Are vampires a mathematical impossibility?

Costas Efthimiou is a professor of physics at the University of Central Florida, who apparently spends his time debunking myths and legends. Judging from his website, he’s also a fan of web aesthetics circa 1995. I’d post a screengrab, but it could never capture the untamed beauty of an animated “Under Construction” gif.

Anyway, Efthimiou has deduced the vampires are a mathematical impossibility with the following simple logic: if a vampire bit once a month, and all victims became vampires, the vampire population would increase exponentially until it wiped out the human population.

Efthimiou states that if the first vampire appeared on January 1st 1600, when the estimated human population was 536,870,911, everyone would be vampires in just “two and a half years”.

It seems pretty straightforward, after all, 1 x 229 is… heywaitjustagoddamminute: 536,870,912?! That’s just one more than Efthimiou’s absurdly precise population estimate for the year 1600. It’s almost as if he made up that population estimate to neatly fit his maths. Of course, with a reproduction rate of, ooh, let’s say 1%, the human population would have increased in that time by roughly 12.4 million, an aberration neatly tied up by Efthimiou’s requisite 30th month. Even starting with a human population of 6.75 billion, it wouldn’t take long for us all to be turned into bloodsucking nightcrawlers.

Of course, there are a lot of assumptions at play here – that vampires feed monthly, that they only attack humans, that they don’t die, that there is no immunity, that vampires are perfect hunters (humans are going to be a lot harder to find toward those end days). What I’m saying is that this is a good idea, but Efthimiou hasn’t geeked out nearly as much as he could have. After all, there’s a whole field of vector biology out there.

I’m sure we can come up with something a little more comprehensive. Your suggestions for factors to be taken into account when calculating the spread of vampires below please. Enough good comments and I’ll plot some lovely graphs and post them.

Finally, it’s worth pointing out that Efthimiou’s conjecture doesn’t rule out the possibility of vampires – just that the outbreak hasn’t happened yet. For all we know, Nosferatu might be tucking into his first victim tonight. We’ll know for sure in two and a half years…

1. #1 johnrobertarcher
February 10, 2009

some valid points ðŸ™‚
i didn’t enjoy twilight too much anyway…

2. #2 Fargo
February 10, 2009

I think that by this math we would have all died of the Spanish flu or similar. If we’re treating vampirism as a contagion in the exercise, then we’d need to establish how successful it is at infection, incubation time, whether antivirals or antibiotics are effective, if there is any percentage of the population that could recover from infection, how much environmental factors impact the effectiveness of the agent (viral or bacterial), and so on.

3. #3 Romeo Vitelli
February 10, 2009

There’s also the assumption that vampires have no natural predators to keep down their numbers. As the number of vampire victims rise, the resistance to vampire attacks also increase. As the vampire population becomes unsustainable, a natural culling occurs through the use of vampire predators who become part of the ecosystem over time(let’s call them Van Helsings for argument’s sake). The Van Helsings can’t be too successful and wipe out all the vampires because that’ll put them out of work. The vampires in turn can’t be too successful because their numbers will cause a surge in the Van Helsing population in turn (along with bad Hammer films). In an ideal scenarios, the numbers will always stay in balance.

4. #4 HP
February 10, 2009

Except that the notion that every vampire bite creates a vampire comes from movies, and only from movies. It has nothing to do with Eastern European vampire lore.

He’s debunked a Hollywood script.

Folkloric vampires are more akin to witches (the 18th c. Hapsburg Latin for vampire is magia posthuma, “witches from beyond the grave.”)

NB: I do not believe in vampires. I do, however, have an appreciation for folklore.

5. #5 Fargo
February 10, 2009

Ohh, good idea Romeo. Though I hope you smiled when calling the Hammer films bad.

February 10, 2009

Bram Stoker, in the novel Dracula, did indeed have every victim bitten turn into a vampire when they died, but one bite did not necessarily kill, so a vampire could feed from one victim for a lifetime, if properly managed. It was a spiritual, not physical contagion though. If the vampire is killed before the victim dies, no matter how many times they have been bitten, the victim does not turn into a vampire. This is what sends everybody chasing Dracula back to Romania, not an altruistic desire to destroy evil, but the fact that Mina has been bitten and only killing Dracula will keep her form becoming a Vampire when she dies, whenever that is.

7. #7 foole
February 10, 2009

(Disclaimer: I know virtually nothing of vampires)

Assuming for a moment that vampires are immortal (strictly meaning incapable of death, thus infinitely comatose vampires are possible), what happens if a vampire doesn’t get a victim within a month? If the probability of getting a fresh victim is x (for a population suitably large, obviously this will decrease as the number of available fresh victims decreases), would the probability of catching a fresh victim decrease for every month that the vampire fails?

