User:Thedukeofnuke/UnBooks:On the Origin of Zombies

Over the years, many have theorised on how zombies came to exist. Only recently, however, have scientists even come close to discovering the origin of this terrible phenomenon. It is now known that zombies' existence is down to one terrible factor: fear.

Chapter One: the Theorem of Diminishing Vitality

Long have zombies struck fear into the hearts of those who beheld them, and it is now known that this, their greatest weapon, is responsible for their existence in the first place. The theorem concerning the origin of zombies can be summed up as such:

When a person is scared half to death, they become only half alive. If the same happens again, they become one-quarter alive, then one-eighth, then one-sixteenth, and so on indefinately. Thus, eventually, the victim will become asymptotically close to dead: this corresponds to the so-called state of undeath. As this person's vitality decreases, their scariness increases.

Chapter Two: the Mathematical Exposition of the Theorem

As explained in the previous chapter, a person can be scared half to death a number of times, each time becoming slightly closer to a moribund state, but never quite dying.

This can be expressed mathematically as an exponential decay:

Let $\lambda$ represent the level of vitality, where $0\leq \lambda \leq 1$.

Let $\phi$ represent the number of times scared.

Let $\beta$ represent the bravery of the subject, where $0\leq \beta \leq 20$.

$\lambda =\left(2-{\frac {\beta }{21}}\right)^{-\phi }$

Chapter Three: Complications

When applied, however, the theorem is more complicated than it first appears: not everyone is fully alive, many people will openly admit to being "half-dead", and some are scarier than others to start with.

The initial formula can be modified as follows to take into account the life force present at the beginning:

Let $\lambda _{0}$ represent the initial level of vitality, where $0\leq \lambda _{0}\leq 1$.

$\lambda ={\frac {\lambda _{0}}{\left(2-{\frac {\beta }{21}}\right)^{\phi }}}$.

Chapter Four: The Law of Affrightment

An extension of the theorem can explain the relationship between the level of vitality and the scariness of the zombie. Effectively, the more dead someone is, the scarier they are (although it should be noted that $s\not \propto {\frac {1}{\lambda }}$).

Let $s$ represent the scariness of the subject.

$s={\frac {{\sqrt {7}}-{\sqrt[{3}]{\left({\frac {1}{e\pi \lambda }}-{\frac {1}{e\pi }}\right)}}}{e\pi }}$

To calculate the total scariness, we must modify the formula by adding the initial scariness:

Let $s_{0}$ represent the initial scariness of the subject, where $s_{0}\geq 0$.

$s=s_{0}+{\frac {{\sqrt {7}}-{\sqrt[{3}]{\left({\frac {1}{e\pi \lambda }}-{\frac {1}{e\pi }}\right)}}}{e\pi }}$