Vampires exist!

Yes, people, they do! Or at least they might exist and their existence does not constitute any contradiction to modern science.

Well, there are plenty blood-sucking animals found in nature, and even humans need to drink the blood from their own spices sometimes just to survive. So, why cannot vampires (the creatures from the myths and legends, as we tend to think of them) exist too?

Most scientists use simple math to prove that the existence of vampires is not possible. Their line of argumentation is the following:

Assume that a vampire needs to feed only once a month (we ignore the mortality rate, since it is irrelevant here). When this process occurs, another vampire is created. If the countdown starts in 1600 AD or some other time around that (on the 1^st of January 1600 the world’s population was 536 870 911), then by February 1600 there would be two vampires (one who turned a human into vampire to start with and another one who was a human but became a vampire after the encounter with a vampire). In March 1600 there would be four vampires in existence, and in April 1600 – eight vampires. Therefore, some scientists say, each month the number of vampires doubles and after n months there are 2^n vampires which gives us a geometric progression with ratio 2.

As some of you might know, the geometric progression is increases at a very quick pace and if you sit with a pencil and paper and calculate it for our vampires example, you will arrive to the conclusion that after 30 months there would be no humans left – everyone would be turned into a vampire and the humanity would be wiped out by June 1602. Even if human birth rate is included into our calculations, it remains a very small fraction deaths caused by the vampires and would have prolonged the extinction of human race by just one month. Therefore, some scientists conclude, vampires cannot exist, since their existence contradicts the existence of human beings. This logical proof is of a type known as reductio ad absurdum, that is, reduction to the absurd.

However, if one starts digging dipper, everything is not that straightforward. Some fiction authors, Stephenie Meyer’s “Twilight series”, Charlaine Harris’s “Sookie Stockhouse (Southern Vampire) series”, “True Blood” (TV series) and Elizabeth Kostova’s “The Historian” show the world where vampires peacefully co-exist with humans.

In Stephenie Meyer’s “Twilight series” vampires can tolerate the sunlight, interact with humans (even fall in love with them) and drink animals’ blood to survive. Of course, they have to live in secrecy and pretend to be human beings. In “True Blood” TV series, however, a world is shown where vampires and humans live side-by-side and are aware of each other. Vampires can buy synthetic blood of different blood types that is sold in bottles and can be bought in every grocery store, bar or gas station. They cannot walk during daytime, so they usually come out at night. Humans also find use of vampires’ essence – vampires’ blood (called “V”) is a powerful hallucinogenic drug that is sought by humans and traded on the black market (sometimes humans capture vampires with the help of silver chains or harnesses and then kill them by draining their blood). Some humans even seek sex with vampires (vampires are stronger and faster than humans and can provide superb erotic experience). There is a possibility to turn a human being into a vampire, but it takes time and effort.

In Elizabeth Kostova’s novel “The Historian”, vampires are rare although real and do not reveal themselves to humans too often (except for the librarians whom for whom they seem to have a strange passion). Their food ratios are limited and they spend lots of time brooding in their well-hidden tombs.

Let us assume that at the time of the events described in the first book of the series, “Dead Until Dark” (2001), the world’s vampire hypothetical population was around five million (the population of the state of Louisiana in 2001 we arbitrarily use in our calculations). The initial conditions of the Harris-Meyer-Kostova model are the following: five million vampires, 6 159 million people, there are organized groups of vampire “drainers”.

Our calculations yield that the human population will be growing until 2046 when it reaches its peak of 9.6 billion people, whereupon it will be declining until 2065 until it reaches its bottom at 6.12 billion people. This process will repeat itself continuously. The vampire population will be declining until 2023 when it reaches its minimum of 289 thousand vampires, whereupon it will be growing until 2055 until it reaches its peak at 397 million vampires. This process will also repeat itself continuously and we will end up with a cyclical system of human-vampire co-existence

Under certain conditions, the Harris-Meyer-Kostova model seems plausible and allows for the existence of vampires in our world. Peaceful co-existence of two spices is a reality. However, this symbiosis is very fragile and whenever the growth rate of human population slows down, the blood thirst of vampires accelerates, or vampire drainers become too greedy, the whole system lies in ruins with just one population remaining.