8. #8 Who Cares
February 10, 2009

Other items to take into account.

Consecrated areas are safe havens.
Sacred items (if visible) are a ward.
Detection is easy using a mirror.
Travel problems due to having to drag a coffin with native soil around at night.
Ability of a vampire to reason (Else said a vampire might be smart enough to expose it’s victims to sunlight, preferably staked so they don’t try to get away).

9. #9 Lola
February 10, 2009

Unfortunately, Dr. Nosferatu is right, but he and you both missed one important part of the equation: Dracula always went for the hotties. He would seduce them in their dreams and draw them to him for more with his hypnotic lust spells. If you take this phenotypic preference into account, what you would end up with is a bunch of sexy, sexy vampires running around–and who wouldn’t give up their soul to join that company? Humans would be throwing their necks into fangs left and right to get a piece of that, and the vamps (self-indulgent creatures) wouldn’t be able to resist feeding more than once a month. If vampires were real, everyone would be turned in way less than 2.5 years, and we would all be partaking in a hot vampire orgy right now, not surfing the web.

10. #10 Fargo
February 10, 2009

Damn Lola, when you put it that way they wouldn’t even have to hunt me. I’d sell out for heavy petting at this point in my life.

11. #11 catgirl
February 10, 2009

This argument is not new at all; I read about it as a child in a children’s encyclopedia that I had.

12. #12 Brian Clegg
February 10, 2009

Worth it for that website alone – they don’t make them like that any more (even if Dr Efthimiou does).

Everyone knows (as it’s on Buffy the Vampire Slayer, so must be true) that vampires don’t turn most of their prey into vampires, they just drink the blood. I really would expect a physics prof to do a bit more research before making a pronouncement.

Oh, and, then there’s the minor matter that vampires are fictional. He’ll be taking on orcs next.

13. #13 Lirone
February 10, 2009

What about vampires that decided to go for animal blood on ethical or dietary grounds (haemoglobin intolerance)? Would animals turn into vampires when bitten? I suspect I’ll dream of being chased by vampire sheep tonight!

I also wonderd about the impact of fast food blood bank joints, offering diluted blood full of flavourings and preservatives (hold the garlic mayo) at extra high prices?

14. #14 Paul
February 10, 2009

“Everyone knows (as it’s on Buffy the Vampire Slayer, so must be true) that vampires don’t turn most of their prey into vampires, they just drink the blood. I really would expect a physics prof to do a bit more research before making a pronouncement.”

True, I believe that in one of the very early episodes Xander asked Buffy about this and she explained that the turning process involved a “basically a lot of sucking” by both parties.

15. #15 Ian
February 10, 2009

Are you saying that Efthimiou’s work sucks? Or that he doesn’t know a bloody thing?!

16. #16 Cannonball Jones
February 10, 2009

This doesn’t prove anything other than the chilling fact that vampires are obviously impervious to mathematics. This bloodsucking menace is much more deadly than we first feared…

17. #17 Romeo Vitelli
February 10, 2009

“Ohh, good idea Romeo. Though I hope you smiled when calling the Hammer films bad.”

Bad is too good a word to describe some of the later Hammer films. I only went with Van Helsing because I didn’t know the plural of Buffy.

18. #18 Lyle
February 10, 2009

“True, I believe that in one of the very early episodes Xander asked Buffy about this and she explained that the turning process involved a “basically a lot of sucking” by both parties.”

Indeed. Vampire lore for most American interpretations means that the vampire has to first suck all but 1 drop of blood out of his chosen person to turn. Then, the vampire slits his own wrist and has the person suck the vampire to about half of the vampire’s maximum blood. Then, the next day/night they are a vampire.

19. #19 warhelmet
February 10, 2009

Eh?

Vampires represent an apex predator. Many years ago I read Paul Colinvaux’s “Why Big Fierce Animals Are Rare”. Vampires need to be understood in an ecological context.

Efthimiou’s point is more about epidemeology. It’s fun but I suspect that he hasn’t seen the BBC’s “Survivors” – now that is a prime candidate for being taken apart by someone with a grasp of numbers.

