Vampires versus Math

In an act of monster-slaying unlikely to make the movies or TV, physicists Costas J. Efthimiou and Sohang Ghandi show mathematically why vampires do not exist.

Their thesis:

Anyone who has seen John Carpenter’s Vampires, Dracula, Blade, or any other vampire film is already quite familiar with the vampire legend. The vampire needs to feed on human blood. After one has stuck his fangs into your neck and sucked you dry, you turn into a vampire yourself and carry on the blood-sucking legacy. The fact of the matter is, if vampires truly feed with even a tiny fraction of the frequency that they are depicted as doing in the movies and folklore, then humanity would have been wiped out quite quickly after the first vampire appeared.

The math is simple. Every time a vampire bites a human, the human becomes a vampire, reducing the human population by one and increasing the vampire population by one.

Let’s say there are 99 humans and 1 vampire. The vampire claims its first victim. Now there are 2 vampires and 98 humans.

The two vampires each claim a new victim. That would make 4 vampires and 96 humans. The four vampires each claim a new victim, leaving 8 vampires and 92 humans.

Because the number of vampires doubles at each step, the vampires eliminate all the original 99 humans three steps later.

What if we started with 1 vampire and 99,999 humans? It would take 18 steps to eliminate all the humans. What about 999,999 humans? Only 21 steps.

The authors provide a scenario in which the first vampire appeared in 1600, and each vampire claimed one victim a month. The world population at the time would have been vampirized in less than three years.

A few comments:

• The authors conveniently assert the year 1600’s total population (humans plus one vampire) to be a number exactly in the 2^n series (536,870,912, which is 2^29). This enables a tidy last step where 268,435,456 vampires have 268,435,456 victims.
• The authors define vampires by way of the movies. However, the authors do not model the fact that, in the movies, the humans usually fight back and vanquish the vampires. If we’re using movies as the guide, perhaps this better explains why vampires do not exist. ;)
  
• Where did that first vampire come from?

If you read the full article, the vampire section is half-way down the page, under the subheading “Vampires.”