In debates over the existence of God and man, the existence of vampires rarely enters the discussion. Whether Count Dracula and his kin exist hardly seems to be a relevant concern. But a fascinating paper by a pair of physicists makes me wonder if the existence—or rather the non-existence—of vampires can shed light on one of the popular arguments for the existence for God—the argument from fine-tuning.
In Ghosts, Vampires and Zombies: Cinema Fiction vs Physics Reality, Costas J. Efthimiou and Sohang Gandhi use math and physics to illuminate inconsistencies associated with the popular myths about ghosts, zombies, and vampires. “The fact of the matter is,” they note, “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.”
Vampires feed on human blood, which causes the victim to suffer not only from blood loss but also from the indignity of turning into a vampire themselves. Each feeding therefore decreases the human population by one and increases the vampire population by one. If only one vampire where to exist on earth it wouldn’t be long before the entire human population was decimated.
To illustrate this point, the authors of the paper show what would happen if the first vampire made his appearance in the year 1600. They note that the global population of humans at the start of that year is estimated to be 536,870,911. Using the conservative estimate that a vampire would only need to feed once a month, they are able to calculate the effect on the human race.
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 time a single vampire feds on a single human in the first month, this would create two vampires—and decrease the human population by one and thus two humans die and two new vampires are born. This gives 4 vampires and (536, 870, 911−3) humans. 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.
The result is a geometric progression with ratio 2. Since all but one of these vampires was once human, 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. As the authors note, the vampire population increases geometrically and the human population decreases geometrically.
This chart shows the vampire and human population at the beginning of each month during a 29-month period.
The authors determine 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:
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 principal 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.
It is this last principle that is particularly intriguing and makes me wonder if it can be applied to the anthropic principle. As Wikipedia explains, “In physics and cosmology, the anthropic principle states that humans should take into account the constraints that human existence imposes on the kind of theoretical universe that can support human life.” The anthropic principle is often stated in a positive way, assuming that certain conditions must be met before human life can exist. At least two dozen demandingly exact physical constants must be in place for carbon-based life to exist on earth, the slightest variation in any of these conditions—even to a minuscule degree—would have rendered the universe unfit for the existence of any kind of life, much less for humans.
But I believe Efthimiou and Gandhi’s paper provides an example of how the anthropic principle can be stated in a negative way. Vampires are a prime example of a class of objects (let’s call them V-class objects) whose non-existence is necessary for the existence of humans. In other words, if humans exist, then it is necessary that V-class objects do not exist since they would have wiped us out long ago. Let’s designate this the V-class principle.
At first glance this seems so obvious as to be unworthy of notice. Since we humans do, in fact, continue to exist, it shouldn’t be surprising that vampires (and other V-class objects) do not exist. But this raises the question of why humans exist and V-class objects do not. Their existence is, after all, as probable (or improbable) as the existence of humans. The obvious answer, of course, is that homo sapiens merely got lucking in the evolutionary process and managed to slip past the obstacles that would lead to extinction.
This is a plausible answer until we consider that to get around the anthropic principle we need to posit something similar to the mulitverse hypothesis. Returning once again to Wikipedia, we find that this theory is,
The concept of other universes has been proposed to explain why our universe seems to be fine-tuned for conscious life as we experience it. If there were a large number (possibly infinite) of different physical laws (or fundamental constants) in as many universes, some of these would have laws that were suitable for stars, planets and life to exist. The anthropic principle could then be applied to conclude that we would only consciously exist in those universes that were finely tuned for our conscious existence. Thus, while the probability might be extremely small that there is life in most of the universes, this scarcity of life-supporting universes does not imply intelligent design as the only explanation of our existence.
Although it seems to be a complex speculation designed to get around the obvious implications of the anthropic principle, this too is possible. But consider what happens when we combine the mulitverse theory, the anthropic principle, and the V-class principle.
The non-existence of any V-class objects is as statistically improbable as the aligning of dozens of independent physical constants that give rise to life. Any universe created by the multiverse generator would need to include both (a) the positive conditions necessary for life (i.e., the fine-tuned laws of nature) and (b) the negative conditions necessary for human existence (i.e., the absence of V-class objects).