20. #20 isa kocher
February 10, 2009

1. vampires are undead [like some other kinds of protein such as viruses and prions, so they have no absolute need to feed. they can do some form of suspended animation/hibernation in times of scarcity
2. not all prey are vampirized, but many are simply fed on and discarded, like some form of snack.
3. not all vampires are equivalent or interchangeable, but on the contrary are as variable as the members of any other class. Every snowflake, every pebble, every drop of dew is unique at some level.
4. like humans, ants, Washoe, and quite possibly dolphins, vampires may keep some humans around for aesthetic reasons, uninfected, unexploited, protected, like prairie dogs or canaries, or elephants in zoos.
5. although we do know quite a bit, no one has done any kind of complete ecological study of vampires, and there are a lot of empty spaces in the picture of vampire life cycles. like what is a vampire exactly, a kind of symbiote, a kind of parasite, a kind of defect in metabolism, genetic defect in the mitochondria, a prion or virus, or some form of protist, an evolved form gene transfer like in a bacterium.
6. there are known strategies of defense, garlic, holy water, mudras and mantras and mandalas which defend against whatever it is that gives reality to vampires as as post biological entity.
7. daytime means that there will always be a given number of humans beyond the reach of vampire infection
8. vampires may actually be maintaining human populations like reindeer or American Bison in protected reserves only we haven’t the higher reasoning requisite to recognizing our relative status like any other fish in aquariums.

21. #21 Heidi Aycock
February 11, 2009

And who’s to say we aren’t all vampires anyway? Maybe we just can’t see it in ourselves because it’s become natural. Now we let the math take its course and begin understand the psychology of identity. Mmmmm. Tasty.

22. #22 Orlysmom
February 11, 2009

A couple ideas to consider: a) that vampires have capable enemies (werewolves, according to lore), and b) what effect that relationship would have on vampire population annually.

23. #23 Dunc
February 12, 2009

I can’t believe that nobody has yet cited the classic paper on this subject: Vampire Population Ecology in Buffy the Vampire Slayer by Brian Thomas of Stanford University [PDF, 189KB].

24. #24 bluefoot
February 14, 2009

Hey Dunc – you beat me to it; I was just about to cite the paper. I knew I had read it at one point, and was just digging around to find the original. ðŸ™‚

June 28, 2009

There is a illness (can’t remember the name of it) that makes you “whiter away” if you do not get fresh blood. It’s even been in some CSI episode with the woman killing people or letting her dogs do it anyway, and drinking the blood etc.

26. #26 Jonathan Vos Post
October 30, 2009

Orlysmom @22 said what I was about to, although I threw in some population biology equations. See also the science fiction novel “Forge of God” by Greg Bear, not just because me and my wife appear as characters in it, under our actual names, but he’s presumed that there are aliens who blow up life-bearing planets, but civilizations that prey on the beings that blow up life-bearing planets, and an entire galactic ecosystem.

Anthropic arguments against Vampires are a subset of such arguments.

Note that, with 3 or more species in a predator-prey interaction, chaotic trajectories exist…

27. #27 Omer Moussaffi
October 31, 2009

I think that I’m getting a very scared now.
As I recall, vampires rarely transform their victims into vampires. Most often they just kill them. So, if your average vampire creates another vampire once every few hundred victims (say, once in 400), then it follows that it should take about a thousand years (if my calculations are correct) for the entire population to become vampiric.

So, given that the evil count from Transylvania started to spread his evil only 600 years ago, we are now half way into human extinction! Why are people so worried about contrived things like global warming, when there is such a clear and present danger from the vampire onslaught?

28. #28 Christopher guerra
November 1, 2009

has anyone played the LARP or Table Top Version of Vampire the Masquerade? When Vampires were cool! Before the Emo Twilight preteens destroyed their rep.

November 1, 2009

This particular proof that “vampires are a mathematical impossibility” was featured in World Book Encyclopedia’s Childcraft series back in … well, the edition I had was from the mid eighties. It was in the Mathemagic volume, and was in fact my first introduction to the concept of a vampire.

30. #30 vampire empire
April 3, 2010

Paul, you almost got it. After they found a dead boy in a locker, Buffy was explaining the whole sucking thing to Giles in the Library and Xander was eavesdropping behind a bookcase.

I’m with Romeo on this one. The vampire hunters would bring balance.

31. #31 DesertHedgehog
April 8, 2010

Four words: Alyson Hannigan Vampire Willow.

All the reason we need to totally ignore this guy.

32. This is something extra in itself…

The estimate 536,870,912 seems quite too accurate and “manufactured” in my view. I have been encouraging my pupils to explore mathematics science fair projects however this takes the cake for me..LOL. Although, one could probably argue that judging by the way some people have their steak extremely rare that there indeed exists a large number of undercover vampires that conceal their dark secrets under the guise of a nice night out at the local steakhouse…

33. This is something extra in itself…

The estimate 536,870,912 seems quite too accurate and “manufactured” in my view. I have been encouraging my pupils to explore mathematics science fair projects however this takes the cake for me..LOL. Although, one could probably argue that judging by the way some people have their steak extremely rare that there indeed exists a large number of undercover vampires that conceal their dark secrets under the guise of a nice night out at the local steakhouse…