There are more interesting implications to our study: consider for example the organized groups of vampire hunters (“Buffy the Vampire Slayer”) or superhero hunters (“Blade”). The results seem even more interesting and all clues lead to the one simple fact – vampires might co-habitate with humans and modern science cannot refute their existence! Please see our poster for more information and turn to us with your questions and comments!

Happy Halloween and be careful not to bump into a vampire on your way to the costume party tonight! :)

WS and EL

The Joss Whedon model and beating the disease

Looks like the disease has passed and we are back to work! Being ill actually made us think about the hypothetical situation in which vampires were real and humans would have decided to develop effective measures to fight this (vampiric) disease. What would have happened?

Well, one possible outcome was portrayed very well in a film called “Daybreakers”, a 2009 science-fiction horror directed by Spierig brothers. In the film some strange disease (a plague) has turned most of the Earth’s population into vampires. Humans lost their war on vampiric disease and became outlaws and human blood (since no substitute was found – ah, where are you, True blood? :)) became scarce (which made it a very desirable commodity – remember the paradox of value (diamonds-water paradox) from your Microeconomics class?). Vampires began to hunt humans and harvested them for blood but almost depleted the resources (we, humans, always do – whether we are turned into vampires or not, it seems). Luckily, the salvation came with one former ragged vampire who calls himself Elvis and who was able to turn himself back into human form after the car crash (we see the Hand of God here, do you?).

Have you ever wondered what would happen if humans turned against vampires as they often do against diseases and succeeded? The concept is not new. The creator of “Buffy the Vampire Slayer” (TV series), Joss Whedon (and its spin-off “Angel”), presents the most simplistic, yet the most dreadful “doomsday” scenario of vampire-human interaction (similar to Zombie infection outbreak in other fiction movies, such as “28 days later” or “Resident Evil”). The vampire bites its victim who (in a very short period of time) rises as another undead vampire and, in turn, bites another human victim, and so on. Luckily enough for humans, the world is populated by an unknown (but considerably large) number of vampire slayers (with a girl named Buffy Summers being their most remarkable representative).
Killing a vampire according to the Whedon model is relatively easy: using a wooden stake, a crucifix or a variety of other methods are pretty efficient. The model reveals how unstable the equilibrium between humans and vampires might be.
The initial conditions of the Whedon model are the following: five million vampires, 6 159 million people, there are organized groups of zealot vampire slayers (who kill vampires not just for profit but out of persuasion and in an altruistic attempt to destroy the Evil and save mankind). The model can be presented in a form of a diagram

where H denotes humans, V denotes vampires and VS denotes vampire slayers. H0 is the initial state of human population, kH denotes the exponential growth of human population, v0 is the initial state of vampire population, aHV and baHV both describe interactions between a human and a vampire (with a as the coefficient of a lethal outcome for vampire-human interaction for humans (which is higher this time) and b as the coefficient describing the rate with which humans are turned into vampires) and cV denotes the death rate for vampires (with a much more higher c).

Although the model allows for the stationary solution, the initial conditions of the problem lead to the disbalance in the system. The Whedon model is too unstable to be realistic. Vampires and humans cannot co-exist for a long period of time because human vampire slayers (e.g. famous Miss Summers) exterminate all vampires entirely. The human population recovers from the damage caused to it by vampires and continues to grow steadily.
Even though, the Whedon model’s structure theoretically allows for co-existence of humans and vampires, the laborious vampire slayers contribute to putting the system out of balance by killing all vampires. This outcome is predetermined by the initial parameters of the Whedon model (vampires constantly need to feed, cannot effectively control their blood thirst and attack humans whenever possible). A very important feature of the Whedon model is for the vampire slayers to exterminate all vampires before they do an irreversible damage to the human population and it will fail to return to its initial state and continue to grow peacefully.