The Rising - Chapter 3: Excerpt from 'Ghosts, Vampires and Zombies: Fiction vs Physics Reality' aka 'The Costas Report'

Anyone who has seen any of the host of vampire films is already quite familiar with how the legend goes. The vampires need 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 to in the movies and folklore, then the human race would have been wiped out quite quickly after the first vampire appeared.

Let us assume that a vampire need feed only once a month. This is certainly a highly conservative assumption given any Hollywood vampire film. Now two things happen when a vampire feeds. The human population decreases by one and the vampire population increases by one. Let us suppose that the first vampire appeared in 1600 AD. It doesn’t really matter what date we choose for the first vampire to appear; it has little bearing on our argument. We list a government website in the references [US Census] which provides an estimate of the world population for any given date. For January 1, 1600 we will accept that the global population was 536,870,911.3 In our argument, we had at the same time 1 vampire.

We will ignore the human mortality and birth rate for the time being and only concentrate on the effects of vampire feeding. On February 1st, 1600 1 human will have died and a new vampire born. This gives 2 vampires and (536, 870, 911−1) humans. The next month there are two vampires feeding and thus two humans die and two new vampires are born. This gives 4 vampires and (536, 870, 911−3) humans.

Month	Vampire Population	Human Population	Month	Vampire Population	Human Population
1	1	536870911	16	32768	536838144
2	2	536870910	17	65536	536805376
3	4	536870908	18	131072	536739840
4	8	536870904	19	262144	536608768
5	16	536870896	20	524288	536346624
6	32	536870880	21	1048576	535822336
7	64	536870848	22	2097152	534773760
8	128	536870784	23	4194304	532676608
9	256	536870656	24	8388608	528482304
10	512	536870400	25	16777216	520093696
11	1024	536869888	26	33554432	503316480
12	2048	536868864	27	67108864	469762048
13	4096	536866816	28	134217728	402653184
14	8192	536862720	29	268435456	268435456
15	16384	536854528	30	536870912	0

Table 1: Vampire and human population at the beginning of each month during a 30-month period.

Now on April 1st, 1600 there are 4 vampires feeding and thus we have 4 human deaths and 4 new vampires being born. This gives us 8 vampires and (536, 870, 911 − 7) humans. By now the reader has probably caught on to the progression. Each month the number of vampires doubles so that after n months have passed there are

2 × 2 × . . . × 2 | {z } n times = 2ⁿ

vampires. This sort of progression is known in mathematics as a geometric progression — more specifically it is a geometric progression with ratio 2, since we multiply by 2 at each step. A geometric progression increases at a tremendous rate, a fact that will become clear shortly. Now all but one of these vampires were once human so that the human population is its original population minus the number of vampires excluding the original one. So after n months have passed there are

536, 870, 911 − 2ⁿ⁺¹

humans. The vampire population increases geometrically and the human population decreases geometrically.

Table 1 lists the vampire and human population at the beginning of each month over a 30-month period. Note that by month number 30, the table lists a human population of zero. We conclude that if the first vampire appeared on January 1st of 1600 AD, humanity would have been wiped out by June of 1602, two and half years later.

All this may seem artificial since we ignored other effects on the human population. Mortality due to factors other than vampires would only make the decline in humans more rapid and therefore strengthen our conclusion. The only thing that can weaken our conclusion is the human birth rate. Note that our vampires have gone from 1 to 536,870,912 in two and a half years. To keep up, the human population would have had to increase by the same amount. The website [US Census] mentioned earlier also provides estimated birth rates for any given time. If you go to it, you will notice that the human birth rate never approaches anything near such a tremendous value. In fact in the long run, for humans to survive, our population must at least essentially double each month! This is clearly way beyond the human capacity for reproduction.

If we factor in the human birthrate into our discussion, we would find that after a few months, the human birthrate becomes a very small fraction of the number of deaths due to vampires. This means that ignoring this factor has a negligibly small impact on our conclusion. In our example, the death of humanity would be prolonged by only one month.

We conclude that vampires cannot exist, since their existence contradicts the existence of human beings. Incidentally, the logical proof that we just presented is of a type known as reductio ad absurdum, that is, reduction to the absurd. Another philosophical principle related to our argument is the truism given the elaborate title, the anthropic principle. This states that if something is necessary for human existence, then it must be true since we do exist. In the present case, the nonexistence of vampires is necessary for human existence.

Costas J. Efthimiou and Sohang Gandhi

arXiv:physics/0608059v1 [physics.soc-ph] 5 Aug 2006

http://www.arxiv.org/abs/physics/0608059v1

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