The anthropic principle could therefore be restated as claiming that the existence of human life requires both (a) the alignment of several cosmological, chemical, and physical constants and (b) the non-existence of all V-class objects. The probability that each of these stochastically independent events could align precisely as they have—without any intervention—is roughly zero. The evidence therefore points to “fine-tuning” of these conditions.
If it is the case that we have reduced the chance hypothesis to a virtual impossibility, then we are left with the obvious conclusion that the fine-tuning is not apparent, but actual. The fine-tuning implies the existence of a tuner; hence we can conclude that the scientific evidence supports the conclusion that God exists. The fact that vampires don’t exist doesn’t prove that God does, of course, but it does seem to shore up the anthropic principle, making the fine-tuning inference more reasonable and probable than its alternative.
Potential Rebuttals: One argument against this conclusion is that there are vampire killers (e.g., Buffy the Vampire Slayer) who are able to keep the vampire race in check. Clive Thompson runs the numbers and concludes that the precise number of vampires that could exist in a Buffy universe is no more than 512. So the unlikely event that V-class objects like vampires could be held at a steady number would undercut my argument.
A much weaker claim is that vampires don’t necessarily have to turn their victims into vampires sine they can kill them before draining their blood. That method, however, would still decimate the human population—it would just take a few years longer.
The other line of attack would be on my claim that the existence of V-class objects is as likely as their non-existence. This is a Bayesian assumption, but I think it’s reasonable. If it could be shown that this is not definitely the case, however, it would likely prove to be an effective defeater to my argument.
February 10th, 2010 | 11:58 am
Nice post Joe. Two trivial comments:
1. The human race would increase by natural childbirth. Assuming that the population in 1600 was constant and that life expectancy was 70 years then roughly 8 million people would be born and would die every year. Vampires never seem to go after babies (at least not in the films) and statistically they would likely “infect” some people who would otherwise have died so the human population would in fact rise slightly every year. Might give humanity another month or two to survive;
2. If there were no vampires we might never have got to see Anna Paquin on TV in England which would have been a shame :-) (Sorry to lower the tone of the board!)
February 10th, 2010 | 12:00 pm
Are there any vampires in fiction and folklore that kill on feeding and transform every preyed on victim to a vampire?
I suppose there may be some forms, but many vampires take a long time to kill and may not kill many of their victims, and not all of those they do kill are vampirized thereby.
February 10th, 2010 | 1:39 pm
A vampire kills a baby in Bram Stoker’s _Dracula_, in a scene not usually dramatized in plays or movies.
February 10th, 2010 | 1:43 pm
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February 10th, 2010 | 3:15 pm
Your “V-class objects” need to be even more narrowly defined. It’s not just that their non-existence is necessary to the present existence of the human race. Instead, it’s that their non-existence within a particular time frame is necessary (which, I suppose, depends heavily on the particular object of class V under discussion). In other words, there’s nothing special about the year 1600 vs. 2010. If vampires came into existence last month, you could have a V-class object which exists while humanity also exists.
The problem with this line of argumentation towards “fine tuning” is that the contribution of any single V-class object to the probability that the existence of humanity is due to the act of a “fine tuner” is vanishingly small. The class of non-existent V-class objects is essentially infinite (or rather, finite but extremely large, limited only by our imagination and the time it takes to think them up). So even if the argument for V-class objects taken together as a class makes a meaningful contribution to shoring up the anthropic principle (which, in the abstract, I think it does), any one example of a V-class object offers only a vanishingly small contribution to that task.
February 10th, 2010 | 7:04 pm
Hi Joe,
What are these twenty independent constants? There’s a point at which these fine tuning arguments start to sound like the number of Communists in the State Department. Do you have a reference?
So now we have a multiverse where some universes are sterile, some contain vampires and some contain humans. Some contain humans briefly, then vampires. Some contain a Chicago Cubs team that has never lost a World Series. Which is the most unlikely? In which is there any warrant to use the Anthropic principle (or Vampthropic Principle) to the existence of God?
February 10th, 2010 | 8:42 pm
99%+ of all the species that have ever existed have gone extinct. Presumably they were killed off by V-class-type objects. E.g. diseases, invasive species, etc., have similar powers of increase as vampires. And then we have abiotic killers like asteroids which have occasionally inflicted massive devastation.
