)
One of the comments on the site linked above suggests that actually counting the vampires by observation in the show might be a good idea.

If Sunnydale==Sunnyvale CA, then population = approx 130,000.

How many vampires do we see on the show present in Sunnydale at any one time? If we use a number like 13 or 26 for the sake of easy maths (what? I'm lazy...), then that would mean there is an observed population density of Vampires of somewhere between 1:10000 and 1:5000 *at a hellmouth* an area in which they are known to congregate.

World population = approx 6.5 billion => if we take the 1:10000 ratio then the world would support 650,000 vampires. Obviously if we scale that number down because away from the hellmouth there would be less vampires then we may end up with a number like 200,000 or so.

In the context of the Buffyverse, where a feeding vampire does not neccessarily kill its victim and where a feeding vampire does not neccessarily sire its victim - this starts to look like a sensible number.

If we have 200,000 immortal Vampires and it's (give or take) a stable population - then by definition, their "birth" rate must equal their deathrate. Plucking numbers out of the air... if we state that the rate of death-by-Slayer, accidental sunlight/decapitation (what? it could happen), fights with other vampires/demons etc. is about the same as the normal human death rate including natural causes (approx 10 per 1000 per annum) then there will be 2000 Vamps killed a year worldwide. This would then mean that there are 2000 Vamps sired a year worldwide. Therefore, on average, a Vampire would sire once every 100 years (200,000/2000). A bit "neat" I know but you can fiddle with any of the above variables to get a different number...
My brain hurts.
Hmm, I count 396. Then again, it could of been 'bite nite' for Dru and Darla so who am I to argue.
There could be 514- Angel and Spike don't feed off people, so their feeding habits are removed from the pool.
My brain hurts.

Which brings us to Zombies (also mentioned in the original paper). Let's just say if you're scared of being buried alive it's a really good idea to avoid a poison called tetrodotoxin. Yeesh *shudders* ...
Well, to take issue with one of the comments, vampires sired to be sent with a specific message aren't always quickly staked, and when they are there is usually at least a secondary reason for it. (For example, Theresa was staked by Xnader while she was "preoccupied." Good thign too, I mena just risen newbie had Buffy down? We're talking potentially female-Angelus territory here;if she'd both escaped and lasted the season "Becoming" would have been a hopeless fight *grin.)

The question of numbers has come up on the shows;didn't one of the bad guys once call Angel "one in a million" and Angel responded "Somewhat less than a million."

The numbers analysis is a good thing;it always bothered me in, for example, _Blacula_, trying to follow out the script's assumptions. Of course the human characters were concerned too.
This approach by Brian Thomas (pdf) is the best attempt to understand the vampire population size that I've seen. It assumes that only a proportion of human victims become vampires. It's limited to just Sunnydale, but it doesn't seem plausible to me to try to estimate a larger global "population" the way the other models have done.

Of course, I am an ecologist, so I would like this version best. ;) I also like some empiricism with my theory, so my approach would be to tag the vampires to get a better estimate of how many there really are.

(I notice this was posted here before on the main page in 2003, but its previous link is dead.)

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