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Math vs. vampires: vampires lose

Oct. 25, 2006
Courtesy University of Central Florida
and World Science staff

If vam­pires—corpses that rise up to suck the blood of the liv­ing—sound bi­o­log­i­cal­ly im­plau­si­ble to you, you’re not alone. They ex­ist pure­ly in leg­end, as vir­tu­al­ly all sci­en­tists agree.

A post­er for one of the first vam­pire films, Nos­fer­atu (1922.)


But for any vampire be­liev­ers un­dis­sua­d­ed by bi­o­log­i­cal facts, a pro­fes­sor has come up with a sec­ond proof of their un­re­al­i­ty, us­ing math.

If vam­pires ever ex­isted in the forms in which mo­v­ies and books por­tray them, they would have quick­ly wiped out hu­ma­n­ity long ago, ac­cord­ing to phys­ics pro­f­es­sor Cos­tas Ef­thi­mi­ou of the Uni­ver­si­ty of Cen­tral Flor­i­da in Or­lan­do, Fla.

Pop­u­lar lo­re pas­sed down through cen­turies holds that vam­pire vic­tims be­come vam­pires them­selves, and launch their own blood-hunts on hap­less hu­mans. 

To rule out vam­pires, Ef­thi­mi­ou re­lied on a bas­ic prin­ci­ple known as ge­o­met­ric pro­gres­sion. 

“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,” Ef­thi­mi­ou and a grad­u­ate stu­dent col­league wrote in a pa­per posted on­line.

Efthimiou sup­posed that the first vam­pire arose Jan. 1, 1600, around the be­gin­ning of a cen­tu­ry dur­ing which some of the first im­por­tant mod­ern writ­ings on vam­pires ap­peared. The re­search­ers es­ti­mat­ed the glob­al pop­u­la­tion at that time, based on his­tor­i­cal re­c­ords, as 537 mil­lion.

As­sum­ing that the vam­pire fed once a month and the vic­tim turned in­to a vam­pire, there would be two vam­pires on Feb. 1, four the next month, and eight the month af­ter that. All hu­mans would be vam­pires with­in 2½ years. “Hu­mans can­not sur­vive un­der these con­di­tions, even if our pop­u­la­tion were dou­bling each mon­th,” which is well be­y­ond hu­man ca­pa­ci­ties, Ef­thi­mi­ou said.

Efthimiou and the grad­u­ate stu­dent, So­hang Gan­dhi, al­so took on ghosts and zom­bie leg­ends. 

Us­ing laws of mo­tion dis­cov­ered by Isaac New­ton in the late 1600s, they not­ed that ghosts would­n’t be able to walk and pass through walls, and not just be­cause walls are sol­id.

In movies such as “Ghost,” star­ring Pat­rick Swayze and Demi Moore, ghosts of­ten walk like hu­mans, pass through walls and pick up ob­jects. How­ever, Ef­thi­mi­ou ar­gues, for ghosts to walk like hu­mans, they would have to put pres­sure on the floor. The floor would ex­ert an equal and op­po­site force in re­turn. But ghosts’ abil­i­ty to pass through walls and have hu­mans walk right through them demon­strates that they can’t ap­ply force, the re­search­ers wrote.

They al­so pro­vid­ed an ex­pla­na­tion for “voodoo zom­bie­fi­ca­tion,” a prod­uct of Hai­tian folklo­re that sug­gests that zom­bies arise when a sor­cer­er places an evil spell on an en­e­my. The re­search­ers re­viewed the case of a Hai­tian ad­o­les­cent who was pro­nounced dead by a lo­cal doc­tor af­ter a week of great con­vul­sions.

Af­ter the boy was bur­ied, he re­turned in an in­co­her­ent state, and Hai­tians said a sor­cer­er had re­s­ur­rec­t­ed him as a zom­bie.

Efthimiou and Gan­dhi attribute the incident to a tox­ic sub­stance called tetrodotox­in, found in a puffer­fish breed na­tive to Hai­tian wa­ters. Con­tact with the sub­stance gen­er­al­ly re­sults in rap­id death. How­ev­er, in some cases, the right dose pro­duces a state that mim­ics death and slows vi­tal signs to un­mea­s­ur­a­ble lev­els. Even­tu­al­ly, the vic­tim snaps out of the death-like co­ma. 

Anal­y­sis has shown that ox­y­gen dep­ri­va­tion could ex­p­lain the boy’s brain dam­age and in­co­her­ent state, Ef­thi­mi­ou said: thus, “it would seem that zom­bie­fi­ca­tion is noth­ing more than a skill­ful act of poi­son­ing.”


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If vampires—corpses that rise up to suck the blood of the living—sound biologically implausible to you, you’re not alone. They exist purely in legend, as virtually all scientists agree. But if biological facts fail to convince some people of the unreality of these monsters, a professor has come up with a second proof of it, using math. If vampires indeed existed in the form that they’re presented in movies and books, they would have wiped out everyone long ago in short order, according to physics professor Costas Efthimiou of the University of Central Florida in Orlando, Fla. Popular lore passed down through centuries holds that victims of vampires soon become vampires themselves, and launch their own blood-hunt on hapless human victims. To disprove the existence of vampires, Efthimiou relied on a basic math principle known as geometric progression. “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,” Efthimiou and a graduate student colleague wrote in a paper posted online. Efthimiou supposed that the first vampire arrived Jan. 1, 1600, around the beginning of a century during which some of the first important modern writings on vampires came out. He estimated the global population at that time, based on historical records, as 537 million. Assuming that the vampire fed once a month and the victim turned into a vampire, there would be two vampires on Feb. 1, four the next month, and eight the month after that. All humans would become vampires within two and a half years. “Humans cannot survive under these conditions, even if our population were doubling each month,” Efthimiou said. “And doubling is clearly way beyond the human capacity of reproduction.” Efthimiou and the graduate student, Sohang Gandhi, also took on ghosts and zombie legends. Using laws of motion discovered by Isaac Newton in the late 1600s, Efthimiou noted out that that ghosts wouldn’t be able to walk and pass through walls, and not just because walls are solid. In movies such as “Ghost,” starring Patrick Swayze and Demi Moore, ghosts often walk like humans, pass through walls and pick up objects. That portrayal can’t be accurate, Efthimiou argues. For ghosts to walk like humans, they would have to put pressure on the floor, which would exert an equal and opposite force in return. But ghosts’ ability to pass through walls and have humans walk right through them demonstrates that they cannot apply force, the researchers wrote. They also provided an explanation for “voodoo zombiefication,” a product of Haitian folklore that suggests that zombies arise when a sorcerer places an evil spell on an enemy. The researchers reviewed the case of a Haitian adolescent who was pronounced dead by a local doctor after a week of great convulsions. After the boy was buried, he returned in an incoherent state, and Haitians pronounced that a sorcerer had raised him from the dead in the state of a zombie. Efthimiou and Gandhi wrote that the explanation lies in a toxic substance called tetrodotoxin, found in a pufferfish breed native to Haitian waters. Contact with the substance generally results in rapid death. However, in some cases, the right dose of the toxin will result in a state that mimics death and slows vital signs to unmeasurable levels. Eventually, the victim snaps out of the death-like coma. Scientific analysis has shown that oxygen deprivation is consistent with the boy’s brain damage and his incoherent state, he added: “It would seem that zombiefication is nothing more than a skillful act of poisoning.”