So, actually, V-class objects probably do exist and are pretty common (there are many now-extinct animals that would consider *humans* to be V-class objects).
However, a large number of species exist anyway. How? (1) Species often genetically adapt when challenged (e.g. disease resistance); (2) species can split, producing new species. In other words, evolution solves this particular problem, no fine-tuning necessary to deal with the V-class object problem.
February 10th, 2010 | 9:31 pm
The paper is unfortunately based on faulty vampirology. Vampires do not create vampires at every feeding: it requires unholy communion, that is, reciprocation of blood, or burial with mutilated rites (but the latter only works with excommunicated apostates); further, they don’t kill every time they feed, either — Bram Stoker milks this fact for all it’s worth, and no doubt there would reach a point at which the vampires would begin to realize that food is getting scarced and start cultivating herds of humans. Moreover, vampires clearly sometimes end up stuck in Romanian and Moldavian castles for several centuries at a time, which complicates the process of draining the entire human race dry.
Ted is right that we can’t properly assess V-class objects without taking time into account.
February 10th, 2010 | 11:13 pm
Given an infinite number of universes, it seems that some of them (in fact, I think an infinite number of them) will contain humans but no vampires.
February 11th, 2010 | 12:09 am
Ted Carnahan Your “V-class objects” need to be even more narrowly defined. It’s not just that their non-existence is necessary to the present existence of the human race. Instead, it’s that their non-existence within a particular time frame is necessary
Good point. We could adjust the V-class principle thusly:
The addition, however, weakens the argument—though I think in a trivial way. It could be claimed that V-class objects do exist or will exist in the future and we are suffering from observer bias (we’re alive and observing our existence in a timeframe in which the V-class objects haven’t completed their task).
This is similar to the observer bias rebuttal to the anthropic principle, so how you feel about its effectiveness probably depends on how you feel about it when applied there.
David vun Kannon What are these twenty independent constants?
Here is a list (of 34) borrowed from astrophysicist Hugh Ross:
1. strong nuclear force constant
if larger: no hydrogen would form; atomic nuclei for most life-essential elements would be unstable; thus, no life chemistry
if smaller: no elements heavier than hydrogen would form: again, no life chemistry
2. weak nuclear force constant
if larger: too much hydrogen would convert to helium in big bang; hence, stars would convert too much matter into heavy elements making life chemistry impossible
if smaller: too little helium would be produced from big bang; hence, stars would convert too little matter into heavy elements making life chemistry impossible
3. gravitational force constant
if larger: stars would be too hot and would burn too rapidly and too unevenly for life chemistry
if smaller: stars would be too cool to ignite nuclear fusion; thus, many of the elements needed for life chemistry would never form
4. electromagnetic force constant
if greater: chemical bonding would be disrupted; elements more massive than boron would be unstable to fission
if lesser: chemical bonding would be insufficient for life chemistry
5. ratio of electromagnetic force constant to gravitational force constant
if larger: all stars would be at least 40% more massive than the sun; hence, stellar burning would be too brief and too uneven for life support
if smaller: all stars would be at least 20% less massive than the sun, thus incapable of producing heavy elements
6. ratio of electron to proton mass
if larger: chemical bonding would be insufficient for life chemistry
if smaller: same as above
7. ratio of number of protons to number of electrons
if larger: electromagnetism would dominate gravity, preventing galaxy, star, and planet formation
if smaller: same as above
8. expansion rate of the universe
if larger: no galaxies would form
if smaller: universe would collapse, even before stars formed
9. entropy level of the universe
if larger: stars would not form within proto-galaxies
if smaller: no proto-galaxies would form
10. mass density of the universe
if larger: overabundance of deuterium from big bang would cause stars to burn rapidly, too rapidly for life to form
if smaller: insufficient helium from big bang would result in a shortage of heavy elements
11. velocity of light
if faster: stars would be too luminous for life support if slower: stars would be insufficiently luminous for life support
12. age of the universe
if older: no solar-type stars in a stable burning phase would exist in the right (for life) part of the galaxy
if younger: solar-type stars in a stable burning phase would not yet have formed
13. initial uniformity of radiation
if more uniform: stars, star clusters, and galaxies would not have formed
if less uniform: universe by now would be mostly black holes and empty space
14. average distance between galaxies
if larger: star formation late enough in the history of the universe would be hampered by lack of material
if smaller: gravitational tug-of-wars would destabilize the sun’s orbit
15. density of galaxy cluster
if denser: galaxy collisions and mergers would disrupt the sun’s orbit
if less dense: star formation late enough in the history of the universe would be hampered by lack of material
16. average distance between stars
if larger: heavy element density would be too sparse for rocky planets to form
if smaller: planetary orbits would be too unstable for life
17. fine structure constant (describing the fine-structure splitting of spectral lines) if larger: all stars would be at least 30% less massive than the sun
if larger than 0.06: matter would be unstable in large magnetic fields
if smaller: all stars would be at least 80% more massive than the sun
18. decay rate of protons
if greater: life would be exterminated by the release of radiation
if smaller: universe would contain insufficient matter for life
19. 12C to 16O nuclear energy level ratio
if larger: universe would contain insufficient oxygen for life
if smaller: universe would contain insufficient carbon for life
20. ground state energy level for 4He
if larger: universe would contain insufficient carbon and oxygen for life
if smaller: same as above
21. decay rate of 8Be
if slower: heavy element fusion would generate catastrophic explosions in all the stars
if faster: no element heavier than beryllium would form; thus, no life chemistry
22. ratio of neutron mass to proton mass
if higher: neutron decay would yield too few neutrons for the formation of many life-essential elements
if lower: neutron decay would produce so many neutrons as to collapse all stars into neutron stars or black holes
23. initial excess of nucleons over anti-nucleons
if greater: radiation would prohibit planet formation
if lesser: matter would be insufficient for galaxy or star formation
24. polarity of the water molecule
if greater: heat of fusion and vaporization would be too high for life
if smaller: heat of fusion and vaporization would be too low for life; liquid water would not work as a solvent for life chemistry; ice would not float, and a runaway freeze-up would result
25. supernovae eruptions
if too close, too frequent, or too late: radiation would exterminate life on the planet
if too distant, too infrequent, or too soon: heavy elements would be too sparse for rocky planets to form
26. white dwarf binaries
if too few: insufficient fluorine would exist for life chemistry
if too many: planetary orbits would be too unstable for life
if formed too soon: insufficient fluorine production
if formed too late: fluorine would arrive too late for life chemistry
27. ratio of exotic matter mass to ordinary matter mass
if larger: universe would collapse before solar-type stars could form
if smaller: no galaxies would form
28. number of effective dimensions in the early universe
if larger: quantum mechanics, gravity, and relativity could not coexist; thus, life would be impossible
if smaller: same result
29. number of effective dimensions in the present universe
if smaller: electron, planet, and star orbits would become unstable
if larger: same result
30. mass of the neutrino
if smaller: galaxy clusters, galaxies, and stars would not form
if larger: galaxy clusters and galaxies would be too dense
31. big bang ripples
if smaller: galaxies would not form; universe would expand too rapidly
if larger: galaxies/galaxy clusters would be too dense for life; black holes would dominate; universe would collapse before life-site could form
32. size of the relativistic dilation factor
if smaller: certain life-essential chemical reactions will not function properly
if larger: same result
33. uncertainty magnitude in the Heisenberg uncertainty principle
if smaller: oxygen transport to body cells would be too small and certain life-essential elements would be unstable
if larger: oxygen transport to body cells would be too great and certain life-essential elements would be unstable
34. cosmological constant
if larger: universe would expand too quickly to form solar-type stars
In which is there any warrant to use the Anthropic principle (or Vampthropic Principle) to the existence of God?
I would say in every universe where (a) humans exist, (b) V-class objects don’t, and (c) the mulitiverse is an unprovable metaphysical speculation. ; )
Nick Matzke In other words, evolution solves this particular problem, no fine-tuning necessary to deal with the V-class object problem.
Fine-tuning is necessary to even get the evolutionary process going.
Bilbo Given an infinite number of universes, it seems that some of them (in fact, I think an infinite number of them) will contain humans but no vampires.
But can an actual infinite (as opposed to an a potential infinite) of anything—much less universes—actually exist? Many mathematicians would say, “No.” In fact, that is the basis for an even more interesting argument for God: the Kalam Cosmological Argument.
February 11th, 2010 | 1:16 am
Hi Joe,
I don’t know if an infinite number of universes can or does exist. But if there are, then your argument collapses. And given the intuitive improbability of vampires who turn their prey into vampires, I don’t think it would take an infinite number of universes to find another one that had humans but no vampires.
Thanks for the fine_tuning list.
February 11th, 2010 | 1:25 am
Assuming that humans are merely physical beings, which I doubt.
February 11th, 2010 | 1:45 am
Reading these comments, one is confronted with numerous possibilities: vampires, fine-tuning, God existing, God not existing, infinite number of universes, a universe existing where the Chicago Cubs are a dominant baseball team….
OK, y’all lost me on that last one…..
February 11th, 2010 | 9:58 am
[...] 6. A fascinating piece on First Things entitled, “Vampires and the Anthropic Principle.” [...]
February 11th, 2010 | 1:30 pm
Joe,
So much for independent parameters. While some of these are independent, many are not. The fine structure constant is built out of the speed of light and other constants on the list. The density of galaxies, stars, etc is dependent on the gravitational constant, the uniformity of the early universe and its mass. And on and on. Some are just irrelevant to fine tuning, such as the current age of our universe.
Moreover, should I take Hugh Ross’ word for it? Where if the published research? How much bigger, and how much smaller? Victor Stenger has done research that stars with lifetimes long enough for life to form (billions of years) form in universes 25% of the time over a wide range of parameters. That result by itself does not defeat the fine tuning argument, but it does force people who use it to up their game. Lists such as Ross’ are embarrassing.
Geronimo – we have to train our minds to consider all possibilities, no matter how outrageous…
February 11th, 2010 | 3:42 pm
[...] UPDATE II: But what about the Vampires? [...]
February 11th, 2010 | 4:25 pm
Joe,
But can an actual infinite (as opposed to an a potential infinite) of anything—much less universes—actually exist? Many mathematicians would say, “No.” In fact, that is the basis for an even more interesting argument for God: the Kalam Cosmological Argument.
Not sure why a mathematician would say that as opposed to an engineer… Anyway, I think you are better off sticking with “Silence of the Vampires” than going with Kalam. Kalam and quantum mechanics don’t mix well. If Kalam worked, black holes wouldn’t shrink due to Hawking radiation.
February 11th, 2010 | 5:08 pm
The infinite number of universes is a problem for the materialist. I would assume an infinite subset of these universes would contain intelligent life. Why should we be the only one or there only be a finite number. Of this infinite number of universes that contain intelligent life, what is to prevent a subset that contains life that is at a much higher level than our universe. In fact such a subset would be infinite in number.
Of this infinite number of universes that contain intelligences much higher than our, there would be an infinite subset of incredibly intelligent life forms who could manipulate the parameters of their universe to visit or control their own or other universes.
Of this infinite number of incredibly high intelligent life forms that can control their own or other universes, there would be many, in fact an infinite number, that should be able to create new universes through their ability to control the parameters that form universes. And there should be at least one of these intelligences who would then have the ability to say, “Let There be Light.”
In fact there would be an infinite number of such intelligences. Zeus watch out because you have competition.
So I think we just reduced the infinite number of universes concept to absurdity.
February 11th, 2010 | 5:29 pm
I’ve always enjoyed arguments like these, but I do feel I have to observe one vital counterfactor: Arguments from improbability are only relevant when assessing the “natural likelihood” of events that can occur *more than once*.
If your event set has only one event and it’s already happened, then you only need to postulate a random possibility that isn’t zero — once it’s happened, it doesn’t matter how unlikely it was if it doesn’t have to happen again.
(This is the gag behind the insurance commercial with the risk assessors who, after reeling off statistical chances of possible events, are momentarily bemused to watch a man ride an ostrich down the street. “What are the odds of that?” asks one. “100% — now,” says the other.)
February 11th, 2010 | 6:15 pm
Jerry,
Errr, no. We have no idea if it is possible to change the properties of a universe, such as the constants and laws of physics. That assumption is very different from your others which are simply based on the properties of infinity.
However, I think your argument could be refined to be “God is a V-class object.” ;)
February 11th, 2010 | 10:04 pm
Errr, probably. Probably, very probable.
There would be no limit to the level of the intelligence in such a scenario. Changing the parameters should be child’s play for such intelligences. Granted we can never be sure of anything but to suppose that the properties of the universe were immutable or not controllable seem to defy imagination if they just happen to be the result of random processes. I wonder what would be so immutable about them. Maybe something created by an omnipotent God?
February 11th, 2010 | 10:40 pm
Stenger and Ross are interesting. Neither has many peer-reviewed articles or “scientifically noteworthy” (whatever that means) contributions. What makes them interesting is that they are best known for their apologetic writings.
If God: The Failed Hypothesis, and his recent defense of the New Atheists had never been written, then Stenger would hardly be known. The same goes for Ross. He has interacted with plenty of big names in science, but primarily because of his Christianity and not because of his scientific work.
Ross quickly gets quoted by Christians in response to fine-tuning and Stenger quickly gets quoted by atheists to defend against it. Honestly, in terms of science, Ross is closer to the concensus (not in terms of his theology of course), but his science is mainly used to support his theology. Stenger has atypical views on the origin of the universe, the nature of time, etc. which play right into the hands of those trying to argue against Craig’s Kalam argument, but considering the overt bias in most of his writing, one has to wonder whether or not his views are just as ideologically shaped as Christian apologists.
February 12th, 2010 | 7:27 am
Kyle,
Fred Adams has published “Stars In Other Universes: Stellar structure with different fundamental constants”
http://www.iop.org/EJ/abstract/1475-7516/2008/08/010/
This is a paper that does support the 25% sort of figure. Adams is a working astrophysicist focused on stellar structure, not an apologist.
February 13th, 2010 | 11:47 pm
Mr. von Kannon,
While I’m sure Dr. Adam’s paper is fascinating to those interested in such things, Dr. Stenger’s work is generally cited not in scientific journals but by anti-religious/anti-Christian polemicists. I do not argue with Dr. Stenger’s science, but I do find the theological and philosophical conclusions he deduces from them to be the result of an almost complete lack of theological insight. Here is Stenger in a nutshell: “God has not acted and does not act in the way I expect him to act -based on my woefully uninformed and unimaginative idea of him – and the universe is not constructed the way it would be if I were God, therefore God does not exist”.
Perhaps Stenger’s work is problematic to biblical fundamentalists and IDers (though David Berlinski, a secular Jew and ID advocate, would disagree with me on the latter), as their views appear to be his primary target. Since I do not belong to either camp, they can fend for themselves. However, as an orthodox Catholic who has no problem with Darwin, Einstein, or any other scientist for that matter, Stenger has yet to make an argument that presents any problem to me, and quite a few that are, quite frankly, built on theological and philosophical ignorance.
Take care,
GR
February 14th, 2010 | 10:29 pm
Geronimo,
I’m sorry I brought in Stenger’s name, then! I usually only reference Adam’s work directly in discussions of fine tuning.
February 16th, 2010 | 6:48 pm
The article has two major flaws:
First, not all actual vampire myths had them drink blood. Some consumed strength, others drained youth, and so on.
Second and more importantly, not all vampire myths said the the act of consuming human life force resulted in additional vampires.
The Astral (everywhere), Baital (India), Ch’iang Shich (China), Gaki, (Japan), Ghul (Arab region), Lamia (ancient Greece), Loogaroo (Haiti), Pananggalen (Malay), Strix0 (ancient Rome), Vyrolakos (Balkan region) are all examples of vampires (or vampire like beings) that did NOT create more of their own kind by feeding.
In fact according to the myth the Vyrolakos could even have children with a human and is the classic origin of the Dhampir (half human half vampire)
March 3rd, 2010 | 6:59 am
David vun Kannon,
You might be interested in this reply to Adams’ work – the 25% figure is meaningless:
http://letterstonature.wordpress.com/2010/02/28/the-shrinking-quarter-a-fine-tuned-critique-of-fred-adams/
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